id	sid	tid	token	lemma	pos
ma-80	1	1	analytical	analytical	ADJ
ma-80	1	2	approximations	approximation	NOUN
ma-80	1	3	for	for	ADP
ma-80	1	4	the	the	DET
ma-80	1	5	principal	principal	ADJ
ma-80	1	6	branch	branch	NOUN
ma-80	1	7	of	of	ADP
ma-80	1	8	the	the	DET
ma-80	1	9	lambert	lambert	PROPN
ma-80	1	10	w	w	PROPN
ma-80	1	11	function	function	PROPN
ma-80	1	12	roy	roy	PROPN
ma-80	1	13	m.	m.	PROPN
ma-80	1	14	howard	howard	PROPN
ma-80	1	15	school	school	PROPN
ma-80	1	16	of	of	ADP
ma-80	1	17	electrical	electrical	ADJ
ma-80	1	18	engineering	engineering	NOUN
ma-80	1	19	,	,	PUNCT
ma-80	1	20	computing	computing	NOUN
ma-80	1	21	and	and	CCONJ
ma-80	1	22	mathematical	mathematical	ADJ
ma-80	1	23	sciences	sciences	PROPN
ma-80	1	24	,	,	PUNCT
ma-80	1	25	curtin	curtin	PROPN
ma-80	1	26	university	university	PROPN
ma-80	1	27	,	,	PUNCT
ma-80	1	28	gpo	gpo	NOUN
ma-80	1	29	box	box	NOUN
ma-80	1	30	u1987	u1987	PROPN
ma-80	1	31	,	,	PUNCT
ma-80	1	32	perth	perth	PROPN
ma-80	1	33	,	,	PUNCT
ma-80	1	34	6845	6845	NUM
ma-80	1	35	,	,	PUNCT
ma-80	1	36	australia	australia	PROPN
ma-80	1	37	abstract	abstract	NOUN
ma-80	1	38	.	.	PUNCT
ma-80	2	1	a	a	DET
ma-80	2	2	geometric	geometric	ADJ
ma-80	2	3	based	base	VERB
ma-80	2	4	approach	approach	NOUN
ma-80	2	5	for	for	ADP
ma-80	2	6	specifying	specify	VERB
ma-80	2	7	approximations	approximation	NOUN
ma-80	2	8	to	to	ADP
ma-80	2	9	the	the	DET
ma-80	2	10	lambert	lambert	PROPN
ma-80	2	11	w	w	PROPN
ma-80	2	12	function	function	PROPN
ma-80	2	13	,	,	PUNCT
ma-80	2	14	which	which	PRON
ma-80	2	15	can	can	AUX
ma-80	2	16	achieve	achieve	VERB
ma-80	2	17	any	any	DET
ma-80	2	18	set	set	ADJ
ma-80	2	19	relative	relative	ADJ
ma-80	2	20	error	error	NOUN
ma-80	2	21	bound	bind	VERB
ma-80	2	22	over	over	ADP
ma-80	2	23	the	the	DET
ma-80	2	24	interval	interval	NOUN
ma-80	2	25	,	,	PUNCT
ma-80	2	26	is	be	AUX
ma-80	2	27	detailed	detail	VERB
ma-80	2	28	.	.	PUNCT
ma-80	3	1	approximations	approximation	NOUN
ma-80	3	2	that	that	PRON
ma-80	3	3	can	can	AUX
ma-80	3	4	achieve	achieve	VERB
ma-80	3	5	arbitrarily	arbitrarily	ADV
ma-80	3	6	high	high	ADJ
ma-80	3	7	accuracy	accuracy	NOUN
ma-80	3	8	for	for	ADP
ma-80	3	9	the	the	DET
ma-80	3	10	interval	interval	NOUN
ma-80	3	11	,	,	PUNCT
ma-80	3	12	based	base	VERB
ma-80	3	13	on	on	ADP
ma-80	3	14	a	a	DET
ma-80	3	15	two	two	NUM
ma-80	3	16	point	point	NOUN
ma-80	3	17	spline	spline	NOUN
ma-80	3	18	approximation	approximation	NOUN
ma-80	3	19	,	,	PUNCT
ma-80	3	20	are	be	AUX
ma-80	3	21	specified	specify	VERB
ma-80	3	22	.	.	PUNCT
ma-80	4	1	iterative	iterative	NOUN
ma-80	4	2	methods	method	NOUN
ma-80	4	3	can	can	AUX
ma-80	4	4	be	be	AUX
ma-80	4	5	used	use	VERB
ma-80	4	6	to	to	PART
ma-80	4	7	improve	improve	VERB
ma-80	4	8	the	the	DET
ma-80	4	9	accuracy	accuracy	NOUN
ma-80	4	10	of	of	ADP
ma-80	4	11	the	the	DET
ma-80	4	12	approximations	approximation	NOUN
ma-80	4	13	.	.	PUNCT
ma-80	5	1	applications	application	NOUN
ma-80	5	2	include	include	VERB
ma-80	5	3	,	,	PUNCT
ma-80	5	4	first	first	ADV
ma-80	5	5	,	,	PUNCT
ma-80	5	6	analytical	analytical	ADJ
ma-80	5	7	expressions	expression	NOUN
ma-80	5	8	,	,	PUNCT
ma-80	5	9	with	with	ADP
ma-80	5	10	set	set	ADJ
ma-80	5	11	relative	relative	ADJ
ma-80	5	12	error	error	NOUN
ma-80	5	13	bounds	bound	NOUN
ma-80	5	14	,	,	PUNCT
ma-80	5	15	for	for	ADP
ma-80	5	16	the	the	DET
ma-80	5	17	lambert	lambert	PROPN
ma-80	5	18	w	w	PROPN
ma-80	5	19	function	function	NOUN
ma-80	5	20	over	over	ADP
ma-80	5	21	the	the	DET
ma-80	5	22	interval	interval	NOUN
ma-80	5	23	.	.	PUNCT
ma-80	6	1	second	second	ADJ
ma-80	6	2	,	,	PUNCT
ma-80	6	3	approximations	approximation	NOUN
ma-80	6	4	,	,	PUNCT
ma-80	6	5	with	with	ADP
ma-80	6	6	an	an	DET
ma-80	6	7	arbitrarily	arbitrarily	ADV
ma-80	6	8	low	low	ADJ
ma-80	6	9	relative	relative	ADJ
ma-80	6	10	error	error	NOUN
ma-80	6	11	,	,	PUNCT
ma-80	6	12	for	for	ADP
ma-80	6	13	upper	upper	ADJ
ma-80	6	14	and	and	CCONJ
ma-80	6	15	lower	low	ADJ
ma-80	6	16	bounds	bound	NOUN
ma-80	6	17	for	for	ADP
ma-80	6	18	the	the	DET
ma-80	6	19	lambert	lambert	PROPN
ma-80	6	20	w	w	PROPN
ma-80	6	21	function	function	PROPN
ma-80	6	22	.	.	PUNCT
ma-80	7	1	third	third	ADJ
ma-80	7	2	,	,	PUNCT
ma-80	7	3	analytical	analytical	ADJ
ma-80	7	4	expressions	expression	NOUN
ma-80	7	5	for	for	ADP
ma-80	7	6	the	the	DET
ma-80	7	7	evaluation	evaluation	NOUN
ma-80	7	8	of	of	ADP
ma-80	7	9	and	and	CCONJ
ma-80	7	10	the	the	DET
ma-80	7	11	integral	integral	ADJ
ma-80	7	12	of	of	ADP
ma-80	7	13	,	,	PUNCT
ma-80	7	14	for	for	ADP
ma-80	7	15	,	,	PUNCT
ma-80	7	16	without	without	ADP
ma-80	7	17	knowledge	knowledge	NOUN
ma-80	7	18	of	of	ADP
ma-80	7	19	.	.	PUNCT
ma-80	8	1	fourth	fourth	ADV
ma-80	8	2	,	,	PUNCT
ma-80	8	3	a	a	DET
ma-80	8	4	direct	direct	ADJ
ma-80	8	5	approach	approach	NOUN
ma-80	8	6	for	for	ADP
ma-80	8	7	evaluating	evaluate	VERB
ma-80	8	8	the	the	DET
ma-80	8	9	lambert	lambert	PROPN
ma-80	8	10	w	w	PROPN
ma-80	8	11	function	function	NOUN
ma-80	8	12	to	to	PART
ma-80	8	13	achieve	achieve	VERB
ma-80	8	14	a	a	DET
ma-80	8	15	prior	prior	ADJ
ma-80	8	16	set	set	VERB
ma-80	8	17	error	error	NOUN
ma-80	8	18	constraint	constraint	NOUN
ma-80	8	19	.	.	PUNCT
ma-80	9	1	1	1	X
ma-80	9	2	.	.	X
ma-80	9	3	introduction	introduction	NOUN
ma-80	9	4	the	the	DET
ma-80	9	5	lambert	lambert	PROPN
ma-80	9	6	w	w	PROPN
ma-80	9	7	function	function	PROPN
ma-80	9	8	is	be	AUX
ma-80	9	9	associated	associate	VERB
ma-80	9	10	with	with	ADP
ma-80	9	11	lambert	lambert	PROPN
ma-80	10	1	[	[	X
ma-80	10	2	19	19	NUM
ma-80	10	3	]	]	PUNCT
ma-80	10	4	and	and	CCONJ
ma-80	10	5	is	be	AUX
ma-80	10	6	a	a	DET
ma-80	10	7	multivalued	multivalue	VERB
ma-80	10	8	complex	complex	ADJ
ma-80	10	9	function	function	NOUN
ma-80	10	10	with	with	ADP
ma-80	10	11	the	the	DET
ma-80	10	12	single	single	ADJ
ma-80	10	13	valued	value	VERB
ma-80	10	14	function	function	NOUN
ma-80	10	15	,	,	PUNCT
ma-80	10	16	associated	associate	VERB
ma-80	10	17	with	with	ADP
ma-80	10	18	the	the	DET
ma-80	10	19	branch	branch	NOUN
ma-80	10	20	,	,	PUNCT
ma-80	10	21	being	be	AUX
ma-80	10	22	denoted	denote	VERB
ma-80	10	23	.	.	PUNCT
ma-80	11	1	the	the	DET
ma-80	11	2	principle	principle	ADJ
ma-80	11	3	branch	branch	NOUN
ma-80	11	4	of	of	ADP
ma-80	11	5	the	the	DET
ma-80	11	6	lambert	lambert	PROPN
ma-80	11	7	w	w	PROPN
ma-80	11	8	function	function	PROPN
ma-80	11	9	,	,	PUNCT
ma-80	11	10	,	,	PUNCT
ma-80	11	11	is	be	AUX
ma-80	11	12	the	the	DET
ma-80	11	13	function	function	NOUN
ma-80	11	14	defined	define	VERB
ma-80	11	15	by	by	ADP
ma-80	11	16	the	the	DET
ma-80	11	17	inverse	inverse	NOUN
ma-80	11	18	of	of	ADP
ma-80	11	19	for	for	ADP
ma-80	11	20	the	the	DET
ma-80	11	21	case	case	NOUN
ma-80	11	22	of	of	ADP
ma-80	11	23	,	,	PUNCT
ma-80	11	24	i.e.	i.e.	X
ma-80	11	25	(	(	PUNCT
ma-80	11	26	1	1	X
ma-80	11	27	)	)	PUNCT
ma-80	11	28	the	the	DET
ma-80	11	29	lambert	lambert	PROPN
ma-80	11	30	w	w	PROPN
ma-80	11	31	function	function	PROPN
ma-80	11	32	does	do	AUX
ma-80	11	33	not	not	PART
ma-80	11	34	have	have	VERB
ma-80	11	35	an	an	DET
ma-80	11	36	explicit	explicit	ADJ
ma-80	11	37	analytical	analytical	ADJ
ma-80	11	38	form	form	NOUN
ma-80	11	39	but	but	CCONJ
ma-80	11	40	is	be	AUX
ma-80	11	41	of	of	ADP
ma-80	11	42	importance	importance	NOUN
ma-80	11	43	consistent	consistent	ADJ
ma-80	11	44	with	with	ADP
ma-80	11	45	increasing	increase	VERB
ma-80	11	46	applications	application	NOUN
ma-80	11	47	as	as	SCONJ
ma-80	11	48	detailed	detailed	ADJ
ma-80	11	49	in	in	ADP
ma-80	11	50	the	the	DET
ma-80	11	51	literature	literature	NOUN
ma-80	11	52	,	,	PUNCT
ma-80	12	1	e.g.	e.g.	ADV
ma-80	12	2	[	[	X
ma-80	12	3	7	7	NUM
ma-80	12	4	]	]	PUNCT
ma-80	12	5	,	,	PUNCT
ma-80	12	6	[	[	X
ma-80	12	7	3	3	NUM
ma-80	12	8	]	]	PUNCT
ma-80	12	9	,	,	PUNCT
ma-80	12	10	[	[	X
ma-80	12	11	25	25	NUM
ma-80	12	12	]	]	PUNCT
ma-80	12	13	,	,	PUNCT
ma-80	13	1	[	[	X
ma-80	13	2	9	9	NUM
ma-80	13	3	]	]	PUNCT
ma-80	13	4	,	,	PUNCT
ma-80	13	5	[	[	X
ma-80	13	6	6	6	NUM
ma-80	13	7	]	]	PUNCT
ma-80	13	8	,	,	PUNCT
ma-80	13	9	[	[	X
ma-80	13	10	14	14	NUM
ma-80	13	11	]	]	PUNCT
ma-80	13	12	,	,	PUNCT
ma-80	13	13	[	[	X
ma-80	13	14	26	26	NUM
ma-80	13	15	]	]	PUNCT
ma-80	13	16	,	,	PUNCT
ma-80	13	17	[	[	X
ma-80	13	18	20	20	NUM
ma-80	13	19	]	]	PUNCT
ma-80	13	20	,	,	PUNCT
ma-80	14	1	[	[	X
ma-80	14	2	18	18	NUM
ma-80	14	3	]	]	PUNCT
ma-80	14	4	,	,	PUNCT
ma-80	14	5	[	[	X
ma-80	14	6	4	4	NUM
ma-80	14	7	]	]	PUNCT
ma-80	14	8	,	,	PUNCT
ma-80	14	9	and	and	CCONJ
ma-80	14	10	[	[	X
ma-80	14	11	11	11	NUM
ma-80	14	12	]	]	PUNCT
ma-80	14	13	.	.	PUNCT
ma-80	15	1	generalizations	generalization	NOUN
ma-80	15	2	of	of	ADP
ma-80	15	3	the	the	DET
ma-80	15	4	lambert	lambert	PROPN
ma-80	15	5	w	w	PROPN
ma-80	15	6	function	function	NOUN
ma-80	15	7	are	be	AUX
ma-80	15	8	also	also	ADV
ma-80	15	9	of	of	ADP
ma-80	15	10	interest	interest	NOUN
ma-80	15	11	,	,	PUNCT
ma-80	15	12	e.g.	e.g.	ADV
ma-80	15	13	[	[	X
ma-80	15	14	8	8	NUM
ma-80	15	15	]	]	PUNCT
ma-80	15	16	and	and	CCONJ
ma-80	15	17	[	[	X
ma-80	15	18	22	22	NUM
ma-80	15	19	]	]	PUNCT
ma-80	15	20	.	.	PUNCT
ma-80	16	1	efficient	efficient	ADJ
ma-80	16	2	numerical	numerical	ADJ
ma-80	16	3	methods	method	NOUN
ma-80	16	4	for	for	ADP
ma-80	16	5	computing	compute	VERB
ma-80	16	6	values	value	NOUN
ma-80	16	7	of	of	ADP
ma-80	16	8	the	the	DET
ma-80	16	9	lambert	lambert	PROPN
ma-80	16	10	w	w	PROPN
ma-80	16	11	function	function	PROPN
ma-80	16	12	have	have	AUX
ma-80	16	13	long	long	ADV
ma-80	16	14	been	be	AUX
ma-80	16	15	known	know	VERB
ma-80	16	16	,	,	PUNCT
ma-80	16	17	e.g.	e.g.	ADV
ma-80	16	18	[	[	X
ma-80	16	19	10	10	NUM
ma-80	16	20	]	]	PUNCT
ma-80	16	21	,	,	PUNCT
ma-80	16	22	and	and	CCONJ
ma-80	16	23	with	with	ADP
ma-80	16	24	an	an	DET
ma-80	16	25	advance	advance	NOUN
ma-80	16	26	detailed	detail	VERB
ma-80	16	27	by	by	ADP
ma-80	16	28	fukushima	fukushima	PROPN
ma-80	16	29	[	[	X
ma-80	16	30	12	12	NUM
ma-80	16	31	]	]	PUNCT
ma-80	16	32	.	.	PUNCT
ma-80	17	1	the	the	DET
ma-80	17	2	focus	focus	NOUN
ma-80	17	3	of	of	ADP
ma-80	17	4	this	this	DET
ma-80	17	5	paper	paper	NOUN
ma-80	17	6	is	be	AUX
ma-80	17	7	on	on	ADP
ma-80	17	8	the	the	DET
ma-80	17	9	principle	principle	ADJ
ma-80	17	10	branch	branch	NOUN
ma-80	17	11	and	and	CCONJ
ma-80	17	12	the	the	DET
ma-80	17	13	real	real	ADJ
ma-80	17	14	case	case	NOUN
ma-80	17	15	which	which	PRON
ma-80	17	16	continues	continue	VERB
ma-80	17	17	to	to	PART
ma-80	17	18	receive	receive	VERB
ma-80	17	19	research	research	NOUN
ma-80	17	20	interest	interest	NOUN
ma-80	17	21	,	,	PUNCT
ma-80	18	1	e.g.	e.g.	ADV
ma-80	18	2	[	[	X
ma-80	18	3	17	17	NUM
ma-80	18	4	]	]	PUNCT
ma-80	18	5	.	.	PUNCT
ma-80	19	1	the	the	DET
ma-80	19	2	graph	graph	NOUN
ma-80	19	3	of	of	ADP
ma-80	19	4	the	the	DET
ma-80	19	5	lambert	lambert	PROPN
ma-80	19	6	w	w	PROPN
ma-80	19	7	function	function	NOUN
ma-80	19	8	,	,	PUNCT
ma-80	19	9	for	for	ADP
ma-80	19	10	this	this	DET
ma-80	19	11	case	case	NOUN
ma-80	19	12	,	,	PUNCT
ma-80	19	13	is	be	AUX
ma-80	19	14	shown	show	VERB
ma-80	19	15	in	in	ADP
ma-80	19	16	figure	figure	NOUN
ma-80	19	17	1	1	NUM
ma-80	19	18	and	and	CCONJ
ma-80	19	19	,	,	PUNCT
ma-80	19	20	for	for	ADP
ma-80	19	21	notational	notational	ADJ
ma-80	19	22	simplicity	simplicity	NOUN
ma-80	19	23	,	,	PUNCT
ma-80	19	24	is	be	AUX
ma-80	19	25	denoted	denote	VERB
ma-80	19	26	in	in	ADP
ma-80	19	27	this	this	DET
ma-80	19	28	paper	paper	NOUN
ma-80	19	29	.	.	PUNCT
ma-80	20	1	existing	exist	VERB
ma-80	20	2	analytical	analytical	ADJ
ma-80	20	3	approximations	approximation	NOUN
ma-80	20	4	for	for	ADP
ma-80	20	5	the	the	DET
ma-80	20	6	principle	principle	ADJ
ma-80	20	7	branch	branch	NOUN
ma-80	20	8	and	and	CCONJ
ma-80	20	9	real	real	ADJ
ma-80	20	10	case	case	NOUN
ma-80	20	11	of	of	ADP
ma-80	20	12	the	the	DET
ma-80	20	13	lambert	lambert	PROPN
ma-80	20	14	w	w	PROPN
ma-80	20	15	function	function	PROPN
ma-80	20	16	,	,	PUNCT
ma-80	20	17	e.g.	e.g.	ADV
ma-80	20	18	[	[	X
ma-80	20	19	5	5	NUM
ma-80	20	20	]	]	PUNCT
ma-80	20	21	,	,	PUNCT
ma-80	20	22	[	[	X
ma-80	20	23	3	3	NUM
ma-80	20	24	]	]	PUNCT
ma-80	20	25	and	and	CCONJ
ma-80	20	26	[	[	X
ma-80	20	27	17	17	NUM
ma-80	20	28	]	]	PUNCT
ma-80	20	29	,	,	PUNCT
ma-80	20	30	are	be	AUX
ma-80	20	31	,	,	PUNCT
ma-80	20	32	in	in	ADP
ma-80	20	33	general	general	ADJ
ma-80	20	34	,	,	PUNCT
ma-80	20	35	custom	custom	NOUN
ma-80	20	36	and	and	CCONJ
ma-80	20	37	can	can	AUX
ma-80	20	38	not	not	PART
ma-80	20	39	be	be	AUX
ma-80	20	40	directly	directly	ADV
ma-80	20	41	generalized	generalize	VERB
ma-80	20	42	to	to	PART
ma-80	20	43	obtain	obtain	VERB
ma-80	20	44	approximations	approximation	NOUN
ma-80	20	45	of	of	ADP
ma-80	20	46	arbitrarily	arbitrarily	ADV
ma-80	20	47	high	high	ADJ
ma-80	20	48	accuracy	accuracy	NOUN
ma-80	20	49	.	.	PUNCT
ma-80	21	1	this	this	DET
ma-80	21	2	paper	paper	NOUN
ma-80	21	3	provides	provide	VERB
ma-80	21	4	a	a	DET
ma-80	21	5	geometrical	geometrical	ADJ
ma-80	21	6	basis	basis	NOUN
ma-80	21	7	for	for	ADP
ma-80	21	8	defining	define	VERB
ma-80	21	9	such	such	ADJ
ma-80	21	10	approximations	approximation	NOUN
ma-80	21	11	.	.	PUNCT
ma-80	22	1	0	0	NUM
ma-80	23	1			NUM
ma-80	23	2			NOUN
ma-80	23	3	1	1	NUM
ma-80	23	4	e	e	NOUN
ma-80	23	5	–	–	PUNCT
ma-80	23	6	0	0	NUM
ma-80	23	7			NOUN
ma-80	23	8	0	0	NUM
ma-80	23	9			VERB
ma-80	23	10	w	w	NOUN
ma-80	23	11	y	y	NOUN
ma-80	23	12			PROPN
ma-80	23	13	w	w	NOUN
ma-80	23	14	y	y	NOUN
ma-80	23	15			PUNCT
ma-80	23	16	y	y	PROPN
ma-80	23	17	0	0	NUM
ma-80	23	18			NUM
ma-80	23	19			PUNCT
ma-80	23	20	w	w	ADP
ma-80	23	21	y	y	NOUN
ma-80	23	22			PROPN
ma-80	23	23	kth	kth	PROPN
ma-80	23	24	wk	wk	INTJ
ma-80	23	25	w0	w0	PROPN
ma-80	23	26	y	y	PROPN
ma-80	23	27	f	f	PROPN
ma-80	23	28	x	x	PROPN
ma-80	24	1			PROPN
ma-80	24	2	xe	xe	PROPN
ma-80	24	3	x	x	PUNCT
ma-80	24	4	=	=	PUNCT
ma-80	24	5	=	=	SYM
ma-80	24	6	re	re	X
ma-80	24	7	x	x	PROPN
ma-80	24	8			PROPN
ma-80	24	9	1–	1–	NUM
ma-80	24	10	x	x	SYM
ma-80	24	11	w0	w0	VERB
ma-80	24	12	y	y	NOUN
ma-80	24	13			PROPN
ma-80	24	14	f	f	PROPN
ma-80	24	15	1	1	NUM
ma-80	24	16	–	–	PUNCT
ma-80	24	17	y	y	NOUN
ma-80	24	18	.=	.=	PUNCT
ma-80	24	19	=	=	SYM
ma-80	24	20	w	w	PROPN
ma-80	24	21	correspondence	correspondence	NOUN
ma-80	24	22	:	:	PUNCT
ma-80	25	1	r.howard@curtin.edu.au	r.howard@curtin.edu.au	PROPN
ma-80	25	2	https://adac.ee/	https://adac.ee/	PROPN
ma-80	25	3	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	PROPN
ma-80	25	4	the	the	DET
ma-80	25	5	advances	advance	NOUN
ma-80	25	6	in	in	ADP
ma-80	25	7	this	this	DET
ma-80	25	8	paper	paper	NOUN
ma-80	25	9	are	be	AUX
ma-80	25	10	twofold	twofold	ADJ
ma-80	25	11	.	.	PUNCT
ma-80	26	1	first	first	ADV
ma-80	26	2	,	,	PUNCT
ma-80	26	3	a	a	DET
ma-80	26	4	systematic	systematic	ADJ
ma-80	26	5	geometric	geometric	ADJ
ma-80	26	6	approach	approach	NOUN
ma-80	26	7	for	for	ADP
ma-80	26	8	defining	define	VERB
ma-80	26	9	approximations	approximation	NOUN
ma-80	26	10	to	to	ADP
ma-80	26	11	the	the	DET
ma-80	26	12	lambert	lambert	PROPN
ma-80	26	13	w	w	PROPN
ma-80	26	14	function	function	PROPN
ma-80	26	15	,	,	PUNCT
ma-80	26	16	over	over	ADP
ma-80	26	17	the	the	DET
ma-80	26	18	interval	interval	NOUN
ma-80	26	19	,	,	PUNCT
ma-80	26	20	with	with	ADP
ma-80	26	21	quadratic	quadratic	ADJ
ma-80	26	22	convergence	convergence	NOUN
ma-80	26	23	.	.	PUNCT
ma-80	27	1	convergence	convergence	NOUN
ma-80	27	2	is	be	AUX
ma-80	27	3	proved	prove	VERB
ma-80	27	4	.	.	PUNCT
ma-80	28	1	the	the	DET
ma-80	28	2	approximations	approximation	NOUN
ma-80	28	3	can	can	AUX
ma-80	28	4	be	be	AUX
ma-80	28	5	used	use	VERB
ma-80	28	6	to	to	PART
ma-80	28	7	specify	specify	VERB
ma-80	28	8	,	,	PUNCT
ma-80	28	9	with	with	ADP
ma-80	28	10	an	an	DET
ma-80	28	11	arbitrarily	arbitrarily	ADV
ma-80	28	12	low	low	ADJ
ma-80	28	13	relative	relative	ADJ
ma-80	28	14	error	error	NOUN
ma-80	28	15	,	,	PUNCT
ma-80	28	16	upper	upper	ADJ
ma-80	28	17	and	and	CCONJ
ma-80	28	18	lower	low	ADJ
ma-80	28	19	bounds	bound	NOUN
ma-80	28	20	for	for	ADP
ma-80	28	21	the	the	DET
ma-80	28	22	lambert	lambert	PROPN
ma-80	28	23	w	w	PROPN
ma-80	28	24	function	function	PROPN
ma-80	28	25	.	.	PUNCT
ma-80	29	1	second	second	ADJ
ma-80	29	2	,	,	PUNCT
ma-80	29	3	a	a	DET
ma-80	29	4	systematic	systematic	ADJ
ma-80	29	5	method	method	NOUN
ma-80	29	6	for	for	ADP
ma-80	29	7	combining	combine	VERB
ma-80	29	8	series	series	NOUN
ma-80	29	9	expansions	expansion	NOUN
ma-80	29	10	at	at	ADP
ma-80	29	11	,	,	PUNCT
ma-80	29	12	and	and	CCONJ
ma-80	29	13	the	the	DET
ma-80	29	14	origin	origin	NOUN
ma-80	29	15	,	,	PUNCT
ma-80	29	16	to	to	PART
ma-80	29	17	define	define	VERB
ma-80	29	18	arbitrarily	arbitrarily	ADV
ma-80	29	19	accurate	accurate	ADJ
ma-80	29	20	approximations	approximation	NOUN
ma-80	29	21	for	for	ADP
ma-80	29	22	the	the	DET
ma-80	29	23	interval	interval	NOUN
ma-80	29	24	.	.	PUNCT
ma-80	30	1	applications	application	NOUN
ma-80	30	2	of	of	ADP
ma-80	30	3	the	the	DET
ma-80	30	4	approximations	approximation	NOUN
ma-80	30	5	include	include	VERB
ma-80	30	6	analytical	analytical	ADJ
ma-80	30	7	expressions	expression	NOUN
ma-80	30	8	,	,	PUNCT
ma-80	30	9	with	with	ADP
ma-80	30	10	set	set	ADJ
ma-80	30	11	relative	relative	ADJ
ma-80	30	12	error	error	NOUN
ma-80	30	13	bounds	bound	NOUN
ma-80	30	14	,	,	PUNCT
ma-80	30	15	for	for	ADP
ma-80	30	16	the	the	DET
ma-80	30	17	lambert	lambert	PROPN
ma-80	30	18	w	w	PROPN
ma-80	30	19	function	function	NOUN
ma-80	30	20	over	over	ADP
ma-80	30	21	the	the	DET
ma-80	30	22	interval	interval	NOUN
ma-80	30	23	,	,	PUNCT
ma-80	30	24	evaluation	evaluation	NOUN
ma-80	30	25	of	of	ADP
ma-80	30	26	and	and	CCONJ
ma-80	30	27	the	the	DET
ma-80	30	28	integral	integral	ADJ
ma-80	30	29	of	of	ADP
ma-80	30	30	,	,	PUNCT
ma-80	30	31	for	for	ADP
ma-80	30	32	,	,	PUNCT
ma-80	30	33	without	without	ADP
ma-80	30	34	knowledge	knowledge	NOUN
ma-80	30	35	of	of	ADP
ma-80	30	36	,	,	PUNCT
ma-80	30	37	and	and	CCONJ
ma-80	30	38	a	a	DET
ma-80	30	39	direct	direct	ADJ
ma-80	30	40	approach	approach	NOUN
ma-80	30	41	for	for	ADP
ma-80	30	42	evaluating	evaluate	VERB
ma-80	30	43	the	the	DET
ma-80	30	44	lambert	lambert	PROPN
ma-80	30	45	w	w	PROPN
ma-80	30	46	function	function	NOUN
ma-80	30	47	to	to	PART
ma-80	30	48	achieve	achieve	VERB
ma-80	30	49	a	a	DET
ma-80	30	50	prior	prior	ADJ
ma-80	30	51	defined	define	VERB
ma-80	30	52	error	error	NOUN
ma-80	30	53	.	.	PUNCT
ma-80	31	1	a	a	DET
ma-80	31	2	review	review	NOUN
ma-80	31	3	of	of	ADP
ma-80	31	4	published	publish	VERB
ma-80	31	5	approximations	approximation	NOUN
ma-80	31	6	for	for	ADP
ma-80	31	7	the	the	DET
ma-80	31	8	lambert	lambert	PROPN
ma-80	31	9	w	w	PROPN
ma-80	31	10	function	function	NOUN
ma-80	31	11	is	be	AUX
ma-80	31	12	provided	provide	VERB
ma-80	31	13	in	in	ADP
ma-80	31	14	section	section	NOUN
ma-80	31	15	2	2	NUM
ma-80	31	16	.	.	PUNCT
ma-80	32	1	the	the	DET
ma-80	32	2	proposed	propose	VERB
ma-80	32	3	geometric	geometric	ADJ
ma-80	32	4	approach	approach	NOUN
ma-80	32	5	for	for	ADP
ma-80	32	6	establishing	establish	VERB
ma-80	32	7	approximations	approximation	NOUN
ma-80	32	8	to	to	ADP
ma-80	32	9	the	the	DET
ma-80	32	10	lambert	lambert	PROPN
ma-80	32	11	w	w	PROPN
ma-80	32	12	function	function	NOUN
ma-80	32	13	is	be	AUX
ma-80	32	14	detailed	detail	VERB
ma-80	32	15	in	in	ADP
ma-80	32	16	section	section	NOUN
ma-80	32	17	3	3	NUM
ma-80	32	18	.	.	PUNCT
ma-80	32	19	convergence	convergence	NOUN
ma-80	32	20	is	be	AUX
ma-80	32	21	discussed	discuss	VERB
ma-80	32	22	in	in	ADP
ma-80	32	23	section	section	NOUN
ma-80	32	24	4	4	NUM
ma-80	32	25	and	and	CCONJ
ma-80	32	26	in	in	ADP
ma-80	32	27	section	section	NOUN
ma-80	32	28	5	5	NUM
ma-80	32	29	convergent	convergent	NOUN
ma-80	32	30	two	two	NUM
ma-80	32	31	point	point	NOUN
ma-80	32	32	spline	spline	NOUN
ma-80	32	33	based	base	VERB
ma-80	32	34	approximations	approximation	NOUN
ma-80	32	35	,	,	PUNCT
ma-80	32	36	for	for	ADP
ma-80	32	37	the	the	DET
ma-80	32	38	interval	interval	NOUN
ma-80	32	39	,	,	PUNCT
ma-80	32	40	are	be	AUX
ma-80	32	41	detailed	detail	VERB
ma-80	32	42	.	.	PUNCT
ma-80	33	1	the	the	DET
ma-80	33	2	use	use	NOUN
ma-80	33	3	of	of	ADP
ma-80	33	4	iterative	iterative	ADJ
ma-80	33	5	methods	method	NOUN
ma-80	33	6	,	,	PUNCT
ma-80	33	7	to	to	PART
ma-80	33	8	improve	improve	VERB
ma-80	33	9	the	the	DET
ma-80	33	10	accuracy	accuracy	NOUN
ma-80	33	11	of	of	ADP
ma-80	33	12	approximations	approximation	NOUN
ma-80	33	13	,	,	PUNCT
ma-80	33	14	is	be	AUX
ma-80	33	15	discussed	discuss	VERB
ma-80	33	16	in	in	ADP
ma-80	33	17	section	section	NOUN
ma-80	33	18	6	6	NUM
ma-80	33	19	.	.	PUNCT
ma-80	34	1	applications	application	NOUN
ma-80	34	2	are	be	AUX
ma-80	34	3	detailed	detail	VERB
ma-80	34	4	in	in	ADP
ma-80	34	5	section	section	NOUN
ma-80	34	6	7	7	NUM
ma-80	34	7	and	and	CCONJ
ma-80	34	8	conclusions	conclusion	NOUN
ma-80	34	9	are	be	AUX
ma-80	34	10	stated	state	VERB
ma-80	34	11	in	in	ADP
ma-80	34	12	section	section	NOUN
ma-80	34	13	8	8	NUM
ma-80	34	14	.	.	PUNCT
ma-80	35	1	1.1	1.1	NUM
ma-80	35	2	.	.	PUNCT
ma-80	36	1	notation	notation	NOUN
ma-80	36	2	and	and	CCONJ
ma-80	36	3	properties	property	NOUN
ma-80	36	4	.	.	PUNCT
ma-80	37	1	the	the	DET
ma-80	37	2	notation	notation	NOUN
ma-80	37	3	of	of	ADP
ma-80	37	4	is	be	AUX
ma-80	37	5	used	use	VERB
ma-80	37	6	which	which	PRON
ma-80	37	7	is	be	AUX
ma-80	37	8	consistent	consistent	ADJ
ma-80	37	9	with	with	ADP
ma-80	37	10	the	the	DET
ma-80	37	11	principle	principle	ADJ
ma-80	37	12	value	value	NOUN
ma-80	37	13	of	of	ADP
ma-80	37	14	the	the	DET
ma-80	37	15	lambert	lambert	PROPN
ma-80	37	16	w	w	PROPN
ma-80	37	17	being	be	AUX
ma-80	37	18	the	the	DET
ma-80	37	19	inverse	inverse	ADJ
ma-80	37	20	function	function	NOUN
ma-80	37	21	of	of	ADP
ma-80	37	22	,	,	PUNCT
ma-80	37	23	,	,	PUNCT
ma-80	37	24	.	.	PUNCT
ma-80	38	1	relevant	relevant	ADJ
ma-80	38	2	properties	property	NOUN
ma-80	38	3	of	of	ADP
ma-80	38	4	the	the	DET
ma-80	38	5	lambert	lambert	PROPN
ma-80	38	6	w	w	PROPN
ma-80	38	7	function	function	NOUN
ma-80	38	8	are	be	AUX
ma-80	38	9	detailed	detail	VERB
ma-80	38	10	in	in	ADP
ma-80	38	11	appendix	appendix	ADJ
ma-80	38	12	a.	a.	NOUN
ma-80	38	13	for	for	ADP
ma-80	38	14	an	an	DET
ma-80	38	15	arbitrary	arbitrary	ADJ
ma-80	38	16	function	function	NOUN
ma-80	38	17	,	,	PUNCT
ma-80	38	18	defined	define	VERB
ma-80	38	19	over	over	ADP
ma-80	38	20	the	the	DET
ma-80	38	21	interval	interval	NOUN
ma-80	38	22	,	,	PUNCT
ma-80	38	23	an	an	DET
ma-80	38	24	approximating	approximate	VERB
ma-80	38	25	function	function	NOUN
ma-80	38	26	has	have	VERB
ma-80	38	27	a	a	DET
ma-80	38	28	relative	relative	ADJ
ma-80	38	29	error	error	NOUN
ma-80	38	30	,	,	PUNCT
ma-80	38	31	at	at	ADP
ma-80	38	32	a	a	DET
ma-80	38	33	point	point	NOUN
ma-80	38	34	,	,	PUNCT
ma-80	38	35	defined	define	VERB
ma-80	38	36	according	accord	VERB
ma-80	38	37	to	to	ADP
ma-80	38	38	.	.	PUNCT
ma-80	39	1	the	the	DET
ma-80	39	2	relative	relative	ADJ
ma-80	39	3	error	error	NOUN
ma-80	39	4	bound	bind	VERB
ma-80	39	5	for	for	ADP
ma-80	39	6	the	the	DET
ma-80	39	7	approximating	approximate	VERB
ma-80	39	8	function	function	NOUN
ma-80	39	9	,	,	PUNCT
ma-80	39	10	over	over	ADP
ma-80	39	11	the	the	DET
ma-80	39	12	interval	interval	NOUN
ma-80	39	13	,	,	PUNCT
ma-80	39	14	is	be	AUX
ma-80	39	15	defined	define	VERB
ma-80	39	16	according	accord	VERB
ma-80	39	17	to	to	ADP
ma-80	39	18	(	(	PUNCT
ma-80	39	19	2	2	X
ma-80	39	20	)	)	PUNCT
ma-80	39	21	the	the	DET
ma-80	39	22	notation	notation	NOUN
ma-80	39	23	is	be	AUX
ma-80	39	24	used	use	VERB
ma-80	39	25	.	.	PUNCT
ma-80	40	1	mathematica	mathematica	PROPN
ma-80	40	2	has	have	AUX
ma-80	40	3	been	be	AUX
ma-80	40	4	used	use	VERB
ma-80	40	5	to	to	PART
ma-80	40	6	facilitate	facilitate	VERB
ma-80	40	7	analysis	analysis	NOUN
ma-80	40	8	and	and	CCONJ
ma-80	40	9	to	to	PART
ma-80	40	10	obtain	obtain	VERB
ma-80	40	11	numerical	numerical	ADJ
ma-80	40	12	results	result	NOUN
ma-80	40	13	.	.	PUNCT
ma-80	41	1	in	in	ADP
ma-80	41	2	general	general	ADJ
ma-80	41	3	,	,	PUNCT
ma-80	41	4	relative	relative	ADJ
ma-80	41	5	error	error	NOUN
ma-80	41	6	results	result	NOUN
ma-80	41	7	,	,	PUNCT
ma-80	41	8	associated	associate	VERB
ma-80	41	9	with	with	ADP
ma-80	41	10	approximations	approximation	NOUN
ma-80	41	11	to	to	ADP
ma-80	41	12	the	the	DET
ma-80	41	13	lambert	lambert	PROPN
ma-80	41	14	w	w	PROPN
ma-80	41	15	function	function	PROPN
ma-80	41	16	,	,	PUNCT
ma-80	41	17	have	have	AUX
ma-80	41	18	been	be	AUX
ma-80	41	19	obtained	obtain	VERB
ma-80	41	20	by	by	ADP
ma-80	41	21	sampling	sample	VERB
ma-80	41	22	specified	specify	VERB
ma-80	41	23	intervals	interval	NOUN
ma-80	41	24	,	,	PUNCT
ma-80	41	25	in	in	ADP
ma-80	41	26	either	either	CCONJ
ma-80	41	27	a	a	DET
ma-80	41	28	linear	linear	NOUN
ma-80	41	29	or	or	CCONJ
ma-80	41	30	a	a	DET
ma-80	41	31	logarithmic	logarithmic	ADJ
ma-80	41	32	manner	manner	NOUN
ma-80	41	33	,	,	PUNCT
ma-80	41	34	as	as	ADP
ma-80	41	35	appropriate	appropriate	ADJ
ma-80	41	36	,	,	PUNCT
ma-80	41	37	with	with	ADP
ma-80	41	38	points	point	NOUN
ma-80	41	39	.	.	PUNCT
ma-80	42	1	figure	figure	NOUN
ma-80	42	2	1	1	NUM
ma-80	42	3	.	.	PUNCT
ma-80	43	1	graph	graph	NOUN
ma-80	43	2	of	of	ADP
ma-80	43	3	and	and	CCONJ
ma-80	43	4	its	its	PRON
ma-80	43	5	inverse	inverse	NOUN
ma-80	43	6	which	which	PRON
ma-80	43	7	is	be	AUX
ma-80	43	8	the	the	DET
ma-80	43	9	lambert	lambert	PROPN
ma-80	43	10	w	w	PROPN
ma-80	43	11	function	function	NOUN
ma-80	43	12	for	for	ADP
ma-80	43	13	the	the	DET
ma-80	43	14	principle	principle	ADJ
ma-80	43	15	branch	branch	NOUN
ma-80	43	16	and	and	CCONJ
ma-80	43	17	the	the	DET
ma-80	43	18	real	real	ADJ
ma-80	43	19	case	case	NOUN
ma-80	43	20	.	.	PUNCT
ma-80	44	1	f	f	X
ma-80	44	2	x	x	PROPN
ma-80	45	1			PUNCT
ma-80	45	2	xe	xe	PROPN
ma-80	45	3	x	x	X
ma-80	46	1	=	=	PUNCT
ma-80	46	2	w	w	NOUN
ma-80	46	3	y	y	NOUN
ma-80	46	4			PROPN
ma-80	46	5	x	x	SYM
ma-80	46	6	y	y	NOUN
ma-80	47	1	f	f	PROPN
ma-80	47	2	x	x	PROPN
ma-80	47	3			PROPN
ma-80	47	4	xe	xe	PROPN
ma-80	47	5	x	x	SYM
ma-80	47	6	=	=	SYM
ma-80	47	7	1	1	NUM
ma-80	47	8	–	–	SYM
ma-80	47	9	1	1	NUM
ma-80	47	10	e–	e–	ADJ
ma-80	47	11			PROPN
ma-80	47	12	1	1	NUM
ma-80	47	13	e	e	ADV
ma-80	47	14	–	–	PUNCT
ma-80	47	15	1–	1–	NUM
ma-80	47	16			PROPN
ma-80	47	17	0	0	SYM
ma-80	47	18			NUM
ma-80	47	19			NOUN
ma-80	47	20	1	1	NUM
ma-80	47	21	e	e	NOUN
ma-80	47	22	–	–	PUNCT
ma-80	47	23	1	1	NUM
ma-80	47	24	e	e	NOUN
ma-80	47	25	–	–	PUNCT
ma-80	47	26	0	0	NUM
ma-80	47	27			NOUN
ma-80	47	28	0	0	NUM
ma-80	47	29			VERB
ma-80	47	30	w	w	NOUN
ma-80	47	31	y	y	NOUN
ma-80	47	32			PROPN
ma-80	47	33	w	w	NOUN
ma-80	47	34	y	y	NOUN
ma-80	47	35			PUNCT
ma-80	47	36	y	y	PROPN
ma-80	47	37	0	0	NUM
ma-80	47	38			NUM
ma-80	47	39			PUNCT
ma-80	47	40	w	w	ADP
ma-80	47	41	y	y	NOUN
ma-80	47	42			PROPN
ma-80	47	43	1	1	NUM
ma-80	47	44	e	e	ADP
ma-80	47	45	–	–	PUNCT
ma-80	47	46	0	0	NUM
ma-80	47	47			NOUN
ma-80	47	48	x	x	SYM
ma-80	47	49	w	w	PROPN
ma-80	47	50	y	y	NOUN
ma-80	47	51	=	=	NOUN
ma-80	47	52	y	y	NOUN
ma-80	47	53	f	f	X
ma-80	47	54	x	x	PROPN
ma-80	48	1			PROPN
ma-80	48	2	xe	xe	PROPN
ma-80	48	3	x	x	PUNCT
ma-80	48	4	=	=	PUNCT
ma-80	48	5	=	=	PUNCT
ma-80	48	6	x	x	SYM
ma-80	48	7	1–	1–	NUM
ma-80	48	8	y	y	PROPN
ma-80	48	9	1	1	NUM
ma-80	48	10	e–	e–	PROPN
ma-80	48	11	f	f	PROPN
ma-80	48	12			PROPN
ma-80	48	13			NOUN
ma-80	48	14			PROPN
ma-80	48	15	fa	fa	PROPN
ma-80	48	16	x1	x1	PROPN
ma-80	48	17	re	re	VERB
ma-80	48	18	x1	x1	PROPN
ma-80	49	1			PROPN
ma-80	49	2	1	1	NUM
ma-80	50	1	fa	fa	NOUN
ma-80	50	2	x1	x1	NUM
ma-80	51	1			PUNCT
ma-80	51	2	f	f	PROPN
ma-80	51	3	x1	x1	NOUN
ma-80	52	1	–=	–=	ADP
ma-80	52	2			X
ma-80	52	3			NOUN
ma-80	52	4			PROPN
ma-80	52	5	reb	reb	PROPN
ma-80	52	6	max	max	PROPN
ma-80	52	7	re	re	ADP
ma-80	52	8	x1	x1	PROPN
ma-80	53	1			PROPN
ma-80	53	2	:	:	PUNCT
ma-80	53	3	x1	x1	NUM
ma-80	53	4			X
ma-80	53	5			NOUN
ma-80	53	6			NOUN
ma-80	53	7	.=	.=	X
ma-80	54	1	f	f	X
ma-80	54	2	k	k	NOUN
ma-80	54	3			PROPN
ma-80	54	4	x	x	PUNCT
ma-80	55	1			PUNCT
ma-80	55	2	x	x	PUNCT
ma-80	56	1	k	k	NOUN
ma-80	56	2	k	k	PROPN
ma-80	57	1	d	d	PROPN
ma-80	58	1	d	d	X
ma-80	58	2	f	f	X
ma-80	58	3	x	x	PROPN
ma-80	58	4	=	=	NOUN
ma-80	58	5	1000	1000	NUM
ma-80	58	6	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	PROPN
ma-80	58	7	2	2	NUM
ma-80	58	8	.	.	PUNCT
ma-80	58	9	published	publish	VERB
ma-80	58	10	approximations	approximation	NOUN
ma-80	58	11	a	a	DET
ma-80	58	12	taylor	taylor	PROPN
ma-80	58	13	series	series	PROPN
ma-80	58	14	expansion	expansion	NOUN
ma-80	58	15	,	,	PUNCT
ma-80	58	16	at	at	ADP
ma-80	58	17	the	the	DET
ma-80	58	18	origin	origin	NOUN
ma-80	58	19	,	,	PUNCT
ma-80	58	20	for	for	ADP
ma-80	58	21	the	the	DET
ma-80	58	22	lambert	lambert	PROPN
ma-80	58	23	w	w	PROPN
ma-80	58	24	function	function	NOUN
ma-80	58	25	is	be	AUX
ma-80	58	26	well	well	ADV
ma-80	58	27	known	know	VERB
ma-80	58	28	,	,	PUNCT
ma-80	58	29	e.g.	e.g.	ADV
ma-80	58	30	[	[	X
ma-80	58	31	17	17	NUM
ma-80	58	32	]	]	PUNCT
ma-80	58	33	,	,	PUNCT
ma-80	58	34	eqn	eqn	NOUN
ma-80	58	35	.	.	PROPN
ma-80	58	36	2	2	NUM
ma-80	58	37	,	,	PUNCT
ma-80	58	38	and	and	CCONJ
ma-80	58	39	yields	yield	VERB
ma-80	58	40	the	the	DET
ma-80	58	41	following	follow	VERB
ma-80	58	42	approximation	approximation	NOUN
ma-80	58	43	which	which	PRON
ma-80	58	44	has	have	VERB
ma-80	58	45	a	a	DET
ma-80	58	46	limited	limited	ADJ
ma-80	58	47	region	region	NOUN
ma-80	58	48	of	of	ADP
ma-80	58	49	convergence	convergence	NOUN
ma-80	58	50	:	:	PUNCT
ma-80	58	51	(	(	PUNCT
ma-80	58	52	3	3	X
ma-80	58	53	)	)	PUNCT
ma-80	58	54	the	the	DET
ma-80	58	55	relationship	relationship	NOUN
ma-80	58	56	implies	imply	VERB
ma-80	58	57	(	(	PUNCT
ma-80	58	58	positive	positive	ADJ
ma-80	58	59	sign	sign	NOUN
ma-80	58	60	for	for	ADP
ma-80	58	61	;	;	PUNCT
ma-80	58	62	negative	negative	ADJ
ma-80	58	63	sign	sign	NOUN
ma-80	58	64	for	for	ADP
ma-80	58	65	)	)	PUNCT
ma-80	58	66	and	and	CCONJ
ma-80	58	67	,	,	PUNCT
ma-80	58	68	hence	hence	ADV
ma-80	58	69	:	:	PUNCT
ma-80	58	70	(	(	PUNCT
ma-80	58	71	4	4	X
ma-80	58	72	)	)	PUNCT
ma-80	58	73	such	such	ADJ
ma-80	58	74	approximations	approximation	NOUN
ma-80	58	75	suggest	suggest	VERB
ma-80	58	76	the	the	DET
ma-80	58	77	more	more	ADV
ma-80	58	78	general	general	ADJ
ma-80	58	79	approximation	approximation	NOUN
ma-80	58	80	for	for	ADP
ma-80	58	81	the	the	DET
ma-80	58	82	lambert	lambert	PROPN
ma-80	58	83	w	w	PROPN
ma-80	58	84	function	function	PROPN
ma-80	58	85	of	of	ADP
ma-80	58	86	(	(	PUNCT
ma-80	58	87	5	5	NUM
ma-80	58	88	)	)	PUNCT
ma-80	58	89	fritsch	fritsch	PROPN
ma-80	58	90	et	et	PROPN
ma-80	58	91	al	al	PROPN
ma-80	58	92	.	.	PROPN
ma-80	58	93	,	,	PUNCT
ma-80	59	1	[	[	X
ma-80	59	2	10	10	NUM
ma-80	59	3	]	]	PUNCT
ma-80	59	4	,	,	PUNCT
ma-80	59	5	eqn	eqn	PROPN
ma-80	59	6	.	.	PROPN
ma-80	59	7	6	6	NUM
ma-80	59	8	,	,	PUNCT
ma-80	59	9	utilizes	utilize	VERB
ma-80	59	10	an	an	DET
ma-80	59	11	initial	initial	ADJ
ma-80	59	12	approximation	approximation	NOUN
ma-80	59	13	of	of	ADP
ma-80	59	14	which	which	PRON
ma-80	59	15	is	be	AUX
ma-80	59	16	suitable	suitable	ADJ
ma-80	59	17	for	for	ADP
ma-80	59	18	.	.	PROPN
ma-80	60	1	2.1	2.1	NUM
ma-80	60	2	.	.	PUNCT
ma-80	61	1	published	publish	VERB
ma-80	61	2	approximations	approximation	NOUN
ma-80	61	3	.	.	PUNCT
ma-80	62	1	the	the	DET
ma-80	62	2	following	follow	VERB
ma-80	62	3	is	be	AUX
ma-80	62	4	an	an	DET
ma-80	62	5	overview	overview	NOUN
ma-80	62	6	of	of	ADP
ma-80	62	7	indicative	indicative	ADJ
ma-80	62	8	published	publish	VERB
ma-80	62	9	approximations	approximation	NOUN
ma-80	62	10	for	for	ADP
ma-80	62	11	the	the	DET
ma-80	62	12	lambert	lambert	PROPN
ma-80	62	13	w	w	PROPN
ma-80	62	14	function	function	PROPN
ma-80	62	15	.	.	PUNCT
ma-80	63	1	additional	additional	ADJ
ma-80	63	2	useful	useful	ADJ
ma-80	63	3	references	reference	NOUN
ma-80	63	4	include	include	VERB
ma-80	63	5	[	[	X
ma-80	63	6	26	26	NUM
ma-80	63	7	]	]	PUNCT
ma-80	63	8	and	and	CCONJ
ma-80	63	9	[	[	X
ma-80	63	10	14	14	NUM
ma-80	63	11	]	]	PUNCT
ma-80	63	12	.	.	PUNCT
ma-80	64	1	boyd	boyd	PROPN
ma-80	65	1	[	[	X
ma-80	65	2	5	5	NUM
ma-80	65	3	]	]	PUNCT
ma-80	65	4	,	,	PUNCT
ma-80	65	5	eqn	eqn	NOUN
ma-80	65	6	.	.	PUNCT
ma-80	66	1	5	5	NUM
ma-80	66	2	-	-	SYM
ma-80	66	3	7	7	NUM
ma-80	66	4	,	,	PUNCT
ma-80	66	5	proposed	propose	VERB
ma-80	66	6	the	the	DET
ma-80	66	7	approximation	approximation	NOUN
ma-80	66	8	(	(	PUNCT
ma-80	66	9	6	6	NUM
ma-80	66	10	)	)	PUNCT
ma-80	66	11	which	which	PRON
ma-80	66	12	is	be	AUX
ma-80	66	13	valid	valid	ADJ
ma-80	66	14	for	for	ADP
ma-80	66	15	.	.	PUNCT
ma-80	67	1	whilst	whilst	SCONJ
ma-80	67	2	the	the	DET
ma-80	67	3	approximation	approximation	NOUN
ma-80	67	4	is	be	AUX
ma-80	67	5	sharp	sharp	ADJ
ma-80	67	6	at	at	ADP
ma-80	67	7	,	,	PUNCT
ma-80	67	8	it	it	PRON
ma-80	67	9	is	be	AUX
ma-80	67	10	not	not	PART
ma-80	67	11	zero	zero	NUM
ma-80	67	12	at	at	ADP
ma-80	67	13	the	the	DET
ma-80	67	14	origin	origin	NOUN
ma-80	67	15	and	and	CCONJ
ma-80	67	16	,	,	PUNCT
ma-80	67	17	thus	thus	ADV
ma-80	67	18	,	,	PUNCT
ma-80	67	19	is	be	AUX
ma-80	67	20	not	not	PART
ma-80	67	21	sharp	sharp	ADJ
ma-80	67	22	at	at	ADP
ma-80	67	23	this	this	DET
ma-80	67	24	point	point	NOUN
ma-80	67	25	.	.	PUNCT
ma-80	68	1	it	it	PRON
ma-80	68	2	has	have	VERB
ma-80	68	3	a	a	DET
ma-80	68	4	relative	relative	ADJ
ma-80	68	5	error	error	NOUN
ma-80	68	6	bound	bind	VERB
ma-80	68	7	for	for	ADP
ma-80	68	8	the	the	DET
ma-80	68	9	interval	interval	NOUN
ma-80	68	10	of	of	ADP
ma-80	68	11	.	.	PUNCT
ma-80	69	1	barry	barry	PROPN
ma-80	69	2	et	et	PROPN
ma-80	69	3	al	al	PROPN
ma-80	69	4	.	.	PUNCT
ma-80	70	1	[	[	X
ma-80	70	2	3	3	NUM
ma-80	70	3	]	]	PUNCT
ma-80	70	4	,	,	PUNCT
ma-80	70	5	eqn	eqn	PROPN
ma-80	70	6	.	.	PROPN
ma-80	70	7	12	12	NUM
ma-80	70	8	,	,	PUNCT
ma-80	70	9	proposed	propose	VERB
ma-80	70	10	the	the	DET
ma-80	70	11	approximation	approximation	NOUN
ma-80	70	12	(	(	PUNCT
ma-80	70	13	7	7	NUM
ma-80	70	14	)	)	PUNCT
ma-80	70	15	for	for	ADP
ma-80	70	16	.	.	PUNCT
ma-80	71	1	this	this	DET
ma-80	71	2	approximation	approximation	NOUN
ma-80	71	3	was	be	AUX
ma-80	71	4	modified	modify	VERB
ma-80	71	5	,	,	PUNCT
ma-80	71	6	[	[	X
ma-80	71	7	3	3	NUM
ma-80	71	8	]	]	PUNCT
ma-80	71	9	,	,	PUNCT
ma-80	71	10	eqn	eqn	PROPN
ma-80	71	11	.	.	PROPN
ma-80	71	12	15	15	NUM
ma-80	71	13	,	,	PUNCT
ma-80	71	14	to	to	PART
ma-80	71	15	be	be	AUX
ma-80	71	16	valid	valid	ADJ
ma-80	71	17	for	for	ADP
ma-80	71	18	according	accord	VERB
ma-80	71	19	to	to	ADP
ma-80	71	20	(	(	PUNCT
ma-80	71	21	8)	8)	NUM
ma-80	71	22	t	t	NOUN
ma-80	71	23	y	y	NOUN
ma-80	71	24			PUNCT
ma-80	71	25	y	y	PROPN
ma-80	71	26	y	y	PROPN
ma-80	71	27	2	2	NUM
ma-80	71	28	–	–	PUNCT
ma-80	71	29	3y	3y	NUM
ma-80	71	30	3	3	NUM
ma-80	71	31	2	2	NUM
ma-80	71	32	-------8y	-------8y	NUM
ma-80	71	33	4	4	NUM
ma-80	71	34	3	3	NUM
ma-80	71	35	--------	--------	SYM
ma-80	71	36	–	–	PUNCT
ma-80	71	37	125y	125y	NUM
ma-80	71	38	5	5	NUM
ma-80	71	39	24	24	NUM
ma-80	71	40	-------------54y	-------------54y	NUM
ma-80	71	41	6	6	NUM
ma-80	71	42	5	5	NUM
ma-80	71	43	----------16807y	----------16807y	SYM
ma-80	71	44	7	7	NUM
ma-80	71	45	720	720	NUM
ma-80	71	46	--------------------+	--------------------+	NUM
ma-80	71	47	–	–	PUNCT
ma-80	71	48	16384y	16384y	NUM
ma-80	71	49	8	8	NUM
ma-80	71	50	315	315	NUM
ma-80	71	51	--------------------	--------------------	SYM
ma-80	71	52	–	–	PUNCT
ma-80	71	53	+	+	PROPN
ma-80	72	1	+	+	NUM
ma-80	73	1	+	+	ADJ
ma-80	73	2	=	=	SYM
ma-80	73	3	y	y	ADJ
ma-80	73	4	1	1	NUM
ma-80	73	5	e	e	VERB
ma-80	73	6	---.	---.	PROPN
ma-80	73	7	y	y	PROPN
ma-80	73	8	xe	xe	PROPN
ma-80	73	9	x	x	PUNCT
ma-80	74	1	=	=	PUNCT
ma-80	74	2	x	x	X
ma-80	74	3	x	x	PROPN
ma-80	74	4	ln+	ln+	PROPN
ma-80	74	5	y	y	PROPN
ma-80	74	6	ln=	ln=	PUNCT
ma-80	75	1	x	x	X
ma-80	76	1	y	y	NOUN
ma-80	76	2	0	0	NUM
ma-80	76	3	x	x	PUNCT
ma-80	77	1	y	y	NOUN
ma-80	77	2	0	0	PUNCT
ma-80	77	3	x	x	PUNCT
ma-80	77	4	y	y	PROPN
ma-80	77	5	y	y	PROPN
ma-80	77	6	1	1	NUM
ma-80	77	7	«	«	PUNCT
ma-80	77	8	y	y	NOUN
ma-80	77	9	ln	ln	PROPN
ma-80	77	10	y	y	NOUN
ma-80	77	11	1.»	1.»	NUM
ma-80	77	12			NUM
ma-80	77	13			NOUN
ma-80	77	14			NOUN
ma-80	77	15	x	x	VERB
ma-80	77	16	w	w	NOUN
ma-80	77	17	y	y	NOUN
ma-80	77	18			PROPN
ma-80	77	19	1	1	NUM
ma-80	77	20	y+	y+	NOUN
ma-80	77	21	ln	ln	PROPN
ma-80	77	22	=	=	PUNCT
ma-80	77	23	y	y	PROPN
ma-80	77	24	1	1	NUM
ma-80	77	25	–	–	PUNCT
ma-80	77	26	e	e	NOUN
ma-80	77	27	------.	------.	NOUN
ma-80	77	28	w	w	NOUN
ma-80	77	29	y	y	PROPN
ma-80	77	30			PROPN
ma-80	77	31	y	y	NOUN
ma-80	77	32	ln	ln	PUNCT
ma-80	77	33	y	y	PROPN
ma-80	77	34	e	e	NOUN
ma-80	77	35	wbd	wbd	VERB
ma-80	77	36	y	y	PROPN
ma-80	77	37			PROPN
ma-80	77	38	1	1	NUM
ma-80	77	39	2	2	NUM
ma-80	77	40	1	1	NUM
ma-80	77	41	ey+	ey+	NOUN
ma-80	77	42			PROPN
ma-80	77	43	10	10	NUM
ma-80	77	44	ln	ln	SYM
ma-80	77	45	10	10	NUM
ma-80	77	46	ln	ln	NOUN
ma-80	77	47	ln	ln	NOUN
ma-80	77	48	–	–	PUNCT
ma-80	77	49	------------------------------------------------11	------------------------------------------------11	NOUN
ma-80	77	50	ey+	ey+	NOUN
ma-80	77	51	ln	ln	PROPN
ma-80	77	52	11	11	NUM
ma-80	77	53	ey+	ey+	X
ma-80	77	54	ln	ln	NOUN
ma-80	77	55	ln–tanh+	ln–tanh+	NOUN
ma-80	77	56	–	–	PUNCT
ma-80	77	57	=	=	NOUN
ma-80	77	58	1	1	NUM
ma-80	77	59	1	1	NUM
ma-80	77	60	10	10	NUM
ma-80	77	61	-----1	-----1	PRON
ma-80	77	62	ey+	ey+	NOUN
ma-80	78	1	ln	ln	PROPN
ma-80	78	2	7	7	NUM
ma-80	78	3	5	5	NUM
ma-80	78	4	---	---	PUNCT
ma-80	78	5	–	–	PUNCT
ma-80	78	6	3	3	NUM
ma-80	78	7	–	–	SYM
ma-80	78	8	40	40	NUM
ma-80	78	9	-----1	-----1	PRON
ma-80	78	10	ey+	ey+	X
ma-80	78	11	ln	ln	PROPN
ma-80	78	12	7	7	NUM
ma-80	78	13	5	5	NUM
ma-80	78	14	---	---	PUNCT
ma-80	78	15	–	–	PUNCT
ma-80	78	16	2	2	NUM
ma-80	78	17	exp+	exp+	PROPN
ma-80	78	18	y	y	PROPN
ma-80	78	19	1	1	NUM
ma-80	78	20	e–	e–	PROPN
ma-80	78	21	y	y	PROPN
ma-80	78	22	1	1	NUM
ma-80	78	23	e–=	e–=	NUM
ma-80	78	24	1	1	NUM
ma-80	78	25			X
ma-80	78	26			NOUN
ma-80	78	27	0.0499	0.0499	NUM
ma-80	78	28	wb1	wb1	X
ma-80	78	29	y	y	VERB
ma-80	78	30			PROPN
ma-80	78	31	6	6	NUM
ma-80	78	32	5	5	NUM
ma-80	78	33	--y	--y	NOUN
ma-80	78	34	12	12	NUM
ma-80	78	35	5	5	NUM
ma-80	78	36	-----y	-----y	NUM
ma-80	78	37	1	1	NUM
ma-80	78	38	12y	12y	NOUN
ma-80	78	39	5+	5+	NUM
ma-80	78	40	ln	ln	NOUN
ma-80	78	41	-----------------------------------ln	-----------------------------------ln	PUNCT
ma-80	79	1	---------------------------------------------------------ln=	---------------------------------------------------------ln=	NOUN
ma-80	80	1	y	y	NOUN
ma-80	80	2	0	0	NUM
ma-80	80	3	y	y	NOUN
ma-80	80	4	1	1	NUM
ma-80	80	5	e–	e–	NOUN
ma-80	80	6	wb2	wb2	ADP
ma-80	80	7	y	y	NOUN
ma-80	80	8			PROPN
ma-80	80	9	1	1	NUM
ma-80	80	10	+	+	NOUN
ma-80	80	11			NOUN
ma-80	80	12	6	6	NUM
ma-80	80	13	5	5	NUM
ma-80	80	14	--y	--y	NOUN
ma-80	80	15	12	12	NUM
ma-80	80	16	5	5	NUM
ma-80	80	17	-----y	-----y	NUM
ma-80	80	18	1	1	NUM
ma-80	80	19	12y	12y	NOUN
ma-80	80	20	5+	5+	NUM
ma-80	80	21	ln	ln	NOUN
ma-80	80	22	-----------------------------------ln	-----------------------------------ln	PUNCT
ma-80	81	1	---------------------------------------------------------ln	---------------------------------------------------------ln	PROPN
ma-80	82	1			NUM
ma-80	82	2	2y	2y	NUM
ma-80	82	3	1	1	NUM
ma-80	82	4	2y+	2y+	NUM
ma-80	82	5	ln	ln	NOUN
ma-80	82	6	-------------------------ln	-------------------------ln	NOUN
ma-80	82	7	–=	–=	NOUN
ma-80	83	1			NUM
ma-80	83	2	0.4586887.=	0.4586887.=	PUNCT
ma-80	84	1	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	NOUN
ma-80	84	2	the	the	DET
ma-80	84	3	relative	relative	ADJ
ma-80	84	4	error	error	NOUN
ma-80	84	5	bound	bind	VERB
ma-80	84	6	,	,	PUNCT
ma-80	84	7	for	for	ADP
ma-80	84	8	,	,	PUNCT
ma-80	84	9	is	be	AUX
ma-80	84	10	.	.	PUNCT
ma-80	85	1	iacono	iacono	NOUN
ma-80	85	2	and	and	CCONJ
ma-80	85	3	boyd	boyd	PROPN
ma-80	85	4	,	,	PUNCT
ma-80	85	5	[	[	X
ma-80	85	6	17	17	NUM
ma-80	85	7	]	]	PUNCT
ma-80	85	8	,	,	PUNCT
ma-80	85	9	eqn	eqn	PROPN
ma-80	85	10	.	.	PROPN
ma-80	85	11	17	17	NUM
ma-80	85	12	,	,	PUNCT
ma-80	85	13	proposed	propose	VERB
ma-80	85	14	the	the	DET
ma-80	85	15	following	follow	VERB
ma-80	85	16	approximation	approximation	NOUN
ma-80	85	17	which	which	PRON
ma-80	85	18	is	be	AUX
ma-80	85	19	valid	valid	ADJ
ma-80	85	20	for	for	ADP
ma-80	85	21	(	(	PUNCT
ma-80	85	22	9	9	X
ma-80	85	23	)	)	PUNCT
ma-80	85	24	this	this	DET
ma-80	85	25	approximation	approximation	NOUN
ma-80	85	26	yields	yield	VERB
ma-80	85	27	a	a	DET
ma-80	85	28	relative	relative	ADJ
ma-80	85	29	error	error	NOUN
ma-80	85	30	bound	bind	VERB
ma-80	85	31	of	of	ADP
ma-80	85	32	for	for	ADP
ma-80	85	33	.	.	PUNCT
ma-80	86	1	an	an	DET
ma-80	86	2	improved	improved	ADJ
ma-80	86	3	approximation	approximation	NOUN
ma-80	86	4	,	,	PUNCT
ma-80	86	5	[	[	X
ma-80	86	6	17	17	NUM
ma-80	86	7	]	]	PUNCT
ma-80	86	8	,	,	PUNCT
ma-80	86	9	eqn	eqn	PROPN
ma-80	86	10	.	.	PROPN
ma-80	86	11	19	19	NUM
ma-80	86	12	,	,	PUNCT
ma-80	86	13	20	20	NUM
ma-80	86	14	,	,	PUNCT
ma-80	86	15	is	be	AUX
ma-80	86	16	(	(	PUNCT
ma-80	86	17	10	10	NUM
ma-80	86	18	)	)	PUNCT
ma-80	86	19	which	which	PRON
ma-80	86	20	yields	yield	VERB
ma-80	86	21	a	a	DET
ma-80	86	22	relative	relative	ADJ
ma-80	86	23	error	error	NOUN
ma-80	86	24	bound	bind	VERB
ma-80	86	25	for	for	ADP
ma-80	86	26	of	of	ADP
ma-80	86	27	(	(	PUNCT
ma-80	86	28	the	the	DET
ma-80	86	29	bound	bind	VERB
ma-80	86	30	occurs	occur	VERB
ma-80	86	31	at	at	ADP
ma-80	86	32	of	of	ADP
ma-80	86	33	the	the	DET
ma-80	86	34	order	order	NOUN
ma-80	86	35	of	of	ADP
ma-80	86	36	)	)	PUNCT
ma-80	86	37	for	for	ADP
ma-80	86	38	the	the	DET
ma-80	86	39	case	case	NOUN
ma-80	86	40	of	of	ADP
ma-80	86	41	optimally	optimally	ADV
ma-80	86	42	chosen	choose	VERB
ma-80	86	43	as	as	ADP
ma-80	86	44	.	.	PUNCT
ma-80	87	1	the	the	DET
ma-80	87	2	approximation	approximation	NOUN
ma-80	87	3	is	be	AUX
ma-80	87	4	sharp	sharp	ADJ
ma-80	87	5	at	at	ADP
ma-80	87	6	.	.	PUNCT
ma-80	88	1	2.1.1	2.1.1	X
ma-80	88	2	.	.	PUNCT
ma-80	88	3	padè	padè	ADJ
ma-80	88	4	approximations	approximation	NOUN
ma-80	88	5	.	.	PUNCT
ma-80	89	1	padè	padè	ADJ
ma-80	89	2	approximates	approximate	VERB
ma-80	89	3	for	for	ADP
ma-80	89	4	the	the	DET
ma-80	89	5	lambert	lambert	PROPN
ma-80	89	6	w	w	PROPN
ma-80	89	7	function	function	NOUN
ma-80	89	8	for	for	ADP
ma-80	89	9	the	the	DET
ma-80	89	10	interval	interval	NOUN
ma-80	89	11	have	have	AUX
ma-80	89	12	been	be	AUX
ma-80	89	13	proposed	propose	VERB
ma-80	89	14	,	,	PUNCT
ma-80	89	15	e.g.	e.g.	ADV
ma-80	89	16	[	[	X
ma-80	89	17	21	21	NUM
ma-80	89	18	]	]	PUNCT
ma-80	89	19	,	,	PUNCT
ma-80	89	20	eqn	eqn	PROPN
ma-80	89	21	.	.	PUNCT
ma-80	90	1	34	34	NUM
ma-80	90	2	:	:	PUNCT
ma-80	90	3	(	(	PUNCT
ma-80	90	4	11	11	NUM
ma-80	90	5	)	)	PUNCT
ma-80	90	6	higher	high	ADJ
ma-80	90	7	order	order	NOUN
ma-80	90	8	padè	padè	ADV
ma-80	90	9	approximates	approximate	NOUN
ma-80	90	10	are	be	AUX
ma-80	90	11	detailed	detail	VERB
ma-80	90	12	in	in	ADP
ma-80	90	13	fukushima	fukushima	PROPN
ma-80	90	14	[	[	X
ma-80	90	15	13	13	NUM
ma-80	90	16	]	]	PUNCT
ma-80	90	17	.	.	PUNCT
ma-80	91	1	2.1.2	2.1.2	NUM
ma-80	91	2	.	.	PUNCT
ma-80	91	3	comparison	comparison	NOUN
ma-80	91	4	of	of	ADP
ma-80	91	5	approximations	approximation	NOUN
ma-80	91	6	.	.	PUNCT
ma-80	92	1	the	the	DET
ma-80	92	2	relative	relative	ADJ
ma-80	92	3	errors	error	NOUN
ma-80	92	4	in	in	ADP
ma-80	92	5	the	the	DET
ma-80	92	6	above	above	ADJ
ma-80	92	7	specified	specified	ADJ
ma-80	92	8	approximations	approximation	NOUN
ma-80	92	9	are	be	AUX
ma-80	92	10	shown	show	VERB
ma-80	92	11	in	in	ADP
ma-80	92	12	figure	figure	NOUN
ma-80	92	13	2	2	NUM
ma-80	92	14	and	and	CCONJ
ma-80	92	15	figure	figure	VERB
ma-80	92	16	3	3	NUM
ma-80	92	17	.	.	PROPN
ma-80	92	18	2.2	2.2	NUM
ma-80	92	19	.	.	PUNCT
ma-80	93	1	classic	classic	ADJ
ma-80	93	2	iterative	iterative	NOUN
ma-80	93	3	approximations	approximation	NOUN
ma-80	93	4	.	.	PUNCT
ma-80	94	1	the	the	DET
ma-80	94	2	classical	classical	ADJ
ma-80	94	3	iterative	iterative	NOUN
ma-80	94	4	approximation	approximation	NOUN
ma-80	94	5	for	for	ADP
ma-80	94	6	the	the	DET
ma-80	94	7	lambert	lambert	PROPN
ma-80	94	8	w	w	PROPN
ma-80	94	9	function	function	PROPN
ma-80	94	10	,	,	PUNCT
ma-80	94	11	e.g.	e.g.	ADV
ma-80	94	12	[	[	X
ma-80	94	13	17	17	NUM
ma-80	94	14	]	]	PUNCT
ma-80	94	15	,	,	PUNCT
ma-80	94	16	eqn	eqn	PROPN
ma-80	94	17	.	.	PUNCT
ma-80	94	18	8	8	NUM
ma-80	94	19	-	-	SYM
ma-80	94	20	10	10	NUM
ma-80	94	21	,	,	PUNCT
ma-80	94	22	is	be	AUX
ma-80	94	23	based	base	VERB
ma-80	94	24	on	on	ADP
ma-80	94	25	the	the	DET
ma-80	94	26	fundamental	fundamental	ADJ
ma-80	94	27	relationship	relationship	NOUN
ma-80	94	28	,	,	PUNCT
ma-80	94	29	,	,	PUNCT
ma-80	94	30	and	and	CCONJ
ma-80	94	31	an	an	DET
ma-80	94	32	initial	initial	ADJ
ma-80	94	33	approximation	approximation	NOUN
ma-80	94	34	as	as	SCONJ
ma-80	94	35	specified	specify	VERB
ma-80	94	36	in	in	ADP
ma-80	94	37	y	y	PROPN
ma-80	94	38	0	0	NUM
ma-80	94	39	1.96	1.96	NUM
ma-80	94	40	10	10	NUM
ma-80	94	41	3–	3–	NUM
ma-80	94	42	y	y	NOUN
ma-80	94	43	1	1	NUM
ma-80	94	44	–	–	PUNCT
ma-80	94	45	e	e	ADV
ma-80	94	46			NUM
ma-80	94	47			NUM
ma-80	94	48	wi1	wi1	NOUN
ma-80	94	49	y	y	NOUN
ma-80	94	50			PROPN
ma-80	94	51	1	1	NUM
ma-80	94	52	y	y	PROPN
ma-80	94	53	1	1	NUM
ma-80	94	54	1	1	NUM
ma-80	94	55	y+	y+	NOUN
ma-80	94	56	ln	ln	PROPN
ma-80	94	57	2	2	NUM
ma-80	94	58	----------------------+	----------------------+	ADJ
ma-80	94	59	--------------------------------+	--------------------------------+	NOUN
ma-80	94	60	.ln=	.ln=	NOUN
ma-80	95	1	3.53	3.53	NUM
ma-80	95	2	10	10	NUM
ma-80	95	3	2–	2–	NUM
ma-80	95	4	y	y	PROPN
ma-80	95	5	0	0	NUM
ma-80	95	6			NUM
ma-80	95	7			PUNCT
ma-80	95	8	wi2	wi2	ADJ
ma-80	95	9	y	y	NOUN
ma-80	95	10			PROPN
ma-80	95	11	1	1	NUM
ma-80	95	12	–	–	PUNCT
ma-80	95	13	a	a	DET
ma-80	95	14	1	1	NUM
ma-80	95	15	b	b	SYM
ma-80	95	16	1	1	NUM
ma-80	95	17	ey++	ey++	NOUN
ma-80	95	18	1	1	NUM
ma-80	95	19	c	c	NOUN
ma-80	95	20	1	1	NUM
ma-80	95	21	1	1	NUM
ma-80	95	22	ey++	ey++	ADP
ma-80	95	23	ln+	ln+	NOUN
ma-80	95	24	---------------------------------------------------ln	---------------------------------------------------ln	NOUN
ma-80	95	25	+=	+=	PUNCT
ma-80	95	26	c	c	X
ma-80	95	27	e	e	PROPN
ma-80	95	28	1	1	NUM
ma-80	95	29	a	a	NOUN
ma-80	95	30	1	1	NUM
ma-80	95	31	–	–	SYM
ma-80	95	32	2	2	NUM
ma-80	95	33	a	a	NOUN
ma-80	95	34	–	–	PUNCT
ma-80	95	35	1	1	NUM
ma-80	95	36	2	2	PROPN
ma-80	95	37	e1	e1	NUM
ma-80	95	38	a	a	NOUN
ma-80	95	39	ln	ln	ADJ
ma-80	95	40	–	–	PUNCT
ma-80	95	41	----------------------------------------=	----------------------------------------=	NOUN
ma-80	95	42	b	b	PROPN
ma-80	95	43	2	2	NUM
ma-80	95	44	a	a	DET
ma-80	95	45	------c+	------c+	PROPN
ma-80	95	46	=	=	PROPN
ma-80	95	47	y	y	NOUN
ma-80	95	48	0	0	NUM
ma-80	95	49	4.53	4.53	NUM
ma-80	95	50	10	10	NUM
ma-80	95	51	3–	3–	NUM
ma-80	95	52	y	y	NOUN
ma-80	95	53	10	10	NUM
ma-80	95	54	12	12	NUM
ma-80	95	55	a	a	DET
ma-80	95	56	a	a	DET
ma-80	95	57	2.036=	2.036=	NUM
ma-80	95	58	y	y	NOUN
ma-80	95	59	1	1	NUM
ma-80	95	60	e–=	e–=	NOUN
ma-80	95	61	y	y	PROPN
ma-80	95	62	1	1	NUM
ma-80	95	63	–	–	PUNCT
ma-80	95	64	e	e	ADV
ma-80	95	65	1	1	NUM
ma-80	95	66			PROPN
ma-80	95	67	wl	wl	X
ma-80	95	68	y	y	PROPN
ma-80	95	69			PROPN
ma-80	95	70	1	1	NUM
ma-80	95	71	123y	123y	NUM
ma-80	95	72	40	40	NUM
ma-80	95	73	-----------21y	-----------21y	NOUN
ma-80	95	74	2	2	NUM
ma-80	95	75	10	10	NUM
ma-80	95	76	-----------+	-----------+	ADJ
ma-80	95	77	+	+	NOUN
ma-80	95	78	1	1	NUM
ma-80	95	79	143y	143y	NUM
ma-80	95	80	40	40	NUM
ma-80	95	81	-----------713y	-----------713y	SYM
ma-80	95	82	2	2	NUM
ma-80	95	83	240	240	NUM
ma-80	95	84	--------------+	--------------+	ADJ
ma-80	95	85	+	+	NUM
ma-80	95	86	-----------------------------------------1	-----------------------------------------1	NOUN
ma-80	95	87	y+	y+	NOUN
ma-80	95	88	.ln=	.ln=	PROPN
ma-80	95	89	figure	figure	NOUN
ma-80	95	90	2	2	NUM
ma-80	95	91	.	.	PUNCT
ma-80	95	92	graph	graph	NOUN
ma-80	95	93	of	of	ADP
ma-80	95	94	the	the	DET
ma-80	95	95	relative	relative	ADJ
ma-80	95	96	errors	error	NOUN
ma-80	95	97	,	,	PUNCT
ma-80	95	98	over	over	ADP
ma-80	95	99	the	the	DET
ma-80	95	100	interval	interval	NOUN
ma-80	95	101	,	,	PUNCT
ma-80	95	102	in	in	ADP
ma-80	95	103	published	publish	VERB
ma-80	95	104	approximations	approximation	NOUN
ma-80	95	105	to	to	ADP
ma-80	95	106	.1	.1	NUM
ma-80	95	107	–	–	PUNCT
ma-80	95	108	e	e	ADV
ma-80	95	109	1	1	NUM
ma-80	95	110			NOUN
ma-80	95	111	w	w	NOUN
ma-80	95	112	y	y	NOUN
ma-80	95	113			PUNCT
ma-80	95	114	y	y	PROPN
ma-80	95	115	re	re	X
ma-80	95	116	y	y	NOUN
ma-80	95	117			PROPN
ma-80	95	118	wi1	wi1	NOUN
ma-80	95	119	y	y	NOUN
ma-80	95	120			PROPN
ma-80	95	121	wi2	wi2	NOUN
ma-80	96	1	y	y	NOUN
ma-80	96	2			PROPN
ma-80	96	3	wb2	wb2	ADP
ma-80	96	4	y	y	NOUN
ma-80	97	1			PUNCT
ma-80	97	2	wbd	wbd	VERB
ma-80	97	3	y	y	PROPN
ma-80	97	4			PROPN
ma-80	97	5	wl	wl	X
ma-80	97	6	y	y	NOUN
ma-80	97	7			PROPN
ma-80	97	8	wl	wl	X
ma-80	97	9	y	y	NOUN
ma-80	97	10			PROPN
ma-80	97	11	wb2	wb2	ADP
ma-80	97	12	y	y	NOUN
ma-80	97	13			NOUN
ma-80	97	14	wi1	wi1	NOUN
ma-80	97	15	y	y	NOUN
ma-80	97	16			PROPN
ma-80	97	17	x	x	PUNCT
ma-80	97	18	y	y	NOUN
ma-80	97	19	ln	ln	PUNCT
ma-80	98	1	x	x	ADV
ma-80	98	2	ln–=	ln–=	NOUN
ma-80	99	1	x	x	SYM
ma-80	99	2	y	y	NOUN
ma-80	99	3	0	0	NUM
ma-80	99	4	x	x	PART
ma-80	99	5	w0	w0	PROPN
ma-80	99	6	y	y	PROPN
ma-80	99	7			NUM
ma-80	99	8	1	1	NUM
ma-80	99	9	y+	y+	NOUN
ma-80	99	10	ln=	ln=	PUNCT
ma-80	100	1	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	PROPN
ma-80	100	2	equation	equation	NOUN
ma-80	100	3	5	5	NUM
ma-80	100	4	.	.	PUNCT
ma-80	101	1	a	a	DET
ma-80	101	2	first	first	ADJ
ma-80	101	3	order	order	NOUN
ma-80	101	4	approximation	approximation	NOUN
ma-80	101	5	arises	arise	VERB
ma-80	101	6	by	by	ADP
ma-80	101	7	substitution	substitution	NOUN
ma-80	101	8	of	of	ADP
ma-80	101	9	this	this	DET
ma-80	101	10	approximation	approximation	NOUN
ma-80	101	11	into	into	ADP
ma-80	101	12	the	the	DET
ma-80	101	13	expression	expression	NOUN
ma-80	101	14	to	to	PART
ma-80	101	15	yield	yield	VERB
ma-80	101	16	(	(	PUNCT
ma-80	101	17	12	12	NUM
ma-80	101	18	)	)	PUNCT
ma-80	101	19	iteration	iteration	NOUN
ma-80	101	20	yields	yield	NOUN
ma-80	101	21	(	(	PUNCT
ma-80	101	22	13	13	NUM
ma-80	101	23	)	)	PUNCT
ma-80	101	24	in	in	ADP
ma-80	101	25	general	general	ADJ
ma-80	101	26	:	:	PUNCT
ma-80	101	27	(	(	PUNCT
ma-80	101	28	14	14	NUM
ma-80	101	29	)	)	PUNCT
ma-80	101	30	2.2.1	2.2.1	NUM
ma-80	101	31	.	.	PUNCT
ma-80	101	32	comparison	comparison	NOUN
ma-80	101	33	of	of	ADP
ma-80	101	34	approximations	approximation	NOUN
ma-80	101	35	.	.	PUNCT
ma-80	102	1	the	the	DET
ma-80	102	2	relative	relative	ADJ
ma-80	102	3	error	error	NOUN
ma-80	102	4	in	in	ADP
ma-80	102	5	the	the	DET
ma-80	102	6	iterative	iterative	NOUN
ma-80	102	7	approximations	approximation	NOUN
ma-80	102	8	,	,	PUNCT
ma-80	102	9	of	of	ADP
ma-80	102	10	orders	order	NOUN
ma-80	102	11	zero	zero	NUM
ma-80	102	12	to	to	ADP
ma-80	102	13	three	three	NUM
ma-80	102	14	,	,	PUNCT
ma-80	102	15	are	be	AUX
ma-80	102	16	detailed	detail	VERB
ma-80	102	17	in	in	ADP
ma-80	102	18	figure	figure	NOUN
ma-80	102	19	4	4	NUM
ma-80	102	20	and	and	CCONJ
ma-80	102	21	figure	figure	VERB
ma-80	102	22	5	5	NUM
ma-80	102	23	.	.	PUNCT
ma-80	103	1	the	the	DET
ma-80	103	2	relative	relative	ADJ
ma-80	103	3	errors	error	NOUN
ma-80	103	4	decrease	decrease	VERB
ma-80	103	5	,	,	PUNCT
ma-80	103	6	for	for	ADP
ma-80	103	7	large	large	ADJ
ma-80	103	8	values	value	NOUN
ma-80	103	9	of	of	ADP
ma-80	103	10	,	,	PUNCT
ma-80	103	11	at	at	ADP
ma-80	103	12	an	an	DET
ma-80	103	13	increasing	increase	VERB
ma-80	103	14	rate	rate	NOUN
ma-80	103	15	as	as	SCONJ
ma-80	103	16	the	the	DET
ma-80	103	17	order	order	NOUN
ma-80	103	18	of	of	ADP
ma-80	103	19	approximation	approximation	NOUN
ma-80	103	20	is	be	AUX
ma-80	103	21	increased	increase	VERB
ma-80	103	22	.	.	PUNCT
ma-80	104	1	the	the	DET
ma-80	104	2	approximations	approximation	NOUN
ma-80	104	3	are	be	AUX
ma-80	104	4	poor	poor	ADJ
ma-80	104	5	for	for	SCONJ
ma-80	104	6	which	which	PRON
ma-80	104	7	is	be	AUX
ma-80	104	8	consistent	consistent	ADJ
ma-80	104	9	with	with	ADP
ma-80	104	10	the	the	DET
ma-80	104	11	assumptions	assumption	NOUN
ma-80	104	12	made	make	VERB
ma-80	104	13	in	in	ADP
ma-80	104	14	the	the	DET
ma-80	104	15	iteration	iteration	NOUN
ma-80	104	16	.	.	PUNCT
ma-80	105	1	2.2.2	2.2.2	X
ma-80	105	2	.	.	NOUN
ma-80	105	3	alternative	alternative	ADJ
ma-80	105	4	iterative	iterative	NOUN
ma-80	105	5	approximations	approximation	NOUN
ma-80	105	6	.	.	PUNCT
ma-80	106	1	an	an	DET
ma-80	106	2	alternative	alternative	ADJ
ma-80	106	3	iterative	iterative	NOUN
ma-80	106	4	approach	approach	NOUN
ma-80	106	5	is	be	AUX
ma-80	106	6	to	to	PART
ma-80	106	7	utilize	utilize	VERB
ma-80	106	8	the	the	DET
ma-80	106	9	relationship	relationship	NOUN
ma-80	106	10	and	and	CCONJ
ma-80	106	11	solve	solve	VERB
ma-80	106	12	for	for	ADP
ma-80	106	13	the	the	DET
ma-80	106	14	error	error	NOUN
ma-80	106	15	given	give	VERB
ma-80	106	16	an	an	DET
ma-80	106	17	initial	initial	ADJ
ma-80	106	18	approximation	approximation	NOUN
ma-80	106	19	figure	figure	NOUN
ma-80	106	20	3	3	NUM
ma-80	106	21	.	.	PUNCT
ma-80	106	22	graph	graph	NOUN
ma-80	106	23	of	of	ADP
ma-80	106	24	the	the	DET
ma-80	106	25	relative	relative	ADJ
ma-80	106	26	errors	error	NOUN
ma-80	106	27	in	in	ADP
ma-80	106	28	published	publish	VERB
ma-80	106	29	approximations	approximation	NOUN
ma-80	106	30	to	to	PART
ma-80	106	31	.w	.w	VERB
ma-80	107	1	y	y	PROPN
ma-80	107	2			PROPN
ma-80	107	3	y	y	PROPN
ma-80	107	4	re	re	X
ma-80	107	5	y	y	NOUN
ma-80	107	6			PROPN
ma-80	107	7	wi1	wi1	NOUN
ma-80	107	8	y	y	NOUN
ma-80	107	9			PROPN
ma-80	108	1	wi2	wi2	ADJ
ma-80	108	2	y	y	NOUN
ma-80	108	3			PROPN
ma-80	108	4	wbd	wbd	VERB
ma-80	108	5	y	y	PROPN
ma-80	108	6			PROPN
ma-80	108	7	wl	wl	X
ma-80	108	8	y	y	NOUN
ma-80	108	9			PROPN
ma-80	108	10	wb2	wb2	ADP
ma-80	108	11	y	y	NOUN
ma-80	109	1			PROPN
ma-80	109	2	wl	wl	X
ma-80	109	3	y	y	NOUN
ma-80	109	4			PROPN
ma-80	109	5	x	x	X
ma-80	110	1	ln	ln	PROPN
ma-80	110	2	w1	w1	NOUN
ma-80	110	3	y	y	NOUN
ma-80	110	4			PROPN
ma-80	110	5	y	y	NOUN
ma-80	110	6	ln	ln	PROPN
ma-80	110	7	1	1	NUM
ma-80	110	8	y+	y+	NOUN
ma-80	110	9	ln	ln	NOUN
ma-80	110	10	ln	ln	NOUN
ma-80	110	11	–	–	PUNCT
ma-80	110	12	y	y	PROPN
ma-80	110	13	1	1	NUM
ma-80	110	14	y+	y+	NOUN
ma-80	110	15	ln	ln	PROPN
ma-80	110	16	---------------------.ln=	---------------------.ln=	NOUN
ma-80	111	1	=	=	PROPN
ma-80	111	2	w2	w2	NOUN
ma-80	111	3	y	y	PROPN
ma-80	111	4			PROPN
ma-80	111	5	y	y	NOUN
ma-80	111	6	ln	ln	PRON
ma-80	111	7	y	y	NOUN
ma-80	112	1	ln	ln	PROPN
ma-80	112	2	1	1	NUM
ma-80	112	3	y+	y+	NOUN
ma-80	112	4	ln	ln	NOUN
ma-80	112	5	ln	ln	NOUN
ma-80	112	6	–	–	PUNCT
ma-80	112	7	ln	ln	ADJ
ma-80	112	8	–	–	PUNCT
ma-80	112	9	y	y	PROPN
ma-80	112	10	y	y	PROPN
ma-80	112	11	1	1	NUM
ma-80	112	12	y+	y+	NOUN
ma-80	112	13	ln	ln	PROPN
ma-80	112	14	----------------------ln	----------------------ln	ADJ
ma-80	112	15	---------------------------------ln	---------------------------------ln	NOUN
ma-80	112	16	.=	.=	PUNCT
ma-80	113	1	=	=	PRON
ma-80	113	2	wi	wi	PROPN
ma-80	113	3	y	y	PROPN
ma-80	113	4			PROPN
ma-80	113	5	y	y	NOUN
ma-80	113	6	ln	ln	PROPN
ma-80	113	7	wi	wi	PROPN
ma-80	113	8	1	1	NUM
ma-80	113	9	–	–	PUNCT
ma-80	113	10	y	y	NOUN
ma-80	113	11			ADJ
ma-80	113	12	ln	ln	NOUN
ma-80	113	13	–	–	PUNCT
ma-80	113	14	=	=	ADJ
ma-80	113	15	i	i	NOUN
ma-80	114	1	1	1	NUM
ma-80	114	2	2	2	NUM
ma-80	114	3	3	3	NUM
ma-80	114	4			NOUN
ma-80	114	5			NUM
ma-80	114	6			X
ma-80	114	7			PROPN
ma-80	114	8	w0	w0	VERB
ma-80	114	9	y	y	NOUN
ma-80	114	10			PROPN
ma-80	114	11	1	1	NUM
ma-80	114	12	y+	y+	NOUN
ma-80	114	13	.ln=	.ln=	NOUN
ma-80	114	14	y	y	PROPN
ma-80	114	15	y	y	PROPN
ma-80	114	16	10	10	PROPN
ma-80	114	17	figure	figure	NOUN
ma-80	114	18	4	4	NUM
ma-80	114	19	.	.	PUNCT
ma-80	115	1	graph	graph	NOUN
ma-80	115	2	of	of	ADP
ma-80	115	3	the	the	DET
ma-80	115	4	relative	relative	ADJ
ma-80	115	5	errors	error	NOUN
ma-80	115	6	,	,	PUNCT
ma-80	115	7	over	over	ADP
ma-80	115	8	the	the	DET
ma-80	115	9	interval	interval	NOUN
ma-80	115	10	,	,	PUNCT
ma-80	115	11	in	in	ADP
ma-80	115	12	iterative	iterative	ADJ
ma-80	115	13	approximations	approximation	NOUN
ma-80	115	14	to	to	ADP
ma-80	115	15	.	.	PUNCT
ma-80	116	1	the	the	DET
ma-80	116	2	relative	relative	ADJ
ma-80	116	3	errors	error	NOUN
ma-80	116	4	in	in	ADP
ma-80	116	5	the	the	DET
ma-80	116	6	approximations	approximation	NOUN
ma-80	116	7	for	for	ADP
ma-80	116	8	and	and	CCONJ
ma-80	116	9	are	be	AUX
ma-80	116	10	high	high	ADJ
ma-80	116	11	.	.	PUNCT
ma-80	117	1	1	1	NUM
ma-80	117	2	–	–	PUNCT
ma-80	117	3	e	e	ADV
ma-80	117	4	1	1	NUM
ma-80	117	5			NOUN
ma-80	117	6	w	w	NOUN
ma-80	117	7	y	y	NOUN
ma-80	117	8			PROPN
ma-80	117	9	w2	w2	NOUN
ma-80	117	10	w3	w3	PROPN
ma-80	117	11	y	y	PROPN
ma-80	117	12	wi3	wi3	VERB
ma-80	117	13	y	y	NOUN
ma-80	117	14			PROPN
ma-80	117	15	re	re	ADP
ma-80	117	16	y	y	NOUN
ma-80	117	17			PROPN
ma-80	117	18	w0	w0	VERB
ma-80	117	19	y	y	NOUN
ma-80	117	20			PROPN
ma-80	117	21	w1	w1	NOUN
ma-80	117	22	y	y	NOUN
ma-80	117	23			PROPN
ma-80	117	24	w2	w2	NOUN
ma-80	117	25	y	y	NOUN
ma-80	117	26			PROPN
ma-80	117	27	x	x	PUNCT
ma-80	117	28	y	y	PROPN
ma-80	117	29	ln	ln	PROPN
ma-80	118	1	x	x	PROPN
ma-80	118	2	ln–=	ln–=	PRON
ma-80	118	3	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	NOUN
ma-80	118	4	of	of	ADP
ma-80	118	5	.	.	PUNCT
ma-80	119	1	for	for	ADP
ma-80	119	2	fixed	fix	VERB
ma-80	119	3	,	,	PUNCT
ma-80	119	4	consider	consider	VERB
ma-80	119	5	an	an	DET
ma-80	119	6	initial	initial	ADJ
ma-80	119	7	approximation	approximation	NOUN
ma-80	119	8	of	of	ADP
ma-80	119	9	,	,	PUNCT
ma-80	119	10	with	with	ADP
ma-80	119	11	an	an	DET
ma-80	119	12	error	error	NOUN
ma-80	119	13	of	of	ADP
ma-80	119	14	,	,	PUNCT
ma-80	119	15	which	which	PRON
ma-80	119	16	implies	imply	VERB
ma-80	119	17	and	and	CCONJ
ma-80	119	18	,	,	PUNCT
ma-80	119	19	thus	thus	ADV
ma-80	119	20	,	,	PUNCT
ma-80	119	21	e.g.	e.g.	ADV
ma-80	119	22	[	[	X
ma-80	119	23	17	17	NUM
ma-80	119	24	]	]	PUNCT
ma-80	119	25	,	,	PUNCT
ma-80	119	26	eqn	eqn	NOUN
ma-80	119	27	.	.	PUNCT
ma-80	120	1	11	11	NUM
ma-80	120	2	:	:	PUNCT
ma-80	120	3	(	(	PUNCT
ma-80	120	4	15	15	NUM
ma-80	120	5	)	)	PUNCT
ma-80	120	6	for	for	ADP
ma-80	120	7	the	the	DET
ma-80	120	8	case	case	NOUN
ma-80	120	9	where	where	SCONJ
ma-80	120	10	the	the	DET
ma-80	120	11	error	error	NOUN
ma-80	120	12	is	be	AUX
ma-80	120	13	small	small	ADJ
ma-80	120	14	and	and	CCONJ
ma-80	120	15	,	,	PUNCT
ma-80	120	16	a	a	DET
ma-80	120	17	first	first	ADJ
ma-80	120	18	order	order	NOUN
ma-80	120	19	taylor	taylor	PROPN
ma-80	120	20	series	series	PROPN
ma-80	120	21	for	for	ADP
ma-80	120	22	the	the	DET
ma-80	120	23	logarithm	logarithm	NOUN
ma-80	120	24	function	function	NOUN
ma-80	120	25	yields	yield	NOUN
ma-80	120	26	(	(	PUNCT
ma-80	120	27	16	16	NUM
ma-80	120	28	)	)	PUNCT
ma-80	120	29	and	and	CCONJ
ma-80	120	30	the	the	DET
ma-80	120	31	first	first	ADJ
ma-80	120	32	order	order	NOUN
ma-80	120	33	approximation	approximation	NOUN
ma-80	120	34	(	(	PUNCT
ma-80	120	35	17	17	NUM
ma-80	120	36	)	)	PUNCT
ma-80	120	37	the	the	DET
ma-80	120	38	general	general	ADJ
ma-80	120	39	iteration	iteration	NOUN
ma-80	120	40	formula	formula	NOUN
ma-80	120	41	,	,	PUNCT
ma-80	120	42	e.g.	e.g.	ADV
ma-80	120	43	[	[	X
ma-80	120	44	17	17	NUM
ma-80	120	45	]	]	PUNCT
ma-80	120	46	,	,	PUNCT
ma-80	120	47	eqn	eqn	PROPN
ma-80	120	48	.	.	PROPN
ma-80	121	1	12	12	NUM
ma-80	121	2	(	(	PUNCT
ma-80	121	3	18	18	NUM
ma-80	121	4	)	)	PUNCT
ma-80	121	5	then	then	ADV
ma-80	121	6	follows	follow	VERB
ma-80	121	7	.	.	PUNCT
ma-80	122	1	higher	high	ADJ
ma-80	122	2	order	order	NOUN
ma-80	122	3	iteration	iteration	NOUN
ma-80	122	4	,	,	PUNCT
ma-80	122	5	based	base	VERB
ma-80	122	6	on	on	ADP
ma-80	122	7	a	a	DET
ma-80	122	8	higher	high	ADJ
ma-80	122	9	order	order	NOUN
ma-80	122	10	approximation	approximation	NOUN
ma-80	122	11	for	for	ADP
ma-80	122	12	,	,	PUNCT
ma-80	122	13	is	be	AUX
ma-80	122	14	detailed	detail	VERB
ma-80	122	15	in	in	ADP
ma-80	122	16	[	[	X
ma-80	122	17	10	10	NUM
ma-80	122	18	]	]	PUNCT
ma-80	122	19	.	.	PUNCT
ma-80	123	1	with	with	ADP
ma-80	123	2	a	a	DET
ma-80	123	3	starting	starting	NOUN
ma-80	123	4	value	value	NOUN
ma-80	123	5	,	,	PUNCT
ma-80	123	6	utilized	utilize	VERB
ma-80	123	7	in	in	ADP
ma-80	123	8	fritsch	fritsch	PROPN
ma-80	123	9	et	et	PROPN
ma-80	123	10	al	al	PROPN
ma-80	123	11	.	.	PUNCT
ma-80	124	1	[	[	X
ma-80	124	2	10	10	NUM
ma-80	124	3	]	]	PUNCT
ma-80	124	4	,	,	PUNCT
ma-80	124	5	of	of	ADP
ma-80	124	6	(	(	PUNCT
ma-80	124	7	suitable	suitable	ADJ
ma-80	124	8	for	for	ADP
ma-80	124	9	)	)	PUNCT
ma-80	124	10	it	it	PRON
ma-80	124	11	follows	follow	VERB
ma-80	124	12	that	that	SCONJ
ma-80	124	13	a	a	DET
ma-80	124	14	first	first	ADJ
ma-80	124	15	order	order	NOUN
ma-80	124	16	approximation	approximation	NOUN
ma-80	124	17	is	be	AUX
ma-80	124	18	(	(	PUNCT
ma-80	124	19	19	19	NUM
ma-80	124	20	)	)	PUNCT
ma-80	124	21	the	the	DET
ma-80	124	22	relative	relative	ADJ
ma-80	124	23	error	error	NOUN
ma-80	124	24	in	in	ADP
ma-80	124	25	this	this	DET
ma-80	124	26	approximation	approximation	NOUN
ma-80	124	27	is	be	AUX
ma-80	124	28	shown	show	VERB
ma-80	124	29	in	in	ADP
ma-80	124	30	figure	figure	NOUN
ma-80	124	31	5	5	NUM
ma-80	124	32	and	and	CCONJ
ma-80	124	33	the	the	DET
ma-80	124	34	relative	relative	ADJ
ma-80	124	35	error	error	NOUN
ma-80	124	36	bound	bind	VERB
ma-80	124	37	for	for	ADP
ma-80	124	38	the	the	DET
ma-80	124	39	interval	interval	NOUN
ma-80	124	40	is	be	AUX
ma-80	124	41	.	.	PUNCT
ma-80	125	1	a	a	DET
ma-80	125	2	first	first	ADJ
ma-80	125	3	order	order	NOUN
ma-80	125	4	iteration	iteration	NOUN
ma-80	125	5	,	,	PUNCT
ma-80	125	6	based	base	VERB
ma-80	125	7	on	on	ADP
ma-80	125	8	equation	equation	NOUN
ma-80	125	9	18	18	NUM
ma-80	125	10	,	,	PUNCT
ma-80	125	11	with	with	ADP
ma-80	125	12	,	,	PUNCT
ma-80	125	13	yields	yield	VERB
ma-80	125	14	the	the	DET
ma-80	125	15	approximation	approximation	NOUN
ma-80	125	16	[	[	X
ma-80	125	17	17	17	NUM
ma-80	125	18	]	]	PUNCT
ma-80	125	19	,	,	PUNCT
ma-80	125	20	eqn	eqn	PROPN
ma-80	125	21	.	.	PUNCT
ma-80	126	1	18	18	NUM
ma-80	126	2	:	:	PUNCT
ma-80	126	3	figure	figure	NOUN
ma-80	126	4	5	5	NUM
ma-80	126	5	.	.	PUNCT
ma-80	127	1	graph	graph	NOUN
ma-80	127	2	of	of	ADP
ma-80	127	3	the	the	DET
ma-80	127	4	relative	relative	ADJ
ma-80	127	5	errors	error	NOUN
ma-80	127	6	in	in	ADP
ma-80	127	7	iterative	iterative	ADJ
ma-80	127	8	approximations	approximation	NOUN
ma-80	127	9	to	to	PART
ma-80	127	10	.w	.w	VERB
ma-80	128	1	y	y	PROPN
ma-80	128	2			PROPN
ma-80	128	3	y	y	PROPN
ma-80	128	4	w0	w0	PROPN
ma-80	128	5	y	y	NOUN
ma-80	128	6			PROPN
ma-80	128	7	w2	w2	NOUN
ma-80	128	8	y	y	NOUN
ma-80	128	9			PROPN
ma-80	128	10	w3	w3	PROPN
ma-80	128	11	y	y	NOUN
ma-80	128	12			PROPN
ma-80	128	13	w1	w1	NOUN
ma-80	128	14	y	y	NOUN
ma-80	128	15			PROPN
ma-80	128	16	wi3	wi3	VERB
ma-80	128	17	y	y	NOUN
ma-80	128	18			PROPN
ma-80	128	19	re	re	ADP
ma-80	128	20	y	y	NOUN
ma-80	128	21			PROPN
ma-80	128	22	wf	wf	NOUN
ma-80	128	23	y	y	NOUN
ma-80	128	24			PROPN
ma-80	128	25	wf	wf	NOUN
ma-80	128	26	y	y	NOUN
ma-80	128	27			PROPN
ma-80	129	1	x0	x0	PROPN
ma-80	130	1	y	y	PROPN
ma-80	130	2	x0	x0	PROPN
ma-80	130	3	0	0	PROPN
ma-80	131	1	y	y	PROPN
ma-80	131	2	x0	x0	PROPN
ma-80	131	3	0+	0+	VERB
ma-80	131	4			PROPN
ma-80	132	1	x0	x0	PROPN
ma-80	132	2	0+	0+	VERB
ma-80	132	3	exp=	exp=	PROPN
ma-80	132	4	x0	x0	PROPN
ma-80	132	5	0	0	PROPN
ma-80	132	6	+	+	CCONJ
ma-80	132	7	y	y	PROPN
ma-80	132	8	ln	ln	PRON
ma-80	133	1	x0	x0	PROPN
ma-80	133	2	0+	0+	PROPN
ma-80	133	3			PROPN
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ma-80	133	5	–	–	PUNCT
ma-80	133	6	y	y	NOUN
ma-80	133	7	x0	x0	NUM
ma-80	133	8	-----ln	-----ln	NOUN
ma-80	133	9	1	1	NUM
ma-80	133	10	0	0	NOUN
ma-80	133	11	x0	x0	PROPN
ma-80	133	12	-----+	-----+	PROPN
ma-80	133	13	.ln–=	.ln–=	PUNCT
ma-80	134	1	=	=	PUNCT
ma-80	134	2	0	0	PROPN
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ma-80	134	4	1	1	NUM
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ma-80	134	6	x0	x0	PROPN
ma-80	134	7	0	0	PROPN
ma-80	134	8	+	+	CCONJ
ma-80	134	9	y	y	PROPN
ma-80	134	10	x0	x0	PROPN
ma-80	134	11	-----ln	-----ln	PROPN
ma-80	134	12	0	0	PROPN
ma-80	134	13	x0	x0	PROPN
ma-80	134	14	-----	-----	PROPN
ma-80	134	15	–	–	PUNCT
ma-80	134	16			NUM
ma-80	134	17	0	0	NOUN
ma-80	134	18	x0	x0	PROPN
ma-80	134	19	1	1	NUM
ma-80	134	20	x0	x0	NUM
ma-80	134	21	+	+	CCONJ
ma-80	134	22	-------------y	-------------y	NOUN
ma-80	134	23	x0	x0	PROPN
ma-80	134	24	-----ln	-----ln	NOUN
ma-80	134	25	x0	x0	PROPN
ma-80	134	26	–	–	PUNCT
ma-80	134	27			ADJ
ma-80	134	28	x1	x1	NUM
ma-80	134	29	x0	x0	PROPN
ma-80	134	30	0	0	PROPN
ma-80	134	31	+	+	CCONJ
ma-80	134	32	x0	x0	PROPN
ma-80	134	33	1	1	NUM
ma-80	134	34	x0	x0	PROPN
ma-80	134	35	+	+	CCONJ
ma-80	134	36	-------------1	-------------1	PROPN
ma-80	135	1	y	y	VERB
ma-80	135	2	x0	x0	PROPN
ma-80	135	3	-----ln+	-----ln+	X
ma-80	135	4	.=	.=	PROPN
ma-80	135	5	xi	xi	ADP
ma-80	136	1	1	1	NUM
ma-80	136	2	+	+	NUM
ma-80	136	3	xi	xi	PART
ma-80	136	4	1	1	NUM
ma-80	136	5	xi+	xi+	PROPN
ma-80	136	6	------------1	------------1	PROPN
ma-80	136	7	y	y	INTJ
ma-80	136	8	xi	xi	INTJ
ma-80	136	9	----ln+	----ln+	PROPN
ma-80	136	10	=	=	NUM
ma-80	136	11	1	1	NUM
ma-80	136	12	0	0	NOUN
ma-80	136	13	x0+	x0+	PUNCT
ma-80	137	1	ln	ln	NOUN
ma-80	137	2	x0	x0	PROPN
ma-80	137	3	y	y	PROPN
ma-80	137	4	ln=	ln=	NOUN
ma-80	138	1	y	y	PROPN
ma-80	138	2	e	e	NOUN
ma-80	138	3	wf	wf	PROPN
ma-80	138	4	y	y	NOUN
ma-80	138	5			PROPN
ma-80	138	6	y	y	NOUN
ma-80	138	7	ln	ln	NOUN
ma-80	138	8	1	1	NUM
ma-80	138	9	y	y	NOUN
ma-80	138	10	ln+	ln+	PROPN
ma-80	138	11	---------------------1	---------------------1	NOUN
ma-80	139	1	y	y	INTJ
ma-80	139	2	y	y	VERB
ma-80	139	3	ln	ln	PROPN
ma-80	139	4	-------------ln+	-------------ln+	PUNCT
ma-80	139	5	.=	.=	PROPN
ma-80	139	6	e	e	PROPN
ma-80	139	7			X
ma-80	139	8			PROPN
ma-80	140	1	1.47	1.47	NUM
ma-80	140	2	10	10	NUM
ma-80	140	3	2–	2–	NUM
ma-80	140	4	x0	x0	PROPN
ma-80	140	5	y	y	NOUN
ma-80	140	6			PROPN
ma-80	140	7	1	1	NUM
ma-80	140	8	y	y	PROPN
ma-80	140	9	1	1	NUM
ma-80	140	10	0.5	0.5	NUM
ma-80	140	11	1	1	NUM
ma-80	140	12	y+	y+	NOUN
ma-80	140	13	ln+	ln+	PROPN
ma-80	140	14	---------------------------------------+ln=	---------------------------------------+ln=	PROPN
ma-80	140	15	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	PROPN
ma-80	140	16	(	(	PUNCT
ma-80	140	17	20	20	NUM
ma-80	140	18	)	)	PUNCT
ma-80	140	19	the	the	DET
ma-80	140	20	relative	relative	ADJ
ma-80	140	21	error	error	NOUN
ma-80	140	22	in	in	ADP
ma-80	140	23	this	this	DET
ma-80	140	24	approximation	approximation	NOUN
ma-80	140	25	is	be	AUX
ma-80	140	26	shown	show	VERB
ma-80	140	27	in	in	ADP
ma-80	140	28	figure	figure	NOUN
ma-80	140	29	4	4	NUM
ma-80	140	30	and	and	CCONJ
ma-80	140	31	figure	figure	VERB
ma-80	140	32	5	5	NUM
ma-80	140	33	.	.	PUNCT
ma-80	141	1	the	the	DET
ma-80	141	2	relative	relative	ADJ
ma-80	141	3	error	error	NOUN
ma-80	141	4	bound	bind	VERB
ma-80	141	5	,	,	PUNCT
ma-80	141	6	over	over	ADP
ma-80	141	7	the	the	DET
ma-80	141	8	interval	interval	NOUN
ma-80	141	9	,	,	PUNCT
ma-80	141	10	is	be	AUX
ma-80	141	11	.	.	PUNCT
ma-80	142	1	2.3	2.3	NUM
ma-80	142	2	.	.	PUNCT
ma-80	142	3	approximations	approximation	NOUN
ma-80	142	4	via	via	ADP
ma-80	142	5	newton	newton	PROPN
ma-80	142	6	-	-	PUNCT
ma-80	142	7	raphson	raphson	PROPN
ma-80	142	8	iteration	iteration	NOUN
ma-80	142	9	.	.	PUNCT
ma-80	143	1	consistent	consistent	ADJ
ma-80	143	2	with	with	ADP
ma-80	143	3	the	the	DET
ma-80	143	4	illustration	illustration	NOUN
ma-80	143	5	shown	show	VERB
ma-80	143	6	in	in	ADP
ma-80	143	7	figure	figure	NOUN
ma-80	143	8	6	6	NUM
ma-80	143	9	,	,	PUNCT
ma-80	143	10	a	a	DET
ma-80	143	11	direct	direct	PROPN
ma-80	143	12	newton	newton	PROPN
ma-80	143	13	-	-	PUNCT
ma-80	143	14	raphson	raphson	NOUN
ma-80	143	15	method	method	NOUN
ma-80	143	16	for	for	ADP
ma-80	143	17	solving	solve	VERB
ma-80	143	18	for	for	ADP
ma-80	143	19	,	,	PUNCT
ma-80	143	20	in	in	ADP
ma-80	143	21	the	the	DET
ma-80	143	22	equation	equation	NOUN
ma-80	143	23	,	,	PUNCT
ma-80	143	24	is	be	AUX
ma-80	143	25	:	:	PUNCT
ma-80	143	26	(	(	PUNCT
ma-80	143	27	21	21	NUM
ma-80	143	28	)	)	PUNCT
ma-80	143	29	a	a	DET
ma-80	143	30	first	first	ADJ
ma-80	143	31	iteration	iteration	NOUN
ma-80	143	32	,	,	PUNCT
ma-80	143	33	based	base	VERB
ma-80	143	34	on	on	ADP
ma-80	143	35	a	a	DET
ma-80	143	36	known	know	VERB
ma-80	143	37	approximating	approximate	VERB
ma-80	143	38	function	function	NOUN
ma-80	143	39	for	for	ADP
ma-80	143	40	,	,	PUNCT
ma-80	143	41	is	be	AUX
ma-80	143	42	,	,	PUNCT
ma-80	143	43	e.g.	e.g.	ADV
ma-80	143	44	[	[	X
ma-80	143	45	17	17	NUM
ma-80	143	46	]	]	PUNCT
ma-80	143	47	,	,	PUNCT
ma-80	143	48	eqn	eqn	PROPN
ma-80	143	49	.	.	PUNCT
ma-80	144	1	15	15	NUM
ma-80	144	2	:	:	PUNCT
ma-80	144	3	(	(	PUNCT
ma-80	144	4	22	22	X
ma-80	144	5	)	)	PUNCT
ma-80	144	6	halley	halley	PROPN
ma-80	144	7	’s	’s	PART
ma-80	144	8	method	method	NOUN
ma-80	144	9	can	can	AUX
ma-80	144	10	similarly	similarly	ADV
ma-80	144	11	be	be	AUX
ma-80	144	12	utilized	utilize	VERB
ma-80	144	13	,	,	PUNCT
ma-80	144	14	e.g.	e.g.	ADV
ma-80	144	15	[	[	X
ma-80	144	16	26	26	NUM
ma-80	144	17	]	]	PUNCT
ma-80	144	18	.	.	PUNCT
ma-80	145	1	with	with	ADP
ma-80	145	2	an	an	DET
ma-80	145	3	initial	initial	ADJ
ma-80	145	4	value	value	NOUN
ma-80	145	5	of	of	ADP
ma-80	145	6	,	,	PUNCT
ma-80	145	7	the	the	DET
ma-80	145	8	first	first	ADJ
ma-80	145	9	and	and	CCONJ
ma-80	145	10	second	second	ADJ
ma-80	145	11	order	order	NOUN
ma-80	145	12	approximations	approximation	NOUN
ma-80	145	13	,	,	PUNCT
ma-80	145	14	respectively	respectively	ADV
ma-80	145	15	,	,	PUNCT
ma-80	145	16	are	be	AUX
ma-80	145	17	:	:	PUNCT
ma-80	145	18	(	(	PUNCT
ma-80	145	19	23	23	NUM
ma-80	145	20	)	)	PUNCT
ma-80	145	21	(	(	PUNCT
ma-80	145	22	24	24	NUM
ma-80	145	23	)	)	PUNCT
ma-80	145	24	2.3.1	2.3.1	NUM
ma-80	145	25	.	.	PUNCT
ma-80	145	26	results	result	NOUN
ma-80	145	27	.	.	PUNCT
ma-80	146	1	graphs	graph	NOUN
ma-80	146	2	of	of	ADP
ma-80	146	3	the	the	DET
ma-80	146	4	variation	variation	NOUN
ma-80	146	5	of	of	ADP
ma-80	146	6	the	the	DET
ma-80	146	7	relative	relative	ADJ
ma-80	146	8	error	error	NOUN
ma-80	146	9	,	,	PUNCT
ma-80	146	10	with	with	ADP
ma-80	146	11	iteration	iteration	NOUN
ma-80	146	12	level	level	NOUN
ma-80	146	13	,	,	PUNCT
ma-80	146	14	are	be	AUX
ma-80	146	15	shown	show	VERB
ma-80	146	16	in	in	ADP
ma-80	146	17	figure	figure	NOUN
ma-80	146	18	7	7	NUM
ma-80	146	19	and	and	CCONJ
ma-80	146	20	figure	figure	VERB
ma-80	146	21	8	8	NUM
ma-80	146	22	for	for	ADP
ma-80	146	23	the	the	DET
ma-80	146	24	case	case	NOUN
ma-80	146	25	of	of	ADP
ma-80	146	26	an	an	DET
ma-80	146	27	initial	initial	ADJ
ma-80	146	28	approximation	approximation	NOUN
ma-80	146	29	of	of	ADP
ma-80	146	30	.	.	PUNCT
ma-80	147	1	wi3	wi3	VERB
ma-80	147	2	y	y	NOUN
ma-80	147	3			PROPN
ma-80	147	4	1	1	NUM
ma-80	147	5	y	y	PROPN
ma-80	147	6	1	1	NUM
ma-80	147	7	0.5	0.5	NUM
ma-80	147	8	1	1	NUM
ma-80	147	9	y+	y+	NOUN
ma-80	147	10	ln+	ln+	PROPN
ma-80	147	11	---------------------------------------+ln	---------------------------------------+ln	PROPN
ma-80	147	12	1	1	NUM
ma-80	147	13	1	1	NUM
ma-80	147	14	y	y	PROPN
ma-80	147	15	1	1	NUM
ma-80	147	16	0.5	0.5	NUM
ma-80	147	17	1	1	NUM
ma-80	147	18	y+	y+	NOUN
ma-80	147	19	ln+	ln+	PROPN
ma-80	147	20	---------------------------------------+ln+	---------------------------------------+ln+	PUNCT
ma-80	147	21	--------------------------------------------------------------------1	--------------------------------------------------------------------1	PROPN
ma-80	147	22	y	y	PROPN
ma-80	147	23	1	1	NUM
ma-80	147	24	y	y	PROPN
ma-80	147	25	1	1	NUM
ma-80	147	26	0.5	0.5	NUM
ma-80	147	27	1	1	NUM
ma-80	147	28	y+	y+	NOUN
ma-80	147	29	ln+	ln+	PROPN
ma-80	147	30	---------------------------------------+ln	---------------------------------------+ln	PROPN
ma-80	147	31	------------------------------------------------------------ln+	------------------------------------------------------------ln+	PUNCT
ma-80	147	32	.=	.=	NOUN
ma-80	147	33	0	0	NUM
ma-80	147	34			NOUN
ma-80	147	35			NOUN
ma-80	147	36	2.16	2.16	NUM
ma-80	147	37	10	10	NUM
ma-80	148	1	4–	4–	NOUN
ma-80	148	2	x	x	PUNCT
ma-80	148	3	y	y	PROPN
ma-80	148	4	xe	xe	PROPN
ma-80	148	5	x	x	PROPN
ma-80	148	6	=	=	PRON
ma-80	148	7	xi	xi	X
ma-80	148	8	xi	xi	PROPN
ma-80	148	9	1	1	NUM
ma-80	148	10	–	–	PUNCT
ma-80	148	11	xi	xi	ADP
ma-80	148	12	1	1	NUM
ma-80	148	13	–	–	PUNCT
ma-80	148	14	e	e	NOUN
ma-80	148	15	xi	xi	ADP
ma-80	148	16	1	1	NUM
ma-80	148	17	–	–	PUNCT
ma-80	148	18	y	y	NOUN
ma-80	148	19	–	–	PUNCT
ma-80	148	20	e	e	NOUN
ma-80	148	21	xi	xi	ADP
ma-80	148	22	1	1	NUM
ma-80	148	23	–	–	PUNCT
ma-80	148	24	xi	xi	ADP
ma-80	148	25	1	1	NUM
ma-80	148	26	–	–	PUNCT
ma-80	148	27	e	e	NOUN
ma-80	148	28	xi	xi	ADP
ma-80	148	29	1–+	1–+	NUM
ma-80	148	30	-----------------------------------------	-----------------------------------------	PUNCT
ma-80	148	31	–	–	PUNCT
ma-80	148	32	xi	xi	ADP
ma-80	148	33	1	1	NUM
ma-80	148	34	–	–	PUNCT
ma-80	148	35	xi	xi	ADP
ma-80	148	36	1	1	NUM
ma-80	148	37	–	–	PUNCT
ma-80	148	38	ye	ye	NOUN
ma-80	148	39	xi	xi	ADP
ma-80	148	40	1	1	NUM
ma-80	148	41	–	–	PUNCT
ma-80	148	42	–	–	PUNCT
ma-80	148	43	–	–	PUNCT
ma-80	148	44	1	1	NUM
ma-80	148	45	xi	xi	PART
ma-80	148	46	1–+	1–+	NUM
ma-80	148	47	----------------------------------.–=	----------------------------------.–=	NOUN
ma-80	148	48	=	=	SYM
ma-80	149	1	g	g	PROPN
ma-80	149	2	w	w	PROPN
ma-80	149	3	w	w	PROPN
ma-80	149	4	y	y	NOUN
ma-80	149	5			PROPN
ma-80	149	6	g	g	NOUN
ma-80	149	7	y	y	NOUN
ma-80	150	1			PROPN
ma-80	150	2	g	g	NOUN
ma-80	150	3	y	y	NOUN
ma-80	150	4			PROPN
ma-80	150	5	g	g	NOUN
ma-80	150	6	y	y	NOUN
ma-80	151	1			ADJ
ma-80	151	2	exp	exp	VERB
ma-80	151	3	y	y	PROPN
ma-80	151	4	–	–	PUNCT
ma-80	151	5	g	g	ADP
ma-80	151	6	y	y	NOUN
ma-80	151	7			ADJ
ma-80	151	8	exp	exp	VERB
ma-80	151	9	g	g	PRON
ma-80	151	10	y	y	NOUN
ma-80	152	1			PROPN
ma-80	152	2	g	g	NOUN
ma-80	152	3	y	y	NOUN
ma-80	152	4			ADP
ma-80	153	1	exp+	exp+	PROPN
ma-80	153	2	--------------------------------------------------------------------–	--------------------------------------------------------------------–	PROPN
ma-80	153	3	g	g	NOUN
ma-80	153	4	y	y	NOUN
ma-80	154	1			PROPN
ma-80	154	2	g	g	NOUN
ma-80	154	3	y	y	NOUN
ma-80	155	1			PROPN
ma-80	155	2	y	y	PROPN
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ma-80	155	4	–	–	PUNCT
ma-80	155	5	y	y	NOUN
ma-80	155	6			ADJ
ma-80	155	7	exp	exp	NOUN
ma-80	155	8	–	–	PUNCT
ma-80	155	9	1	1	NUM
ma-80	155	10	g	g	NOUN
ma-80	155	11	y	y	NOUN
ma-80	155	12	+	+	PUNCT
ma-80	155	13	------------------------------------------------.–=	------------------------------------------------.–=	NOUN
ma-80	155	14	figure	figure	NOUN
ma-80	155	15	6	6	NUM
ma-80	155	16	.	.	PUNCT
ma-80	156	1	newton	newton	PROPN
ma-80	156	2	-	-	PUNCT
ma-80	156	3	raphson	raphson	PROPN
ma-80	156	4	iteration	iteration	NOUN
ma-80	156	5	for	for	ADP
ma-80	156	6	determining	determine	VERB
ma-80	156	7	an	an	DET
ma-80	156	8	approximation	approximation	NOUN
ma-80	156	9	to	to	ADP
ma-80	156	10	the	the	DET
ma-80	156	11	solution	solution	NOUN
ma-80	156	12	,	,	PUNCT
ma-80	156	13	denoted	denote	VERB
ma-80	156	14	,	,	PUNCT
ma-80	156	15	of	of	ADP
ma-80	156	16	for	for	ADP
ma-80	156	17	fixed	fix	VERB
ma-80	156	18	and	and	CCONJ
ma-80	156	19	based	base	VERB
ma-80	156	20	on	on	ADP
ma-80	156	21	an	an	DET
ma-80	156	22	initial	initial	ADJ
ma-80	156	23	value	value	NOUN
ma-80	156	24	of	of	ADP
ma-80	156	25	.	.	PUNCT
ma-80	157	1	xo	xo	PROPN
ma-80	157	2	y	y	PROPN
ma-80	157	3	x	x	PROPN
ma-80	157	4	x	x	PROPN
ma-80	158	1	exp=	exp=	PROPN
ma-80	158	2	y	y	NOUN
ma-80	158	3	x0	x0	PROPN
ma-80	158	4	x	x	PROPN
ma-80	159	1	xo	xo	PROPN
ma-80	159	2	h	h	PROPN
ma-80	159	3	x0	x0	PROPN
ma-80	160	1			PUNCT
ma-80	161	1	x0x1	x0x1	PUNCT
ma-80	162	1	h	h	NOUN
ma-80	162	2	x	x	PUNCT
ma-80	163	1			PUNCT
ma-80	163	2	xe	xe	PROPN
ma-80	163	3	x	x	SYM
ma-80	163	4	y–=	y–=	PROPN
ma-80	164	1	x2	x2	INTJ
ma-80	164	2	h	h	NOUN
ma-80	164	3	x1	x1	PUNCT
ma-80	165	1			PUNCT
ma-80	165	2	x0	x0	NOUN
ma-80	165	3	1	1	NUM
ma-80	165	4	y+	y+	NOUN
ma-80	165	5	ln=	ln=	NOUN
ma-80	165	6	wn1	wn1	VERB
ma-80	165	7	y	y	NOUN
ma-80	165	8			PROPN
ma-80	165	9	1	1	NUM
ma-80	165	10	y+	y+	NOUN
ma-80	165	11	ln	ln	PROPN
ma-80	165	12	1	1	NUM
ma-80	165	13	y+	y+	NOUN
ma-80	165	14	ln	ln	PROPN
ma-80	165	15	y	y	PROPN
ma-80	165	16	1	1	NUM
ma-80	165	17	y+	y+	NOUN
ma-80	165	18			PROPN
ma-80	165	19	–	–	PUNCT
ma-80	165	20	1	1	NUM
ma-80	165	21	1	1	NUM
ma-80	165	22	y+	y+	NOUN
ma-80	165	23	ln+	ln+	PROPN
ma-80	166	1	----------------------------------------------------	----------------------------------------------------	PROPN
ma-80	166	2	–	–	PUNCT
ma-80	166	3	=	=	NOUN
ma-80	166	4	wn2	wn2	VERB
ma-80	166	5	y	y	NOUN
ma-80	166	6			PROPN
ma-80	166	7	1	1	NUM
ma-80	166	8	y+	y+	NOUN
ma-80	166	9	ln	ln	PROPN
ma-80	166	10	1	1	NUM
ma-80	166	11	y+	y+	NOUN
ma-80	166	12	ln	ln	PROPN
ma-80	166	13	y	y	PROPN
ma-80	166	14	1	1	NUM
ma-80	166	15	y+	y+	NOUN
ma-80	166	16			PROPN
ma-80	166	17	–	–	PUNCT
ma-80	166	18	1	1	NUM
ma-80	166	19	1	1	NUM
ma-80	166	20	y+	y+	NOUN
ma-80	166	21	ln+	ln+	PROPN
ma-80	167	1	----------------------------------------------------	----------------------------------------------------	PUNCT
ma-80	167	2	–	–	PUNCT
ma-80	167	3	–	–	PUNCT
ma-80	167	4	=	=	SYM
ma-80	167	5	1	1	NUM
ma-80	167	6	y+	y+	NOUN
ma-80	167	7	ln	ln	PROPN
ma-80	167	8	1	1	NUM
ma-80	167	9	y+	y+	NOUN
ma-80	167	10	ln	ln	PROPN
ma-80	167	11	y	y	PROPN
ma-80	167	12	1	1	NUM
ma-80	167	13	y+	y+	NOUN
ma-80	167	14			PROPN
ma-80	167	15	–	–	PUNCT
ma-80	167	16	1	1	NUM
ma-80	167	17	1	1	NUM
ma-80	167	18	y+	y+	NOUN
ma-80	167	19	ln+	ln+	PROPN
ma-80	168	1	----------------------------------------------------	----------------------------------------------------	PROPN
ma-80	168	2	–	–	PUNCT
ma-80	168	3	y	y	PROPN
ma-80	168	4	1	1	NUM
ma-80	168	5	y+	y+	NUM
ma-80	168	6	-----------1	-----------1	PROPN
ma-80	168	7	y+	y+	NOUN
ma-80	168	8	ln	ln	PROPN
ma-80	168	9	y	y	PROPN
ma-80	168	10	1	1	NUM
ma-80	168	11	y+	y+	NOUN
ma-80	168	12			PROPN
ma-80	168	13	–	–	PUNCT
ma-80	168	14	1	1	NUM
ma-80	168	15	1	1	NUM
ma-80	168	16	y+	y+	NOUN
ma-80	168	17	ln+	ln+	PROPN
ma-80	169	1	----------------------------------------------------exp	----------------------------------------------------exp	PROPN
ma-80	169	2	–	–	PUNCT
ma-80	169	3	1	1	NUM
ma-80	169	4	1	1	NUM
ma-80	169	5	y+	y+	NOUN
ma-80	169	6	ln	ln	PROPN
ma-80	169	7	1	1	NUM
ma-80	169	8	y+	y+	NOUN
ma-80	170	1	ln	ln	PROPN
ma-80	170	2	y	y	PROPN
ma-80	170	3	1	1	NUM
ma-80	170	4	y+	y+	NOUN
ma-80	170	5			PROPN
ma-80	170	6	–	–	PUNCT
ma-80	170	7	1	1	NUM
ma-80	170	8	1	1	NUM
ma-80	170	9	y+	y+	NOUN
ma-80	170	10	ln+	ln+	PROPN
ma-80	170	11	----------------------------------------------------–+	----------------------------------------------------–+	PROPN
ma-80	170	12	--------------------------------------------------------------------------------------------------------------------------------------------------------------------------	--------------------------------------------------------------------------------------------------------------------------------------------------------------------------	PROPN
ma-80	170	13	.	.	PUNCT
ma-80	171	1	x0	x0	PROPN
ma-80	171	2	1	1	NUM
ma-80	171	3	y+	y+	NOUN
ma-80	171	4	ln=	ln=	PUNCT
ma-80	172	1	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	PROPN
ma-80	172	2	note	note	NOUN
ma-80	172	3	,	,	PUNCT
ma-80	172	4	for	for	ADP
ma-80	172	5	higher	high	ADJ
ma-80	172	6	order	order	NOUN
ma-80	172	7	iteration	iteration	NOUN
ma-80	172	8	,	,	PUNCT
ma-80	172	9	the	the	DET
ma-80	172	10	relative	relative	ADJ
ma-80	172	11	error	error	NOUN
ma-80	172	12	increases	increase	NOUN
ma-80	172	13	,	,	PUNCT
ma-80	172	14	from	from	ADP
ma-80	172	15	an	an	DET
ma-80	172	16	increasingly	increasingly	ADV
ma-80	172	17	low	low	ADJ
ma-80	172	18	level	level	NOUN
ma-80	172	19	,	,	PUNCT
ma-80	172	20	as	as	ADP
ma-80	172	21	increases	increase	NOUN
ma-80	172	22	.	.	PUNCT
ma-80	173	1	3	3	X
ma-80	173	2	.	.	X
ma-80	173	3	geometric	geometric	ADJ
ma-80	173	4	basis	basis	NOUN
ma-80	173	5	for	for	ADP
ma-80	173	6	iterative	iterative	ADJ
ma-80	173	7	approximations	approximation	NOUN
ma-80	173	8	to	to	ADP
ma-80	173	9	lambert	lambert	PROPN
ma-80	173	10	w	w	PROPN
ma-80	173	11	function	function	PROPN
ma-80	173	12	3.1	3.1	NUM
ma-80	173	13	.	.	PUNCT
ma-80	174	1	geometric	geometric	ADJ
ma-80	174	2	basis	basis	NOUN
ma-80	174	3	.	.	PUNCT
ma-80	175	1	to	to	PART
ma-80	175	2	establish	establish	VERB
ma-80	175	3	a	a	DET
ma-80	175	4	systematic	systematic	ADJ
ma-80	175	5	,	,	PUNCT
ma-80	175	6	geometrically	geometrically	ADV
ma-80	175	7	based	base	VERB
ma-80	175	8	,	,	PUNCT
ma-80	175	9	approach	approach	NOUN
ma-80	175	10	for	for	ADP
ma-80	175	11	establishing	establish	VERB
ma-80	175	12	approximations	approximation	NOUN
ma-80	175	13	to	to	ADP
ma-80	175	14	the	the	DET
ma-80	175	15	lambert	lambert	PROPN
ma-80	175	16	w	w	PROPN
ma-80	175	17	function	function	NOUN
ma-80	175	18	of	of	ADP
ma-80	175	19	arbitrarily	arbitrarily	ADV
ma-80	175	20	high	high	ADJ
ma-80	175	21	accuracy	accuracy	NOUN
ma-80	175	22	,	,	PUNCT
ma-80	175	23	consider	consider	VERB
ma-80	175	24	a	a	DET
ma-80	175	25	set	set	ADJ
ma-80	175	26	value	value	NOUN
ma-80	175	27	of	of	ADP
ma-80	175	28	.	.	PUNCT
ma-80	176	1	the	the	DET
ma-80	176	2	lambert	lambert	PROPN
ma-80	176	3	w	w	PROPN
ma-80	176	4	function	function	NOUN
ma-80	176	5	associated	associate	VERB
ma-80	176	6	with	with	ADP
ma-80	176	7	,	,	PUNCT
ma-80	176	8	denoted	denote	VERB
ma-80	176	9	,	,	PUNCT
ma-80	176	10	is	be	AUX
ma-80	176	11	such	such	ADJ
ma-80	176	12	that	that	PRON
ma-80	176	13	and	and	CCONJ
ma-80	176	14	is	be	AUX
ma-80	176	15	the	the	DET
ma-80	176	16	point	point	NOUN
ma-80	176	17	defined	define	VERB
ma-80	176	18	by	by	ADP
ma-80	176	19	the	the	DET
ma-80	176	20	intersection	intersection	NOUN
ma-80	176	21	of	of	ADP
ma-80	176	22	the	the	DET
ma-80	176	23	two	two	NUM
ma-80	176	24	curves	curve	NOUN
ma-80	176	25	and	and	CCONJ
ma-80	176	26	as	as	SCONJ
ma-80	176	27	illustrated	illustrate	VERB
ma-80	176	28	in	in	ADP
ma-80	176	29	figure	figure	NOUN
ma-80	176	30	9	9	NUM
ma-80	176	31	for	for	ADP
ma-80	176	32	the	the	DET
ma-80	176	33	case	case	NOUN
ma-80	176	34	of	of	ADP
ma-80	176	35	.	.	PUNCT
ma-80	177	1	the	the	DET
ma-80	177	2	geometry	geometry	NOUN
ma-80	177	3	associated	associate	VERB
ma-80	177	4	with	with	ADP
ma-80	177	5	this	this	DET
ma-80	177	6	intersection	intersection	NOUN
ma-80	177	7	of	of	ADP
ma-80	177	8	the	the	DET
ma-80	177	9	two	two	NUM
ma-80	177	10	curves	curve	NOUN
ma-80	177	11	is	be	AUX
ma-80	177	12	the	the	DET
ma-80	177	13	basis	basis	NOUN
ma-80	177	14	for	for	ADP
ma-80	177	15	an	an	DET
ma-80	177	16	initial	initial	ADJ
ma-80	177	17	approximation	approximation	NOUN
ma-80	177	18	and	and	CCONJ
ma-80	177	19	for	for	ADP
ma-80	177	20	the	the	DET
ma-80	177	21	iterative	iterative	ADJ
ma-80	177	22	approximations	approximation	NOUN
ma-80	177	23	detailed	detail	VERB
ma-80	177	24	in	in	ADP
ma-80	177	25	the	the	DET
ma-80	177	26	following	follow	VERB
ma-80	177	27	theorem	theorem	PROPN
ma-80	177	28	.	.	PUNCT
ma-80	177	29	theorem	theorem	PROPN
ma-80	177	30	3.1	3.1	NUM
ma-80	177	31	.	.	PUNCT
ma-80	177	32	iterative	iterative	NOUN
ma-80	177	33	approximations	approximation	NOUN
ma-80	177	34	for	for	ADP
ma-80	177	35	lambert	lambert	PROPN
ma-80	177	36	w	w	PROPN
ma-80	177	37	function	function	PROPN
ma-80	177	38	.	.	PUNCT
ma-80	178	1	for	for	ADP
ma-80	178	2	fixed	fix	VERB
ma-80	178	3	,	,	PUNCT
ma-80	178	4	,	,	PUNCT
ma-80	178	5	approximations	approximation	NOUN
ma-80	178	6	to	to	ADP
ma-80	178	7	the	the	DET
ma-80	178	8	lambert	lambert	PROPN
ma-80	178	9	w	w	PROPN
ma-80	178	10	function	function	NOUN
ma-80	178	11	can	can	AUX
ma-80	178	12	be	be	AUX
ma-80	178	13	iteratively	iteratively	ADV
ma-80	178	14	defined	define	VERB
ma-80	178	15	according	accord	VERB
ma-80	178	16	to	to	ADP
ma-80	178	17	(	(	PUNCT
ma-80	178	18	25	25	NUM
ma-80	178	19	)	)	PUNCT
ma-80	178	20	y	y	PRON
ma-80	178	21	figure	figure	NOUN
ma-80	178	22	7	7	NUM
ma-80	178	23	.	.	PUNCT
ma-80	179	1	graph	graph	NOUN
ma-80	179	2	of	of	ADP
ma-80	179	3	the	the	DET
ma-80	179	4	relative	relative	ADJ
ma-80	179	5	errors	error	NOUN
ma-80	179	6	,	,	PUNCT
ma-80	179	7	in	in	ADP
ma-80	179	8	the	the	DET
ma-80	179	9	zero	zero	NUM
ma-80	179	10	to	to	ADP
ma-80	179	11	fourth	fourth	ADJ
ma-80	179	12	order	order	NOUN
ma-80	179	13	iterative	iterative	NOUN
ma-80	179	14	approximations	approximation	NOUN
ma-80	179	15	to	to	ADP
ma-80	179	16	,	,	PUNCT
ma-80	179	17	based	base	VERB
ma-80	179	18	on	on	ADP
ma-80	179	19	newton	newton	PROPN
ma-80	179	20	-	-	PUNCT
ma-80	179	21	raphson	raphson	PROPN
ma-80	179	22	iteration	iteration	NOUN
ma-80	179	23	with	with	ADP
ma-80	179	24	an	an	DET
ma-80	179	25	initial	initial	ADJ
ma-80	179	26	approximation	approximation	NOUN
ma-80	179	27	of	of	ADP
ma-80	179	28	.	.	PUNCT
ma-80	180	1	w	w	PRON
ma-80	180	2	y	y	PROPN
ma-80	180	3			PROPN
ma-80	180	4	wn0	wn0	X
ma-80	180	5	y	y	NOUN
ma-80	180	6			PROPN
ma-80	180	7	1	1	NUM
ma-80	180	8	y+	y+	NOUN
ma-80	180	9	ln=	ln=	NOUN
ma-80	181	1	y	y	PROPN
ma-80	181	2	wn1	wn1	VERB
ma-80	181	3	y	y	NOUN
ma-80	181	4			PROPN
ma-80	181	5	re	re	ADP
ma-80	181	6	y	y	PROPN
ma-80	181	7			PROPN
ma-80	181	8	wn2	wn2	VERB
ma-80	181	9	y	y	NOUN
ma-80	181	10			PROPN
ma-80	181	11	wn4	wn4	PROPN
ma-80	182	1	y	y	NOUN
ma-80	182	2			PUNCT
ma-80	182	3	wn3	wn3	NOUN
ma-80	182	4	y	y	PROPN
ma-80	182	5			PROPN
ma-80	182	6	wn0	wn0	X
ma-80	182	7	y	y	NOUN
ma-80	182	8			PROPN
ma-80	182	9	figure	figure	NOUN
ma-80	182	10	8	8	NUM
ma-80	182	11	.	.	PUNCT
ma-80	183	1	graph	graph	NOUN
ma-80	183	2	of	of	ADP
ma-80	183	3	the	the	DET
ma-80	183	4	relative	relative	ADJ
ma-80	183	5	errors	error	NOUN
ma-80	183	6	,	,	PUNCT
ma-80	183	7	in	in	ADP
ma-80	183	8	the	the	DET
ma-80	183	9	zero	zero	NUM
ma-80	183	10	to	to	ADP
ma-80	183	11	fifth	fifth	ADJ
ma-80	183	12	order	order	NOUN
ma-80	183	13	iterative	iterative	NOUN
ma-80	183	14	approximations	approximation	NOUN
ma-80	183	15	to	to	ADP
ma-80	183	16	,	,	PUNCT
ma-80	183	17	based	base	VERB
ma-80	183	18	on	on	ADP
ma-80	183	19	newton	newton	PROPN
ma-80	183	20	-	-	PUNCT
ma-80	183	21	raphson	raphson	PROPN
ma-80	183	22	iteration	iteration	NOUN
ma-80	183	23	with	with	ADP
ma-80	183	24	an	an	DET
ma-80	183	25	initial	initial	ADJ
ma-80	183	26	approximation	approximation	NOUN
ma-80	183	27	of	of	ADP
ma-80	183	28	.	.	PUNCT
ma-80	184	1	w	w	PRON
ma-80	184	2	y	y	PROPN
ma-80	184	3			PROPN
ma-80	184	4	wn0	wn0	X
ma-80	184	5	y	y	NOUN
ma-80	184	6			PROPN
ma-80	184	7	1	1	NUM
ma-80	184	8	y+	y+	NOUN
ma-80	184	9	ln=	ln=	NOUN
ma-80	185	1	y	y	PROPN
ma-80	185	2	wn0	wn0	PROPN
ma-80	186	1	y	y	PROPN
ma-80	186	2			PROPN
ma-80	186	3	re	re	ADP
ma-80	186	4	y	y	NOUN
ma-80	186	5			PUNCT
ma-80	186	6	wn3	wn3	NOUN
ma-80	186	7	y	y	NOUN
ma-80	187	1			PROPN
ma-80	187	2	wn4	wn4	PROPN
ma-80	188	1	y	y	NOUN
ma-80	188	2			PROPN
ma-80	188	3	wn5	wn5	NOUN
ma-80	188	4	y	y	NOUN
ma-80	188	5			PROPN
ma-80	189	1	y	y	PROPN
ma-80	189	2	y	y	PROPN
ma-80	189	3	xo	xo	PROPN
ma-80	189	4	xo	xo	PROPN
ma-80	189	5	ye	ye	PROPN
ma-80	189	6	xo	xo	PROPN
ma-80	189	7	–	–	PUNCT
ma-80	190	1	=	=	PUNCT
ma-80	190	2	x	x	SYM
ma-80	190	3	ye	ye	NUM
ma-80	190	4	x	x	NOUN
ma-80	190	5	–	–	PUNCT
ma-80	190	6	y	y	NOUN
ma-80	190	7	0	0	NUM
ma-80	191	1	y	y	NOUN
ma-80	191	2	y	y	PROPN
ma-80	191	3	1	1	NUM
ma-80	191	4	e–	e–	NUM
ma-80	191	5	wli	wli	NOUN
ma-80	191	6	wli	wli	PROPN
ma-80	191	7	1	1	NUM
ma-80	191	8	–	–	SYM
ma-80	191	9	1	1	NUM
ma-80	191	10	wui	wui	NOUN
ma-80	191	11	1	1	NUM
ma-80	191	12	–	–	PUNCT
ma-80	191	13	+	+	ADJ
ma-80	191	14			NOUN
ma-80	191	15			SYM
ma-80	191	16	1	1	NUM
ma-80	191	17	wli	wli	NOUN
ma-80	191	18	1	1	NUM
ma-80	191	19	–	–	PUNCT
ma-80	192	1	+	+	NUM
ma-80	193	1	--------------------------------------------=	--------------------------------------------=	NOUN
ma-80	193	2	i	i	PRON
ma-80	193	3	1	1	NUM
ma-80	193	4	2	2	NUM
ma-80	193	5			NOUN
ma-80	193	6			NOUN
ma-80	193	7			VERB
ma-80	193	8	wl0	wl0	VERB
ma-80	193	9	y=	y=	PROPN
ma-80	193	10	wui	wui	PROPN
ma-80	193	11	y	y	PROPN
ma-80	193	12	wli	wli	PROPN
ma-80	193	13	---------ln	---------ln	NOUN
ma-80	194	1	=	=	NOUN
ma-80	194	2	i	i	NOUN
ma-80	194	3	1	1	NUM
ma-80	194	4	2	2	NUM
ma-80	194	5			NOUN
ma-80	194	6			X
ma-80	194	7			NUM
ma-80	194	8	wu0	wu0	NOUN
ma-80	194	9	0.=	0.=	NOUN
ma-80	195	1	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	NOUN
ma-80	195	2	proof	proof	NOUN
ma-80	195	3	.	.	PUNCT
ma-80	196	1	consider	consider	VERB
ma-80	196	2	the	the	DET
ma-80	196	3	geometry	geometry	NOUN
ma-80	196	4	detailed	detail	VERB
ma-80	196	5	in	in	ADP
ma-80	196	6	figure	figure	NOUN
ma-80	196	7	9	9	NUM
ma-80	196	8	,	,	PUNCT
ma-80	196	9	for	for	ADP
ma-80	196	10	the	the	DET
ma-80	196	11	case	case	NOUN
ma-80	196	12	of	of	ADP
ma-80	196	13	,	,	PUNCT
ma-80	196	14	and	and	CCONJ
ma-80	196	15	an	an	DET
ma-80	196	16	initial	initial	ADJ
ma-80	196	17	approximation	approximation	NOUN
ma-80	196	18	to	to	ADP
ma-80	196	19	of	of	ADP
ma-80	196	20	which	which	PRON
ma-80	196	21	is	be	AUX
ma-80	196	22	based	base	VERB
ma-80	196	23	the	the	DET
ma-80	196	24	intersection	intersection	NOUN
ma-80	196	25	of	of	ADP
ma-80	196	26	the	the	DET
ma-80	196	27	first	first	ADJ
ma-80	196	28	order	order	NOUN
ma-80	196	29	taylor	taylor	PROPN
ma-80	196	30	series	series	PROPN
ma-80	196	31	for	for	ADP
ma-80	196	32	at	at	ADP
ma-80	196	33	the	the	DET
ma-80	196	34	origin	origin	NOUN
ma-80	196	35	,	,	PUNCT
ma-80	196	36	i.e.	i.e.	X
ma-80	196	37	,	,	PUNCT
ma-80	196	38	and	and	CCONJ
ma-80	196	39	.	.	PUNCT
ma-80	197	1	an	an	DET
ma-80	197	2	associated	associated	ADJ
ma-80	197	3	approximation	approximation	NOUN
ma-80	197	4	,	,	PUNCT
ma-80	197	5	denoted	denote	VERB
ma-80	197	6	,	,	PUNCT
ma-80	197	7	arises	arise	VERB
ma-80	197	8	from	from	ADP
ma-80	197	9	the	the	DET
ma-80	197	10	intersection	intersection	NOUN
ma-80	197	11	of	of	ADP
ma-80	197	12	the	the	DET
ma-80	197	13	level	level	NOUN
ma-80	197	14	defined	define	VERB
ma-80	197	15	by	by	ADP
ma-80	197	16	and	and	CCONJ
ma-80	197	17	the	the	DET
ma-80	197	18	curve	curve	NOUN
ma-80	197	19	.	.	PUNCT
ma-80	198	1	the	the	DET
ma-80	198	2	solution	solution	NOUN
ma-80	198	3	is	be	AUX
ma-80	198	4	(	(	PUNCT
ma-80	198	5	26	26	NUM
ma-80	198	6	)	)	PUNCT
ma-80	198	7	second	second	ADJ
ma-80	198	8	order	order	NOUN
ma-80	198	9	approximations	approximation	NOUN
ma-80	198	10	follow	follow	VERB
ma-80	198	11	from	from	ADP
ma-80	198	12	the	the	DET
ma-80	198	13	intersection	intersection	NOUN
ma-80	198	14	of	of	ADP
ma-80	198	15	with	with	ADP
ma-80	198	16	a	a	DET
ma-80	198	17	first	first	ADJ
ma-80	198	18	order	order	NOUN
ma-80	198	19	taylor	taylor	PROPN
ma-80	198	20	series	series	PROPN
ma-80	198	21	of	of	ADP
ma-80	198	22	,	,	PUNCT
ma-80	198	23	based	base	VERB
ma-80	198	24	on	on	ADP
ma-80	198	25	the	the	DET
ma-80	198	26	point	point	NOUN
ma-80	198	27	,	,	PUNCT
ma-80	198	28	i.e.	i.e.	X
ma-80	198	29	,	,	PUNCT
ma-80	198	30	to	to	PART
ma-80	198	31	yield	yield	VERB
ma-80	198	32	(	(	PUNCT
ma-80	198	33	27	27	NUM
ma-80	198	34	)	)	PUNCT
ma-80	198	35	and	and	CCONJ
ma-80	198	36	by	by	ADP
ma-80	198	37	the	the	DET
ma-80	198	38	intersection	intersection	NOUN
ma-80	198	39	of	of	ADP
ma-80	198	40	this	this	DET
ma-80	198	41	level	level	NOUN
ma-80	198	42	with	with	ADP
ma-80	198	43	the	the	DET
ma-80	198	44	curve	curve	NOUN
ma-80	198	45	to	to	PART
ma-80	198	46	yield	yield	VERB
ma-80	198	47	(	(	PUNCT
ma-80	198	48	28	28	NUM
ma-80	198	49	)	)	PUNCT
ma-80	198	50	the	the	DET
ma-80	198	51	general	general	ADJ
ma-80	198	52	iterative	iterative	NOUN
ma-80	198	53	form	form	NOUN
ma-80	198	54	:	:	PUNCT
ma-80	198	55	(	(	PUNCT
ma-80	198	56	29	29	NUM
ma-80	198	57	)	)	PUNCT
ma-80	198	58	then	then	ADV
ma-80	198	59	follows	follow	VERB
ma-80	198	60	.	.	PUNCT
ma-80	199	1	whilst	whilst	SCONJ
ma-80	199	2	the	the	DET
ma-80	199	3	geometry	geometry	NOUN
ma-80	199	4	,	,	PUNCT
ma-80	199	5	and	and	CCONJ
ma-80	199	6	the	the	DET
ma-80	199	7	defined	define	VERB
ma-80	199	8	approximations	approximation	NOUN
ma-80	199	9	,	,	PUNCT
ma-80	199	10	are	be	AUX
ma-80	199	11	clearly	clearly	ADV
ma-80	199	12	defined	define	VERB
ma-80	199	13	for	for	ADP
ma-80	199	14	the	the	DET
ma-80	199	15	case	case	NOUN
ma-80	199	16	of	of	ADP
ma-80	199	17	,	,	PUNCT
ma-80	199	18	the	the	DET
ma-80	199	19	approximations	approximation	NOUN
ma-80	199	20	are	be	AUX
ma-80	199	21	also	also	ADV
ma-80	199	22	valid	valid	ADJ
ma-80	199	23	for	for	ADP
ma-80	199	24	as	as	ADP
ma-80	199	25	simulation	simulation	NOUN
ma-80	199	26	results	result	NOUN
ma-80	199	27	,	,	PUNCT
ma-80	199	28	shown	show	VERB
ma-80	199	29	in	in	ADP
ma-80	199	30	figure	figure	NOUN
ma-80	199	31	10	10	NUM
ma-80	199	32	,	,	PUNCT
ma-80	199	33	demonstrate	demonstrate	NOUN
ma-80	199	34	.	.	PUNCT
ma-80	200	1	3.1.1	3.1.1	X
ma-80	200	2	.	.	PUNCT
ma-80	200	3	explicit	explicit	ADJ
ma-80	200	4	approximations	approximation	NOUN
ma-80	200	5	.	.	PUNCT
ma-80	201	1	approximations	approximation	NOUN
ma-80	201	2	to	to	ADP
ma-80	201	3	the	the	DET
ma-80	201	4	lambert	lambert	PROPN
ma-80	201	5	w	w	PROPN
ma-80	201	6	function	function	PROPN
ma-80	201	7	,	,	PUNCT
ma-80	201	8	of	of	ADP
ma-80	201	9	orders	order	NOUN
ma-80	201	10	one	one	NUM
ma-80	201	11	to	to	ADP
ma-80	201	12	five	five	NUM
ma-80	201	13	,	,	PUNCT
ma-80	201	14	are	be	AUX
ma-80	201	15	:	:	PUNCT
ma-80	201	16	(	(	PUNCT
ma-80	201	17	30	30	X
ma-80	201	18	)	)	PUNCT
ma-80	201	19	y	y	PROPN
ma-80	201	20	0	0	NUM
ma-80	202	1	xo	xo	PROPN
ma-80	202	2	wl1	wl1	PROPN
ma-80	202	3	y	y	PROPN
ma-80	202	4	1	1	NUM
ma-80	202	5	y+	y+	NOUN
ma-80	202	6	=	=	NOUN
ma-80	202	7	ye	ye	NUM
ma-80	202	8	x	x	PROPN
ma-80	202	9	–	–	PUNCT
ma-80	202	10	y	y	PROPN
ma-80	202	11	yx	yx	PROPN
ma-80	202	12	–	–	PUNCT
ma-80	202	13	x	x	SYM
ma-80	202	14	wu1	wu1	NOUN
ma-80	202	15	wl1	wl1	PROPN
ma-80	202	16	ye	ye	NUM
ma-80	202	17	x	x	NOUN
ma-80	202	18	–	–	PUNCT
ma-80	202	19	figure	figure	NOUN
ma-80	202	20	9	9	NUM
ma-80	202	21	.	.	PUNCT
ma-80	203	1	illustration	illustration	NOUN
ma-80	203	2	of	of	ADP
ma-80	203	3	the	the	DET
ma-80	203	4	geometry	geometry	NOUN
ma-80	203	5	underpinning	underpin	VERB
ma-80	203	6	an	an	DET
ma-80	203	7	iterative	iterative	NOUN
ma-80	203	8	relationship	relationship	NOUN
ma-80	203	9	to	to	PART
ma-80	203	10	find	find	VERB
ma-80	203	11	an	an	DET
ma-80	203	12	approximation	approximation	NOUN
ma-80	203	13	to	to	ADP
ma-80	203	14	which	which	PRON
ma-80	203	15	is	be	AUX
ma-80	203	16	the	the	DET
ma-80	203	17	solution	solution	NOUN
ma-80	203	18	of	of	ADP
ma-80	203	19	for	for	ADP
ma-80	203	20	fixed	fix	VERB
ma-80	203	21	,	,	PUNCT
ma-80	203	22	.xo	.xo	PUNCT
ma-80	203	23	x	x	PUNCT
ma-80	204	1	y	y	NOUN
ma-80	204	2	x–	x–	PUNCT
ma-80	205	1	exp=	exp=	PROPN
ma-80	205	2	y	y	NOUN
ma-80	205	3	y	y	NOUN
ma-80	205	4	0	0	NUM
ma-80	206	1	wl1	wl1	PROPN
ma-80	206	2	wl2	wl2	PROPN
ma-80	206	3	wl2	wl2	PROPN
ma-80	206	4	x	x	PROPN
ma-80	207	1	wl1	wl1	PROPN
ma-80	207	2	xo	xo	PROPN
ma-80	208	1	y	y	PROPN
ma-80	208	2	x	x	PROPN
ma-80	208	3	wu1	wu1	NOUN
ma-80	208	4	ye	ye	NOUN
ma-80	208	5	x	x	PROPN
ma-80	208	6	–	–	PUNCT
ma-80	208	7	xo	xo	PROPN
ma-80	208	8	wu2	wu2	VERB
ma-80	208	9	y	y	PROPN
ma-80	208	10	yx	yx	PROPN
ma-80	208	11	–	–	PUNCT
ma-80	208	12	wl1	wl1	NOUN
ma-80	208	13	x	x	NOUN
ma-80	208	14	wu1	wu1	NOUN
ma-80	208	15	–	–	PUNCT
ma-80	208	16			NUM
ma-80	208	17	wl1	wl1	PUNCT
ma-80	208	18	–	–	PUNCT
ma-80	208	19	wu1	wu1	NOUN
ma-80	208	20	y	y	PROPN
ma-80	208	21	wl1	wl1	PROPN
ma-80	208	22	---------ln	---------ln	VERB
ma-80	208	23	1	1	NUM
ma-80	208	24	y+	y+	NOUN
ma-80	208	25	.ln=	.ln=	NUM
ma-80	209	1	=	=	PUNCT
ma-80	209	2	x	x	PUNCT
ma-80	209	3	ye	ye	NUM
ma-80	209	4	x	x	NOUN
ma-80	209	5	–	–	PUNCT
ma-80	209	6	wu1	wu1	NOUN
ma-80	209	7	wl1	wl1	PROPN
ma-80	209	8	x	x	NOUN
ma-80	209	9	wu1	wu1	NOUN
ma-80	209	10	–	–	PUNCT
ma-80	209	11			NUM
ma-80	209	12	wl1	wl1	PUNCT
ma-80	209	13	–	–	PUNCT
ma-80	209	14	wl2	wl2	PROPN
ma-80	209	15	wl1	wl1	PROPN
ma-80	210	1	1	1	NUM
ma-80	210	2	wu1	wu1	NOUN
ma-80	210	3	+	+	ADJ
ma-80	210	4			ADJ
ma-80	210	5			ADP
ma-80	210	6	1	1	NUM
ma-80	210	7	wl1	wl1	NOUN
ma-80	210	8	+	+	CCONJ
ma-80	210	9	-----------------------------------=	-----------------------------------=	X
ma-80	210	10	ye	ye	NUM
ma-80	210	11	x	x	NOUN
ma-80	210	12	–	–	PUNCT
ma-80	210	13	wu2	wu2	VERB
ma-80	210	14	y	y	NOUN
ma-80	210	15	wl2	wl2	PROPN
ma-80	210	16	---------ln	---------ln	VERB
ma-80	210	17	1	1	NUM
ma-80	210	18	2y+	2y+	NUM
ma-80	210	19	1	1	NUM
ma-80	210	20	1	1	NUM
ma-80	210	21	y+	y+	NOUN
ma-80	210	22	ln+	ln+	NOUN
ma-80	210	23	------------------------------.ln=	------------------------------.ln=	PROPN
ma-80	211	1	=	=	SYM
ma-80	211	2	wli	wli	PROPN
ma-80	211	3	wli	wli	PROPN
ma-80	211	4	1	1	NUM
ma-80	211	5	–	–	SYM
ma-80	211	6	1	1	NUM
ma-80	211	7	wui	wui	NOUN
ma-80	211	8	1	1	NUM
ma-80	211	9	–	–	PUNCT
ma-80	211	10	+	+	ADJ
ma-80	211	11			NOUN
ma-80	211	12			SYM
ma-80	211	13	1	1	NUM
ma-80	211	14	wli	wli	NOUN
ma-80	211	15	1	1	NUM
ma-80	211	16	–	–	PUNCT
ma-80	211	17	+	+	NUM
ma-80	211	18	--------------------------------------------=	--------------------------------------------=	X
ma-80	211	19	wui	wui	PROPN
ma-80	211	20	y	y	PROPN
ma-80	211	21	wli	wli	PROPN
ma-80	211	22	---------ln	---------ln	NOUN
ma-80	211	23	=	=	NOUN
ma-80	212	1	i	i	NOUN
ma-80	212	2	2	2	NUM
ma-80	212	3	3	3	NUM
ma-80	212	4			NOUN
ma-80	212	5			NOUN
ma-80	212	6			NOUN
ma-80	213	1	y	y	PROPN
ma-80	213	2	0	0	NUM
ma-80	214	1	y	y	PROPN
ma-80	214	2	1	1	NUM
ma-80	214	3	e	e	ADV
ma-80	214	4	–	–	PUNCT
ma-80	214	5	0	0	ADP
ma-80	214	6			PROPN
ma-80	214	7	wl1	wl1	PROPN
ma-80	214	8	y	y	NOUN
ma-80	214	9			PUNCT
ma-80	214	10	y	y	PROPN
ma-80	214	11	1	1	NUM
ma-80	214	12	y+	y+	NUM
ma-80	214	13	------------=	------------=	X
ma-80	214	14	wu1	wu1	NOUN
ma-80	214	15	y	y	NOUN
ma-80	214	16			PROPN
ma-80	214	17	1	1	NUM
ma-80	214	18	y+	y+	NOUN
ma-80	214	19	ln=	ln=	PUNCT
ma-80	215	1	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	PROPN
ma-80	215	2	(	(	PUNCT
ma-80	215	3	31	31	NUM
ma-80	215	4	)	)	PUNCT
ma-80	215	5	(	(	PUNCT
ma-80	215	6	32	32	NUM
ma-80	215	7	)	)	PUNCT
ma-80	215	8	(	(	PUNCT
ma-80	215	9	33	33	NUM
ma-80	215	10	)	)	PUNCT
ma-80	215	11	(	(	PUNCT
ma-80	215	12	34	34	NUM
ma-80	215	13	)	)	PUNCT
ma-80	215	14	(	(	PUNCT
ma-80	215	15	35	35	NUM
ma-80	215	16	)	)	PUNCT
ma-80	215	17	(	(	PUNCT
ma-80	215	18	36	36	NUM
ma-80	215	19	)	)	PUNCT
ma-80	216	1	where	where	SCONJ
ma-80	216	2	(	(	PUNCT
ma-80	216	3	37	37	NUM
ma-80	216	4	)	)	PUNCT
ma-80	216	5	wl2	wl2	PROPN
ma-80	216	6	y	y	PROPN
ma-80	217	1			PUNCT
ma-80	218	1	y	y	PROPN
ma-80	219	1	1	1	NUM
ma-80	219	2	1	1	NUM
ma-80	219	3	y+	y+	NOUN
ma-80	219	4	ln+	ln+	PUNCT
ma-80	219	5			NOUN
ma-80	219	6	1	1	NUM
ma-80	219	7	2y+	2y+	NUM
ma-80	219	8	---------------------------------------=	---------------------------------------=	NOUN
ma-80	219	9	wu2	wu2	VERB
ma-80	219	10	y	y	NOUN
ma-80	219	11			PROPN
ma-80	219	12	1	1	NUM
ma-80	219	13	2y+	2y+	NUM
ma-80	219	14	1	1	NUM
ma-80	219	15	1	1	NUM
ma-80	219	16	y+	y+	NOUN
ma-80	219	17	ln+	ln+	PROPN
ma-80	219	18	-------------------------------ln=	-------------------------------ln=	ADJ
ma-80	219	19	wl3	wl3	PROPN
ma-80	219	20	y	y	NOUN
ma-80	219	21			PUNCT
ma-80	219	22	y	y	PROPN
ma-80	219	23	1	1	NUM
ma-80	219	24	1	1	NUM
ma-80	219	25	y+	y+	NOUN
ma-80	219	26	ln+	ln+	PUNCT
ma-80	219	27			NOUN
ma-80	219	28	1	1	NUM
ma-80	219	29	1	1	NUM
ma-80	219	30	2y+	2y+	NUM
ma-80	219	31	1	1	NUM
ma-80	219	32	1	1	NUM
ma-80	219	33	y+	y+	NOUN
ma-80	219	34	ln+	ln+	NOUN
ma-80	219	35	-------------------------------ln+	-------------------------------ln+	PROPN
ma-80	219	36	1	1	NUM
ma-80	219	37	3y	3y	NUM
ma-80	219	38	y	y	PROPN
ma-80	219	39	1	1	NUM
ma-80	219	40	y+	y+	NOUN
ma-80	219	41	ln+	ln+	PROPN
ma-80	219	42	+	+	CCONJ
ma-80	219	43	--------------------------------------------------------------------------------------------------=	--------------------------------------------------------------------------------------------------=	PUNCT
ma-80	219	44	wu3	wu3	VERB
ma-80	219	45	y	y	NOUN
ma-80	219	46			PROPN
ma-80	219	47	1	1	NUM
ma-80	219	48	3y	3y	NUM
ma-80	219	49	y	y	PROPN
ma-80	219	50	1	1	NUM
ma-80	219	51	y+	y+	NOUN
ma-80	219	52	ln+	ln+	PROPN
ma-80	220	1	+	+	CCONJ
ma-80	220	2	1	1	NUM
ma-80	220	3	1	1	NUM
ma-80	220	4	y+	y+	NOUN
ma-80	220	5	ln+	ln+	PUNCT
ma-80	220	6			NOUN
ma-80	220	7	1	1	NUM
ma-80	220	8	1	1	NUM
ma-80	220	9	2y+	2y+	NUM
ma-80	220	10	1	1	NUM
ma-80	220	11	1	1	NUM
ma-80	220	12	y+	y+	NOUN
ma-80	220	13	ln+	ln+	PROPN
ma-80	220	14	-------------------------------ln+	-------------------------------ln+	PUNCT
ma-80	220	15	-----------------------------------------------------------------------------------------------ln=	-----------------------------------------------------------------------------------------------ln=	ADJ
ma-80	220	16	wl4	wl4	ADJ
ma-80	220	17	y	y	NOUN
ma-80	221	1			PUNCT
ma-80	221	2	=	=	SYM
ma-80	221	3	y	y	PROPN
ma-80	221	4	1	1	NUM
ma-80	221	5	1	1	NUM
ma-80	221	6	y+	y+	NOUN
ma-80	221	7	ln+	ln+	PUNCT
ma-80	221	8			NOUN
ma-80	221	9	1	1	NUM
ma-80	221	10	1	1	NUM
ma-80	221	11	2y+	2y+	NUM
ma-80	221	12	1	1	NUM
ma-80	221	13	1	1	NUM
ma-80	221	14	y+	y+	NOUN
ma-80	221	15	ln+	ln+	NOUN
ma-80	221	16	-------------------------------ln+	-------------------------------ln+	PUNCT
ma-80	221	17	1	1	NUM
ma-80	221	18	1	1	NUM
ma-80	221	19	3y	3y	NUM
ma-80	221	20	y	y	PROPN
ma-80	221	21	1	1	NUM
ma-80	221	22	y+	y+	NOUN
ma-80	221	23	ln+	ln+	PROPN
ma-80	222	1	+	+	CCONJ
ma-80	222	2	1	1	NUM
ma-80	222	3	1	1	NUM
ma-80	222	4	y+	y+	NOUN
ma-80	222	5	ln+	ln+	PUNCT
ma-80	222	6			NOUN
ma-80	222	7	1	1	NUM
ma-80	222	8	1	1	NUM
ma-80	222	9	2y+	2y+	NUM
ma-80	222	10	1	1	NUM
ma-80	222	11	1	1	NUM
ma-80	222	12	y+	y+	NOUN
ma-80	222	13	ln+	ln+	PROPN
ma-80	222	14	-------------------------------ln+	-------------------------------ln+	X
ma-80	222	15	-----------------------------------------------------------------------------------------------ln+	-----------------------------------------------------------------------------------------------ln+	PROPN
ma-80	222	16	1	1	NUM
ma-80	222	17	4y	4y	PROPN
ma-80	222	18	y	y	PROPN
ma-80	222	19	1	1	NUM
ma-80	222	20	2y+	2y+	NUM
ma-80	222	21	1	1	NUM
ma-80	222	22	1	1	NUM
ma-80	222	23	y+	y+	NOUN
ma-80	222	24	ln+	ln+	NOUN
ma-80	222	25	-------------------------------ln	-------------------------------ln	NOUN
ma-80	222	26	y	y	PROPN
ma-80	222	27	1	1	NUM
ma-80	222	28	y+	y+	NOUN
ma-80	222	29	ln	ln	PROPN
ma-80	222	30	2	2	NUM
ma-80	222	31	1	1	NUM
ma-80	222	32	2y+	2y+	NUM
ma-80	222	33	1	1	NUM
ma-80	222	34	1	1	NUM
ma-80	222	35	y+	y+	NOUN
ma-80	222	36	ln+	ln+	PROPN
ma-80	222	37	-------------------------------ln++	-------------------------------ln++	PROPN
ma-80	223	1	+	+	CCONJ
ma-80	223	2	+	+	NUM
ma-80	223	3	---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------wu4	---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------wu4	NOUN
ma-80	223	4	y	y	NOUN
ma-80	223	5			PUNCT
ma-80	223	6	=	=	SYM
ma-80	223	7	1	1	NUM
ma-80	223	8	4y	4y	PROPN
ma-80	223	9	y	y	PROPN
ma-80	223	10	1	1	NUM
ma-80	223	11	2y+	2y+	NUM
ma-80	223	12	1	1	NUM
ma-80	223	13	1	1	NUM
ma-80	223	14	y+	y+	NOUN
ma-80	223	15	ln+	ln+	NOUN
ma-80	223	16	-------------------------------ln	-------------------------------ln	NOUN
ma-80	223	17	y	y	PROPN
ma-80	223	18	1	1	NUM
ma-80	223	19	y+	y+	NOUN
ma-80	223	20	ln	ln	PROPN
ma-80	223	21	2	2	NUM
ma-80	223	22	1	1	NUM
ma-80	223	23	2y+	2y+	NUM
ma-80	223	24	1	1	NUM
ma-80	223	25	1	1	NUM
ma-80	223	26	y+	y+	NOUN
ma-80	223	27	ln+	ln+	PROPN
ma-80	223	28	-------------------------------ln++	-------------------------------ln++	PROPN
ma-80	224	1	+	+	CCONJ
ma-80	224	2	+	+	CCONJ
ma-80	224	3	1	1	NUM
ma-80	224	4	1	1	NUM
ma-80	224	5	y+	y+	NOUN
ma-80	224	6	ln+	ln+	PUNCT
ma-80	224	7			NOUN
ma-80	224	8	1	1	NUM
ma-80	224	9	1	1	NUM
ma-80	224	10	2y+	2y+	NUM
ma-80	224	11	1	1	NUM
ma-80	224	12	1	1	NUM
ma-80	224	13	y+	y+	NOUN
ma-80	224	14	ln+	ln+	NOUN
ma-80	224	15	-------------------------------ln+	-------------------------------ln+	PUNCT
ma-80	224	16	1	1	NUM
ma-80	224	17	1	1	NUM
ma-80	224	18	3y	3y	NUM
ma-80	224	19	y	y	PROPN
ma-80	224	20	1	1	NUM
ma-80	224	21	y+	y+	NOUN
ma-80	224	22	ln+	ln+	PROPN
ma-80	225	1	+	+	CCONJ
ma-80	225	2	1	1	NUM
ma-80	225	3	1	1	NUM
ma-80	225	4	y+	y+	NOUN
ma-80	225	5	ln+	ln+	PUNCT
ma-80	225	6			NOUN
ma-80	225	7	1	1	NUM
ma-80	225	8	1	1	NUM
ma-80	225	9	2y+	2y+	NUM
ma-80	225	10	1	1	NUM
ma-80	225	11	1	1	NUM
ma-80	225	12	y+	y+	NOUN
ma-80	225	13	ln+	ln+	NOUN
ma-80	225	14	-------------------------------ln+	-------------------------------ln+	X
ma-80	225	15	-----------------------------------------------------------------------------------------------ln+	-----------------------------------------------------------------------------------------------ln+	PUNCT
ma-80	225	16	-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ln	-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ln	PROPN
ma-80	225	17	wl5	wl5	NOUN
ma-80	225	18	y	y	PROPN
ma-80	226	1			PROPN
ma-80	226	2	yn5	yn5	NOUN
ma-80	226	3	y	y	NOUN
ma-80	226	4			PROPN
ma-80	226	5	d5	d5	NOUN
ma-80	226	6	y	y	NOUN
ma-80	226	7			PUNCT
ma-80	226	8	----------------=	----------------=	PUNCT
ma-80	226	9	wu5	wu5	ADP
ma-80	226	10	y	y	PROPN
ma-80	226	11			PROPN
ma-80	226	12	d5	d5	NOUN
ma-80	226	13	y	y	NOUN
ma-80	226	14			PROPN
ma-80	226	15	n5	n5	PROPN
ma-80	226	16	y	y	NOUN
ma-80	226	17			PROPN
ma-80	226	18	-------------ln=	-------------ln=	NOUN
ma-80	226	19	n5	n5	PROPN
ma-80	226	20	y	y	NOUN
ma-80	227	1			NOUN
ma-80	227	2	1	1	NUM
ma-80	227	3	1	1	NUM
ma-80	227	4	y+	y+	NOUN
ma-80	227	5	ln+	ln+	PUNCT
ma-80	227	6			NOUN
ma-80	227	7	1	1	NUM
ma-80	227	8	1	1	NUM
ma-80	227	9	2y+	2y+	NUM
ma-80	227	10	1	1	NUM
ma-80	227	11	1	1	NUM
ma-80	227	12	y+	y+	NOUN
ma-80	227	13	ln+	ln+	NOUN
ma-80	227	14	-------------------------------ln+	-------------------------------ln+	PUNCT
ma-80	227	15	1	1	NUM
ma-80	227	16	1	1	NUM
ma-80	227	17	3y	3y	NUM
ma-80	227	18	y	y	PROPN
ma-80	227	19	1	1	NUM
ma-80	227	20	y+	y+	NOUN
ma-80	227	21	ln+	ln+	PROPN
ma-80	228	1	+	+	CCONJ
ma-80	228	2	1	1	NUM
ma-80	228	3	1	1	NUM
ma-80	228	4	y+	y+	NOUN
ma-80	228	5	ln+	ln+	PUNCT
ma-80	228	6			NOUN
ma-80	228	7	1	1	NUM
ma-80	228	8	1	1	NUM
ma-80	228	9	2y+	2y+	NUM
ma-80	228	10	1	1	NUM
ma-80	228	11	1	1	NUM
ma-80	228	12	y+	y+	NOUN
ma-80	228	13	ln+	ln+	PROPN
ma-80	228	14	-------------------------------ln+	-------------------------------ln+	X
ma-80	228	15	-----------------------------------------------------------------------------------------------ln+	-----------------------------------------------------------------------------------------------ln+	PUNCT
ma-80	228	16	=	=	NOUN
ma-80	228	17	1	1	NUM
ma-80	228	18	1	1	NUM
ma-80	228	19	4y	4y	PROPN
ma-80	228	20	y+	y+	NUM
ma-80	228	21	+	+	CCONJ
ma-80	228	22	1	1	NUM
ma-80	228	23	2y+	2y+	NUM
ma-80	228	24	1	1	NUM
ma-80	228	25	1	1	NUM
ma-80	228	26	y+	y+	NOUN
ma-80	228	27	ln+	ln+	PROPN
ma-80	228	28	-------------------------------ln	-------------------------------ln	PUNCT
ma-80	229	1	y	y	PROPN
ma-80	229	2	1	1	NUM
ma-80	229	3	y+	y+	NOUN
ma-80	229	4	ln	ln	PROPN
ma-80	229	5	2	2	NUM
ma-80	229	6	1	1	NUM
ma-80	229	7	2y+	2y+	NUM
ma-80	229	8	1	1	NUM
ma-80	229	9	1	1	NUM
ma-80	229	10	y+	y+	NOUN
ma-80	229	11	ln+	ln+	PROPN
ma-80	229	12	-------------------------------ln++	-------------------------------ln++	PROPN
ma-80	229	13	1	1	NUM
ma-80	229	14	1	1	NUM
ma-80	229	15	y+	y+	NOUN
ma-80	229	16	ln+	ln+	PUNCT
ma-80	229	17			NOUN
ma-80	229	18	1	1	NUM
ma-80	229	19	1	1	NUM
ma-80	229	20	2y+	2y+	NUM
ma-80	229	21	1	1	NUM
ma-80	229	22	1	1	NUM
ma-80	229	23	y+	y+	NOUN
ma-80	229	24	ln+	ln+	NOUN
ma-80	229	25	-------------------------------ln+	-------------------------------ln+	PUNCT
ma-80	229	26	1	1	NUM
ma-80	229	27	1	1	NUM
ma-80	229	28	3y	3y	NUM
ma-80	229	29	y	y	PROPN
ma-80	229	30	1	1	NUM
ma-80	229	31	y+	y+	NOUN
ma-80	229	32	ln+	ln+	PROPN
ma-80	230	1	+	+	CCONJ
ma-80	230	2	1	1	NUM
ma-80	230	3	1	1	NUM
ma-80	230	4	y+	y+	NOUN
ma-80	230	5	ln+	ln+	PUNCT
ma-80	230	6			NOUN
ma-80	230	7	1	1	NUM
ma-80	230	8	1	1	NUM
ma-80	230	9	2y+	2y+	NUM
ma-80	230	10	1	1	NUM
ma-80	230	11	1	1	NUM
ma-80	230	12	y+	y+	NOUN
ma-80	230	13	ln+	ln+	PROPN
ma-80	230	14	-------------------------------ln+	-------------------------------ln+	PROPN
ma-80	230	15	-----------------------------------------------------------------------------------------------ln+	-----------------------------------------------------------------------------------------------ln+	PUNCT
ma-80	230	16	-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ln+	-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ln+	PROPN
ma-80	230	17	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	PROPN
ma-80	230	18	(	(	PUNCT
ma-80	230	19	38	38	NUM
ma-80	230	20	)	)	PUNCT
ma-80	230	21	3.1.2	3.1.2	NUM
ma-80	230	22	.	.	PUNCT
ma-80	230	23	notes	note	NOUN
ma-80	230	24	.	.	PUNCT
ma-80	231	1	the	the	DET
ma-80	231	2	approximation	approximation	NOUN
ma-80	231	3	is	be	AUX
ma-80	231	4	the	the	DET
ma-80	231	5	approximation	approximation	NOUN
ma-80	231	6	stated	state	VERB
ma-80	231	7	in	in	ADP
ma-80	231	8	equation	equation	NOUN
ma-80	231	9	5	5	NUM
ma-80	231	10	and	and	CCONJ
ma-80	231	11	is	be	AUX
ma-80	231	12	the	the	DET
ma-80	231	13	basis	basis	NOUN
ma-80	231	14	for	for	ADP
ma-80	231	15	the	the	DET
ma-80	231	16	newton	newton	PROPN
ma-80	231	17	-	-	PUNCT
ma-80	231	18	raphson	raphson	NOUN
ma-80	231	19	iteration	iteration	NOUN
ma-80	231	20	leading	lead	VERB
ma-80	231	21	to	to	ADP
ma-80	231	22	equation	equation	NOUN
ma-80	231	23	23	23	NUM
ma-80	231	24	and	and	CCONJ
ma-80	231	25	equation	equation	NOUN
ma-80	231	26	24	24	NUM
ma-80	231	27	.	.	PUNCT
ma-80	232	1	consider	consider	VERB
ma-80	232	2	the	the	DET
ma-80	232	3	iteration	iteration	NOUN
ma-80	232	4	formula	formula	NOUN
ma-80	232	5	specified	specify	VERB
ma-80	232	6	in	in	ADP
ma-80	232	7	equation	equation	NOUN
ma-80	232	8	18	18	NUM
ma-80	232	9	(	(	PUNCT
ma-80	232	10	[	[	X
ma-80	232	11	17	17	NUM
ma-80	232	12	]	]	PUNCT
ma-80	232	13	,	,	PUNCT
ma-80	232	14	eqn	eqn	PROPN
ma-80	232	15	.	.	PROPN
ma-80	232	16	12	12	NUM
ma-80	232	17	)	)	PUNCT
ma-80	232	18	.	.	PUNCT
ma-80	233	1	with	with	ADP
ma-80	233	2	a	a	DET
ma-80	233	3	starting	starting	NOUN
ma-80	233	4	value	value	NOUN
ma-80	233	5	of	of	ADP
ma-80	233	6	,	,	PUNCT
ma-80	233	7	it	it	PRON
ma-80	233	8	follows	follow	VERB
ma-80	233	9	that	that	SCONJ
ma-80	233	10	a	a	DET
ma-80	233	11	first	first	ADJ
ma-80	233	12	order	order	NOUN
ma-80	233	13	iteration	iteration	NOUN
ma-80	233	14	leads	lead	VERB
ma-80	233	15	to	to	ADP
ma-80	233	16	the	the	DET
ma-80	233	17	approximation	approximation	NOUN
ma-80	233	18	(	(	PUNCT
ma-80	233	19	39	39	NUM
ma-80	233	20	)	)	PUNCT
ma-80	233	21	which	which	PRON
ma-80	233	22	is	be	AUX
ma-80	233	23	as	as	ADP
ma-80	233	24	specified	specify	VERB
ma-80	233	25	by	by	ADP
ma-80	233	26	equation	equation	NOUN
ma-80	233	27	31	31	NUM
ma-80	233	28	.	.	PUNCT
ma-80	234	1	3.1.3	3.1.3	NUM
ma-80	234	2	.	.	PUNCT
ma-80	234	3	results	result	NOUN
ma-80	234	4	.	.	PUNCT
ma-80	235	1	the	the	DET
ma-80	235	2	relative	relative	ADJ
ma-80	235	3	errors	error	NOUN
ma-80	235	4	associated	associate	VERB
ma-80	235	5	with	with	ADP
ma-80	235	6	the	the	DET
ma-80	235	7	approximations	approximation	NOUN
ma-80	235	8	,	,	PUNCT
ma-80	235	9	specified	specify	VERB
ma-80	235	10	in	in	ADP
ma-80	235	11	theorem	theorem	NOUN
ma-80	235	12	3.1	3.1	NUM
ma-80	235	13	,	,	PUNCT
ma-80	235	14	are	be	AUX
ma-80	235	15	shown	show	VERB
ma-80	235	16	in	in	ADP
ma-80	235	17	figure	figure	NOUN
ma-80	235	18	10	10	NUM
ma-80	235	19	and	and	CCONJ
ma-80	235	20	figure	figure	VERB
ma-80	235	21	11	11	NUM
ma-80	235	22	,	,	PUNCT
ma-80	235	23	whilst	whilst	SCONJ
ma-80	235	24	the	the	DET
ma-80	235	25	relative	relative	ADJ
ma-80	235	26	error	error	NOUN
ma-80	235	27	bounds	bound	NOUN
ma-80	235	28	,	,	PUNCT
ma-80	235	29	for	for	ADP
ma-80	235	30	the	the	DET
ma-80	235	31	interval	interval	NOUN
ma-80	235	32	,	,	PUNCT
ma-80	235	33	are	be	AUX
ma-80	235	34	detailed	detail	VERB
ma-80	235	35	in	in	ADP
ma-80	235	36	table	table	NOUN
ma-80	235	37	1	1	NUM
ma-80	235	38	.	.	PUNCT
ma-80	236	1	note	note	VERB
ma-80	236	2	the	the	DET
ma-80	236	3	quadratic	quadratic	ADJ
ma-80	236	4	convergence	convergence	NOUN
ma-80	236	5	.	.	PUNCT
ma-80	237	1	table	table	NOUN
ma-80	237	2	1	1	NUM
ma-80	237	3	.	.	PUNCT
ma-80	237	4	relative	relative	ADJ
ma-80	237	5	error	error	NOUN
ma-80	237	6	bounds	bound	NOUN
ma-80	237	7	,	,	PUNCT
ma-80	237	8	over	over	ADP
ma-80	237	9	the	the	DET
ma-80	237	10	interval	interval	NOUN
ma-80	237	11	,	,	PUNCT
ma-80	237	12	for	for	ADP
ma-80	237	13	the	the	DET
ma-80	237	14	iterative	iterative	ADJ
ma-80	237	15	approximations	approximation	NOUN
ma-80	237	16	to	to	ADP
ma-80	237	17	the	the	DET
ma-80	237	18	lambert	lambert	PROPN
ma-80	237	19	w	w	PROPN
ma-80	237	20	function	function	NOUN
ma-80	237	21	defined	define	VERB
ma-80	237	22	in	in	ADP
ma-80	237	23	theorem	theorem	ADJ
ma-80	237	24	3.1	3.1	NUM
ma-80	237	25	.	.	PUNCT
ma-80	238	1	iteration	iteration	NOUN
ma-80	238	2	order	order	NOUN
ma-80	238	3	:	:	PUNCT
ma-80	239	1	i	i	PRON
ma-80	239	2	relative	relative	ADJ
ma-80	239	3	error	error	NOUN
ma-80	239	4	bound	bind	VERB
ma-80	239	5	for	for	ADP
ma-80	239	6	relative	relative	ADJ
ma-80	239	7	error	error	NOUN
ma-80	239	8	bound	bind	VERB
ma-80	239	9	for	for	ADP
ma-80	239	10	1	1	NUM
ma-80	239	11	increasing	increase	VERB
ma-80	239	12	0.381	0.381	NUM
ma-80	239	13	2	2	NUM
ma-80	239	14	increasing	increase	VERB
ma-80	239	15	0.0569	0.0569	NUM
ma-80	239	16	3	3	NUM
ma-80	239	17	4	4	NUM
ma-80	239	18	5	5	NUM
ma-80	239	19	6	6	NUM
ma-80	239	20	d5	d5	NOUN
ma-80	239	21	y	y	NOUN
ma-80	239	22			NOUN
ma-80	239	23	1	1	NUM
ma-80	239	24	5y	5y	NOUN
ma-80	239	25	y	y	NOUN
ma-80	239	26	1	1	NUM
ma-80	239	27	3y	3y	NUM
ma-80	239	28	y	y	PROPN
ma-80	239	29	1	1	NUM
ma-80	239	30	y+	y+	NOUN
ma-80	239	31	ln+	ln+	PROPN
ma-80	240	1	+	+	CCONJ
ma-80	240	2	1	1	NUM
ma-80	240	3	1	1	NUM
ma-80	240	4	y+	y+	NOUN
ma-80	240	5	ln+	ln+	PUNCT
ma-80	240	6			NOUN
ma-80	240	7	1	1	NUM
ma-80	240	8	1	1	NUM
ma-80	240	9	2y+	2y+	NUM
ma-80	240	10	1	1	NUM
ma-80	240	11	1	1	NUM
ma-80	240	12	y+	y+	NOUN
ma-80	240	13	ln+	ln+	NOUN
ma-80	240	14	-------------------------------ln+	-------------------------------ln+	X
ma-80	240	15	-----------------------------------------------------------------------------------------------ln+	-----------------------------------------------------------------------------------------------ln+	PUNCT
ma-80	241	1	+	+	PUNCT
ma-80	241	2	+	+	ADJ
ma-80	241	3	=	=	SYM
ma-80	241	4	y	y	ADJ
ma-80	241	5	1	1	NUM
ma-80	241	6	2y+	2y+	NUM
ma-80	241	7	1	1	NUM
ma-80	241	8	1	1	NUM
ma-80	241	9	y+	y+	NOUN
ma-80	241	10	ln+	ln+	PROPN
ma-80	241	11	------------------------------2	------------------------------2	PROPN
ma-80	242	1	1	1	NUM
ma-80	242	2	3y	3y	NUM
ma-80	242	3	y	y	PROPN
ma-80	242	4	1	1	NUM
ma-80	242	5	y+	y+	NOUN
ma-80	242	6	ln+	ln+	PROPN
ma-80	243	1	+	+	CCONJ
ma-80	243	2	1	1	NUM
ma-80	243	3	1	1	NUM
ma-80	243	4	y+	y+	NOUN
ma-80	243	5	ln+	ln+	PUNCT
ma-80	243	6			NOUN
ma-80	243	7	1	1	NUM
ma-80	243	8	1	1	NUM
ma-80	243	9	2y+	2y+	NUM
ma-80	243	10	1	1	NUM
ma-80	243	11	1	1	NUM
ma-80	243	12	y+	y+	NOUN
ma-80	243	13	ln+	ln+	NOUN
ma-80	243	14	-------------------------------ln+	-------------------------------ln+	PUNCT
ma-80	243	15	-----------------------------------------------------------------------------------------------ln+ln	-----------------------------------------------------------------------------------------------ln+ln	PROPN
ma-80	244	1	+	+	CCONJ
ma-80	244	2	y	y	PROPN
ma-80	244	3	1	1	NUM
ma-80	244	4	y+	y+	NOUN
ma-80	244	5			NOUN
ma-80	244	6	3	3	NUM
ma-80	244	7	1	1	NUM
ma-80	244	8	3y	3y	NUM
ma-80	244	9	y	y	PROPN
ma-80	244	10	1	1	NUM
ma-80	244	11	y+	y+	NOUN
ma-80	244	12	ln+	ln+	PROPN
ma-80	245	1	+	+	CCONJ
ma-80	245	2	1	1	NUM
ma-80	245	3	1	1	NUM
ma-80	245	4	y+	y+	NOUN
ma-80	245	5	ln+	ln+	PUNCT
ma-80	245	6			NOUN
ma-80	245	7	1	1	NUM
ma-80	245	8	1	1	NUM
ma-80	245	9	2y+	2y+	NUM
ma-80	245	10	1	1	NUM
ma-80	245	11	1	1	NUM
ma-80	245	12	y+	y+	NOUN
ma-80	245	13	ln+	ln+	NOUN
ma-80	245	14	-------------------------------ln+	-------------------------------ln+	PUNCT
ma-80	245	15	-----------------------------------------------------------------------------------------------ln+	-----------------------------------------------------------------------------------------------ln+	PUNCT
ma-80	246	1	+	+	NUM
ma-80	246	2	1	1	NUM
ma-80	246	3	2y+	2y+	NUM
ma-80	246	4	1	1	NUM
ma-80	246	5	1	1	NUM
ma-80	246	6	y+	y+	NOUN
ma-80	246	7	ln+	ln+	PROPN
ma-80	246	8	------------------------------2	------------------------------2	PROPN
ma-80	246	9	1	1	NUM
ma-80	246	10	3y	3y	NUM
ma-80	246	11	y	y	PROPN
ma-80	246	12	1	1	NUM
ma-80	246	13	y+	y+	NOUN
ma-80	246	14	ln+	ln+	PROPN
ma-80	247	1	+	+	CCONJ
ma-80	247	2	1	1	NUM
ma-80	247	3	1	1	NUM
ma-80	247	4	y+	y+	NOUN
ma-80	247	5	ln+	ln+	PUNCT
ma-80	247	6			NOUN
ma-80	247	7	1	1	NUM
ma-80	247	8	1	1	NUM
ma-80	247	9	2y+	2y+	NUM
ma-80	247	10	1	1	NUM
ma-80	247	11	1	1	NUM
ma-80	247	12	y+	y+	NOUN
ma-80	247	13	ln+	ln+	PROPN
ma-80	247	14	-------------------------------ln+	-------------------------------ln+	PROPN
ma-80	247	15	-----------------------------------------------------------------------------------------------ln+ln	-----------------------------------------------------------------------------------------------ln+ln	NOUN
ma-80	247	16	ln	ln	ADJ
ma-80	247	17	wu1	wu1	NOUN
ma-80	247	18	y	y	NOUN
ma-80	247	19			PROPN
ma-80	247	20	1	1	NUM
ma-80	247	21	y+	y+	NOUN
ma-80	247	22	ln=	ln=	PUNCT
ma-80	248	1	x0	x0	PROPN
ma-80	248	2	y	y	PROPN
ma-80	248	3	1	1	NUM
ma-80	248	4	y+	y+	NOUN
ma-80	248	5	=	=	NOUN
ma-80	248	6	w1	w1	NOUN
ma-80	248	7	y	y	NOUN
ma-80	248	8			PUNCT
ma-80	248	9	y	y	PROPN
ma-80	248	10	1	1	NUM
ma-80	248	11	2y+	2y+	NUM
ma-80	248	12	--------------1	--------------1	NOUN
ma-80	248	13	1	1	NUM
ma-80	248	14	y+	y+	NOUN
ma-80	248	15	ln+	ln+	PUNCT
ma-80	248	16			PROPN
ma-80	248	17	=	=	NOUN
ma-80	248	18	wl2	wl2	NOUN
ma-80	248	19	y	y	PROPN
ma-80	248	20			PROPN
ma-80	248	21	0	0	NUM
ma-80	248	22			NOUN
ma-80	248	23			NOUN
ma-80	248	24	0	0	NUM
ma-80	248	25			NOUN
ma-80	248	26			PROPN
ma-80	248	27	wli	wli	PROPN
ma-80	248	28	wui	wui	PROPN
ma-80	249	1	8.32	8.32	NUM
ma-80	249	2	10	10	NUM
ma-80	249	3	3–	3–	NUM
ma-80	249	4	1.33	1.33	NUM
ma-80	249	5	10	10	NUM
ma-80	250	1	3–	3–	NUM
ma-80	250	2	3.88	3.88	NUM
ma-80	250	3	10	10	NUM
ma-80	251	1	6–	6–	PROPN
ma-80	251	2	7.23	7.23	NUM
ma-80	251	3	10	10	NUM
ma-80	251	4	7–	7–	NOUN
ma-80	251	5	1.08	1.08	NUM
ma-80	251	6	10	10	NUM
ma-80	251	7	12–	12–	NUM
ma-80	251	8	2.15	2.15	NUM
ma-80	251	9	10	10	NUM
ma-80	251	10	13–	13–	NUM
ma-80	251	11	9.33	9.33	NUM
ma-80	251	12	10	10	NUM
ma-80	251	13	26–	26–	NUM
ma-80	251	14	1.90	1.90	NUM
ma-80	251	15	10	10	NUM
ma-80	251	16	26–	26–	NUM
ma-80	251	17	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	NOUN
ma-80	251	18	3.2	3.2	NUM
ma-80	251	19	.	.	PUNCT
ma-80	252	1	alternative	alternative	ADJ
ma-80	252	2	iterative	iterative	NOUN
ma-80	252	3	formulas	formula	NOUN
ma-80	252	4	.	.	PUNCT
ma-80	253	1	the	the	DET
ma-80	253	2	approximations	approximation	NOUN
ma-80	253	3	and	and	CCONJ
ma-80	253	4	for	for	ADP
ma-80	253	5	the	the	DET
ma-80	253	6	lambert	lambert	PROPN
ma-80	253	7	w	w	PROPN
ma-80	253	8	function	function	PROPN
ma-80	253	9	,	,	PUNCT
ma-80	253	10	as	as	SCONJ
ma-80	253	11	specified	specify	VERB
ma-80	253	12	in	in	ADP
ma-80	253	13	theorem	theorem	ADJ
ma-80	253	14	3.1	3.1	NUM
ma-80	253	15	,	,	PUNCT
ma-80	253	16	can	can	AUX
ma-80	253	17	be	be	AUX
ma-80	253	18	also	also	ADV
ma-80	253	19	be	be	AUX
ma-80	253	20	defined	define	VERB
ma-80	253	21	via	via	ADP
ma-80	253	22	iterative	iterative	NOUN
ma-80	253	23	formulas	formula	NOUN
ma-80	253	24	based	base	VERB
ma-80	253	25	on	on	ADP
ma-80	253	26	numerator	numerator	NOUN
ma-80	253	27	and	and	CCONJ
ma-80	253	28	denominator	denominator	NOUN
ma-80	253	29	expressions	expression	NOUN
ma-80	253	30	.	.	PUNCT
ma-80	254	1	theorem	theorem	VERB
ma-80	254	2	3.2	3.2	NUM
ma-80	254	3	.	.	PUNCT
ma-80	255	1	alternative	alternative	ADJ
ma-80	255	2	iterative	iterative	NOUN
ma-80	255	3	formulas	formula	NOUN
ma-80	255	4	for	for	ADP
ma-80	255	5	lambert	lambert	PROPN
ma-80	255	6	w.	w.	PROPN
ma-80	255	7	the	the	DET
ma-80	255	8	approximations	approximation	NOUN
ma-80	255	9	and	and	CCONJ
ma-80	255	10	,	,	PUNCT
ma-80	255	11	,	,	PUNCT
ma-80	255	12	for	for	SCONJ
ma-80	255	13	the	the	DET
ma-80	255	14	lambert	lambert	PROPN
ma-80	255	15	w	w	PROPN
ma-80	255	16	function	function	NOUN
ma-80	255	17	can	can	AUX
ma-80	255	18	be	be	AUX
ma-80	255	19	specified	specify	VERB
ma-80	255	20	according	accord	VERB
ma-80	255	21	to	to	ADP
ma-80	255	22	(	(	PUNCT
ma-80	255	23	40	40	NUM
ma-80	255	24	)	)	PUNCT
ma-80	255	25	where	where	SCONJ
ma-80	255	26	(	(	PUNCT
ma-80	255	27	41	41	NUM
ma-80	255	28	)	)	PUNCT
ma-80	255	29	proof	proof	NOUN
ma-80	255	30	.	.	PUNCT
ma-80	256	1	the	the	DET
ma-80	256	2	proof	proof	NOUN
ma-80	256	3	is	be	AUX
ma-80	256	4	detailed	detail	VERB
ma-80	256	5	in	in	ADP
ma-80	256	6	appendix	appendix	PROPN
ma-80	256	7	b.	b.	PROPN
ma-80	256	8	figure	figure	NOUN
ma-80	256	9	10	10	NUM
ma-80	256	10	.	.	PUNCT
ma-80	257	1	graph	graph	NOUN
ma-80	257	2	of	of	ADP
ma-80	257	3	the	the	DET
ma-80	257	4	relative	relative	ADJ
ma-80	257	5	errors	error	NOUN
ma-80	257	6	in	in	ADP
ma-80	257	7	the	the	DET
ma-80	257	8	iterative	iterative	NOUN
ma-80	257	9	approximations	approximation	NOUN
ma-80	257	10	to	to	ADP
ma-80	257	11	the	the	DET
ma-80	257	12	lambert	lambert	PROPN
ma-80	257	13	w	w	PROPN
ma-80	257	14	function	function	NOUN
ma-80	257	15	defined	define	VERB
ma-80	257	16	in	in	ADP
ma-80	257	17	theorem	theorem	NOUN
ma-80	257	18	3.1	3.1	NUM
ma-80	257	19	.	.	PUNCT
ma-80	258	1	y	y	PROPN
ma-80	258	2	wl1	wl1	PROPN
ma-80	258	3	y	y	PROPN
ma-80	258	4			PROPN
ma-80	258	5	re	re	ADP
ma-80	258	6	y	y	NOUN
ma-80	258	7			PROPN
ma-80	258	8	wl2	wl2	PROPN
ma-80	258	9	y	y	PROPN
ma-80	258	10			PROPN
ma-80	258	11	wu1	wu1	NOUN
ma-80	258	12	y	y	NOUN
ma-80	258	13			NOUN
ma-80	258	14	wu2	wu2	VERB
ma-80	258	15	y	y	NOUN
ma-80	258	16			NOUN
ma-80	258	17	wl3	wl3	NOUN
ma-80	258	18	y	y	NOUN
ma-80	258	19			PROPN
ma-80	258	20	wu3	wu3	VERB
ma-80	258	21	y	y	NOUN
ma-80	258	22			PROPN
ma-80	258	23	wu4	wu4	NOUN
ma-80	258	24	y	y	NOUN
ma-80	258	25			PROPN
ma-80	258	26	figure	figure	NOUN
ma-80	258	27	11	11	NUM
ma-80	258	28	.	.	PUNCT
ma-80	259	1	graph	graph	NOUN
ma-80	259	2	of	of	ADP
ma-80	259	3	the	the	DET
ma-80	259	4	relative	relative	ADJ
ma-80	259	5	errors	error	NOUN
ma-80	259	6	in	in	ADP
ma-80	259	7	the	the	DET
ma-80	259	8	iterative	iterative	NOUN
ma-80	259	9	approximations	approximation	NOUN
ma-80	259	10	to	to	ADP
ma-80	259	11	the	the	DET
ma-80	259	12	lambert	lambert	PROPN
ma-80	259	13	w	w	PROPN
ma-80	259	14	function	function	NOUN
ma-80	259	15	defined	define	VERB
ma-80	259	16	in	in	ADP
ma-80	259	17	theorem	theorem	NOUN
ma-80	259	18	3.1	3.1	NUM
ma-80	259	19	.	.	PUNCT
ma-80	260	1	y	y	PROPN
ma-80	260	2	wl1	wl1	PROPN
ma-80	260	3	y	y	INTJ
ma-80	260	4	re	re	X
ma-80	261	1	y	y	NOUN
ma-80	261	2			NOUN
ma-80	261	3	wu1	wu1	NOUN
ma-80	261	4	y	y	NOUN
ma-80	261	5			PROPN
ma-80	261	6	wl2	wl2	PROPN
ma-80	261	7	y	y	NOUN
ma-80	262	1			PROPN
ma-80	262	2	wu2	wu2	VERB
ma-80	262	3	y	y	NOUN
ma-80	262	4			NOUN
ma-80	262	5	wl3	wl3	NOUN
ma-80	262	6	y	y	NOUN
ma-80	262	7			PROPN
ma-80	262	8	wu3	wu3	VERB
ma-80	262	9	y	y	NOUN
ma-80	262	10			PUNCT
ma-80	262	11	wl4	wl4	ADJ
ma-80	262	12	y	y	NOUN
ma-80	262	13			PROPN
ma-80	262	14	wu4	wu4	NOUN
ma-80	262	15	y	y	PROPN
ma-80	262	16			PROPN
ma-80	262	17	wli	wli	PROPN
ma-80	262	18	wui	wui	PROPN
ma-80	262	19	wli	wli	PROPN
ma-80	262	20	wui	wui	PROPN
ma-80	263	1	i	i	ADV
ma-80	263	2	1	1	NUM
ma-80	263	3	2	2	NUM
ma-80	263	4			NOUN
ma-80	263	5			X
ma-80	264	1			VERB
ma-80	264	2	wli	wli	NOUN
ma-80	264	3	y	y	NOUN
ma-80	264	4			PROPN
ma-80	264	5	ni	ni	NOUN
ma-80	264	6	y	y	NOUN
ma-80	264	7			PROPN
ma-80	264	8	di	di	NOUN
ma-80	264	9	y	y	NOUN
ma-80	264	10			PROPN
ma-80	264	11	------------=	------------=	X
ma-80	264	12	wui	wui	PROPN
ma-80	264	13	y	y	PROPN
ma-80	264	14			PROPN
ma-80	264	15	di	di	X
ma-80	264	16	y	y	NOUN
ma-80	264	17			X
ma-80	264	18	ln	ln	NOUN
ma-80	264	19	ni	ni	PROPN
ma-80	264	20	y	y	PROPN
ma-80	264	21			PROPN
ma-80	264	22	y	y	PROPN
ma-80	264	23	------------ln	------------ln	PROPN
ma-80	264	24	–	–	PUNCT
ma-80	264	25	=	=	ADJ
ma-80	264	26	i	i	NOUN
ma-80	264	27	1	1	NUM
ma-80	264	28	2	2	NUM
ma-80	264	29			NOUN
ma-80	264	30			NOUN
ma-80	264	31			NOUN
ma-80	264	32	ni	ni	PROPN
ma-80	264	33	y	y	PROPN
ma-80	264	34			PROPN
ma-80	264	35	ni	ni	PROPN
ma-80	264	36	1	1	NUM
ma-80	264	37	–	–	PUNCT
ma-80	264	38	y	y	NOUN
ma-80	264	39			PROPN
ma-80	264	40	1	1	NUM
ma-80	264	41	di	di	NOUN
ma-80	264	42	1	1	NUM
ma-80	264	43	–	–	PUNCT
ma-80	264	44	y	y	NOUN
ma-80	264	45			NOUN
ma-80	264	46	ln	ln	NOUN
ma-80	264	47	ni	ni	PROPN
ma-80	264	48	1	1	NUM
ma-80	264	49	–	–	PUNCT
ma-80	264	50	y	y	NOUN
ma-80	264	51			PROPN
ma-80	264	52	y	y	PROPN
ma-80	264	53	-------------------ln–+	-------------------ln–+	PUNCT
ma-80	264	54	=	=	PROPN
ma-80	264	55	n0	n0	ADJ
ma-80	264	56	y	y	NOUN
ma-80	265	1			PROPN
ma-80	266	1	y=	y=	SYM
ma-80	267	1	d0	d0	VERB
ma-80	267	2	y	y	PROPN
ma-80	267	3			PROPN
ma-80	267	4	1=	1=	NUM
ma-80	267	5	di	di	X
ma-80	267	6	y	y	NOUN
ma-80	267	7			PROPN
ma-80	267	8	ni	ni	PROPN
ma-80	267	9	1	1	NUM
ma-80	267	10	–	–	PUNCT
ma-80	267	11	y	y	NOUN
ma-80	267	12			PROPN
ma-80	267	13	di	di	NOUN
ma-80	267	14	1	1	NUM
ma-80	267	15	–	–	PUNCT
ma-80	267	16	y	y	NOUN
ma-80	267	17	.+=	.+=	PROPN
ma-80	267	18	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	NOUN
ma-80	267	19	3.2.1	3.2.1	NUM
ma-80	267	20	.	.	PUNCT
ma-80	268	1	explicit	explicit	ADJ
ma-80	268	2	formulas	formula	NOUN
ma-80	268	3	.	.	PUNCT
ma-80	269	1	explicit	explicit	ADJ
ma-80	269	2	formulas	formula	NOUN
ma-80	269	3	,	,	PUNCT
ma-80	269	4	for	for	ADP
ma-80	269	5	the	the	DET
ma-80	269	6	first	first	ADJ
ma-80	269	7	to	to	ADP
ma-80	269	8	fourth	fourth	ADJ
ma-80	269	9	order	order	NOUN
ma-80	269	10	approximations	approximation	NOUN
ma-80	269	11	,	,	PUNCT
ma-80	269	12	are	be	AUX
ma-80	269	13	:	:	PUNCT
ma-80	269	14	(	(	PUNCT
ma-80	269	15	42	42	NUM
ma-80	269	16	)	)	PUNCT
ma-80	269	17	(	(	PUNCT
ma-80	269	18	43	43	NUM
ma-80	269	19	)	)	PUNCT
ma-80	269	20	(	(	PUNCT
ma-80	269	21	44	44	NUM
ma-80	269	22	)	)	PUNCT
ma-80	269	23	(	(	PUNCT
ma-80	269	24	45	45	NUM
ma-80	269	25	)	)	PUNCT
ma-80	269	26	(	(	PUNCT
ma-80	269	27	46	46	NUM
ma-80	269	28	)	)	PUNCT
ma-80	269	29	3.3	3.3	NUM
ma-80	269	30	.	.	PUNCT
ma-80	270	1	alternative	alternative	ADJ
ma-80	270	2	geometrical	geometrical	ADJ
ma-80	270	3	approach	approach	NOUN
ma-80	270	4	.	.	PUNCT
ma-80	271	1	an	an	DET
ma-80	271	2	alternative	alternative	ADJ
ma-80	271	3	approach	approach	NOUN
ma-80	271	4	that	that	PRON
ma-80	271	5	leads	lead	VERB
ma-80	271	6	to	to	ADP
ma-80	271	7	the	the	DET
ma-80	271	8	approximations	approximation	NOUN
ma-80	271	9	,	,	PUNCT
ma-80	271	10	,	,	PUNCT
ma-80	271	11	,	,	PUNCT
ma-80	271	12	as	as	SCONJ
ma-80	271	13	specified	specify	VERB
ma-80	271	14	in	in	ADP
ma-80	271	15	theorem	theorem	ADJ
ma-80	271	16	3.1	3.1	NUM
ma-80	271	17	,	,	PUNCT
ma-80	271	18	is	be	AUX
ma-80	271	19	to	to	PART
ma-80	271	20	utilize	utilize	VERB
ma-80	271	21	the	the	DET
ma-80	271	22	transformation	transformation	NOUN
ma-80	271	23	,	,	PUNCT
ma-80	271	24	,	,	PUNCT
ma-80	271	25	in	in	ADP
ma-80	271	26	the	the	DET
ma-80	271	27	relationship	relationship	NOUN
ma-80	271	28	which	which	PRON
ma-80	271	29	implies	imply	VERB
ma-80	271	30	.	.	PUNCT
ma-80	272	1	the	the	DET
ma-80	272	2	geometry	geometry	NOUN
ma-80	272	3	underpinning	underpin	VERB
ma-80	272	4	the	the	DET
ma-80	272	5	iteration	iteration	NOUN
ma-80	272	6	that	that	PRON
ma-80	272	7	leads	lead	VERB
ma-80	272	8	to	to	ADP
ma-80	272	9	the	the	DET
ma-80	272	10	approximations	approximation	NOUN
ma-80	272	11	is	be	AUX
ma-80	272	12	illustrated	illustrate	VERB
ma-80	272	13	in	in	ADP
ma-80	272	14	figure	figure	NOUN
ma-80	272	15	12	12	NUM
ma-80	272	16	.	.	PUNCT
ma-80	273	1	theorem	theorem	VERB
ma-80	273	2	3.3	3.3	NUM
ma-80	273	3	.	.	PUNCT
ma-80	274	1	alternative	alternative	ADJ
ma-80	274	2	geometrical	geometrical	ADJ
ma-80	274	3	iteration	iteration	NOUN
ma-80	274	4	.	.	PUNCT
ma-80	275	1	for	for	ADP
ma-80	275	2	fixed	fix	VERB
ma-80	275	3	,	,	PUNCT
ma-80	275	4	,	,	PUNCT
ma-80	275	5	iterative	iterative	NOUN
ma-80	275	6	approximations	approximation	NOUN
ma-80	275	7	for	for	ADP
ma-80	275	8	the	the	DET
ma-80	275	9	lambert	lambert	PROPN
ma-80	275	10	w	w	PROPN
ma-80	275	11	function	function	NOUN
ma-80	275	12	can	can	AUX
ma-80	275	13	be	be	AUX
ma-80	275	14	defined	define	VERB
ma-80	275	15	according	accord	VERB
ma-80	275	16	to	to	ADP
ma-80	275	17	(	(	PUNCT
ma-80	275	18	47	47	NUM
ma-80	275	19	)	)	PUNCT
ma-80	275	20	and	and	CCONJ
ma-80	275	21	it	it	PRON
ma-80	275	22	is	be	AUX
ma-80	275	23	the	the	DET
ma-80	275	24	case	case	NOUN
ma-80	275	25	that	that	SCONJ
ma-80	275	26	as	as	SCONJ
ma-80	275	27	specified	specify	VERB
ma-80	275	28	in	in	ADP
ma-80	275	29	theorem	theorem	ADJ
ma-80	275	30	3.1	3.1	NUM
ma-80	275	31	.	.	PUNCT
ma-80	276	1	proof	proof	NOUN
ma-80	276	2	.	.	PUNCT
ma-80	277	1	consider	consider	VERB
ma-80	277	2	the	the	DET
ma-80	277	3	case	case	NOUN
ma-80	277	4	of	of	ADP
ma-80	277	5	fixed	fix	VERB
ma-80	277	6	and	and	CCONJ
ma-80	277	7	the	the	DET
ma-80	277	8	geometry	geometry	NOUN
ma-80	277	9	illustrated	illustrate	VERB
ma-80	277	10	in	in	ADP
ma-80	277	11	figure	figure	NOUN
ma-80	277	12	12	12	NUM
ma-80	277	13	which	which	PRON
ma-80	277	14	is	be	AUX
ma-80	277	15	based	base	VERB
ma-80	277	16	on	on	ADP
ma-80	277	17	affine	affine	ADJ
ma-80	277	18	approximations	approximation	NOUN
ma-80	277	19	to	to	PART
ma-80	277	20	find	find	VERB
ma-80	277	21	,	,	PUNCT
ma-80	277	22	iteratively	iteratively	ADV
ma-80	277	23	,	,	PUNCT
ma-80	277	24	the	the	DET
ma-80	277	25	solution	solution	NOUN
ma-80	277	26	to	to	ADP
ma-80	277	27	.	.	PUNCT
ma-80	278	1	the	the	DET
ma-80	278	2	inin1	inin1	NOUN
ma-80	278	3	y	y	NOUN
ma-80	278	4			PROPN
ma-80	278	5	y=	y=	VERB
ma-80	278	6	d1	d1	PROPN
ma-80	278	7	y	y	NOUN
ma-80	278	8			PROPN
ma-80	278	9	1	1	NUM
ma-80	278	10	y+	y+	NUM
ma-80	278	11	=	=	PROPN
ma-80	278	12	n2	n2	ADJ
ma-80	278	13	y	y	NOUN
ma-80	278	14			PUNCT
ma-80	278	15	y	y	NOUN
ma-80	278	16	1	1	NUM
ma-80	278	17	1	1	NUM
ma-80	278	18	y+	y+	NOUN
ma-80	278	19	ln+	ln+	PUNCT
ma-80	278	20	=	=	PROPN
ma-80	278	21	d2	d2	PROPN
ma-80	278	22	y	y	PROPN
ma-80	278	23			PROPN
ma-80	278	24	1	1	NUM
ma-80	278	25	2y+	2y+	NUM
ma-80	278	26	=	=	NOUN
ma-80	278	27	n3	n3	VERB
ma-80	278	28	y	y	NOUN
ma-80	278	29			PROPN
ma-80	278	30	y	y	NOUN
ma-80	278	31	1	1	NUM
ma-80	278	32	1	1	NUM
ma-80	278	33	y+	y+	NOUN
ma-80	278	34	ln+	ln+	PUNCT
ma-80	278	35			NOUN
ma-80	278	36	1	1	NUM
ma-80	278	37	1	1	NUM
ma-80	278	38	2y+	2y+	NUM
ma-80	278	39	ln	ln	NOUN
ma-80	278	40	1	1	NUM
ma-80	278	41	1	1	NUM
ma-80	278	42	y+	y+	NOUN
ma-80	278	43	ln+	ln+	NOUN
ma-80	278	44	ln–+	ln–+	ADJ
ma-80	278	45	=	=	NOUN
ma-80	278	46	d3	d3	VERB
ma-80	278	47	y	y	NOUN
ma-80	278	48			PROPN
ma-80	278	49	1	1	NUM
ma-80	278	50	3y	3y	NUM
ma-80	278	51	y	y	PROPN
ma-80	278	52	1	1	NUM
ma-80	278	53	y+	y+	NOUN
ma-80	278	54	ln+	ln+	PROPN
ma-80	278	55	+	+	NUM
ma-80	278	56	=	=	PROPN
ma-80	278	57	n4	n4	PROPN
ma-80	278	58	y	y	NOUN
ma-80	279	1			PUNCT
ma-80	279	2	y	y	NOUN
ma-80	279	3	1	1	NUM
ma-80	279	4	1	1	NUM
ma-80	279	5	y+	y+	NOUN
ma-80	279	6	ln+	ln+	PUNCT
ma-80	279	7			NOUN
ma-80	279	8	1	1	NUM
ma-80	279	9	1	1	NUM
ma-80	279	10	2y+	2y+	NUM
ma-80	279	11	ln	ln	NOUN
ma-80	279	12	1	1	NUM
ma-80	279	13	1	1	NUM
ma-80	279	14	y+	y+	NOUN
ma-80	279	15	ln+	ln+	PUNCT
ma-80	279	16	ln–+	ln–+	PUNCT
ma-80	279	17	=	=	NOUN
ma-80	279	18	1	1	NUM
ma-80	279	19	1	1	NUM
ma-80	279	20	3y	3y	NUM
ma-80	279	21	y	y	PROPN
ma-80	279	22	1	1	NUM
ma-80	279	23	y+	y+	NOUN
ma-80	279	24	ln+	ln+	PROPN
ma-80	280	1	+	+	PROPN
ma-80	280	2			ADJ
ma-80	280	3	ln	ln	NOUN
ma-80	280	4	1	1	NUM
ma-80	280	5	1	1	NUM
ma-80	280	6	y+	y+	NOUN
ma-80	280	7	ln+	ln+	PUNCT
ma-80	280	8			NOUN
ma-80	280	9	1	1	NUM
ma-80	280	10	1	1	NUM
ma-80	280	11	2y+	2y+	NUM
ma-80	280	12	ln	ln	NOUN
ma-80	280	13	1	1	NUM
ma-80	280	14	1	1	NUM
ma-80	280	15	y+	y+	NOUN
ma-80	280	16	ln+	ln+	PUNCT
ma-80	280	17	ln–+ln–+	ln–+ln–+	PROPN
ma-80	280	18	,	,	PUNCT
ma-80	280	19	d4	d4	PROPN
ma-80	280	20	y	y	PROPN
ma-80	280	21			PROPN
ma-80	280	22	1	1	NUM
ma-80	280	23	3y	3y	NUM
ma-80	280	24	y	y	PROPN
ma-80	280	25	1	1	NUM
ma-80	280	26	y+	y+	NOUN
ma-80	280	27	ln+	ln+	PROPN
ma-80	281	1	+	+	CCONJ
ma-80	281	2	y	y	PROPN
ma-80	281	3	1	1	NUM
ma-80	281	4	1	1	NUM
ma-80	281	5	y+	y+	NOUN
ma-80	281	6	ln+	ln+	PUNCT
ma-80	281	7			NOUN
ma-80	281	8	1	1	NUM
ma-80	281	9	1	1	NUM
ma-80	281	10	2y+	2y+	NOUN
ma-80	281	11	ln	ln	PROPN
ma-80	281	12	1	1	NUM
ma-80	281	13	1	1	NUM
ma-80	281	14	y+	y+	NOUN
ma-80	281	15	ln+	ln+	NOUN
ma-80	281	16	ln–+	ln–+	X
ma-80	281	17	.+=	.+=	PUNCT
ma-80	282	1	wu1	wu1	NOUN
ma-80	282	2	wu2	wu2	NOUN
ma-80	282	3			NOUN
ma-80	282	4	x	x	X
ma-80	283	1	z	z	VERB
ma-80	283	2	ln=	ln=	NOUN
ma-80	284	1	x	x	PUNCT
ma-80	285	1	0	0	NOUN
ma-80	285	2	z	z	NOUN
ma-80	285	3	1	1	NUM
ma-80	285	4	y	y	PROPN
ma-80	285	5	xe	xe	PROPN
ma-80	285	6	x	x	PUNCT
ma-80	285	7	=	=	PUNCT
ma-80	285	8	y	y	PROPN
ma-80	285	9	z	z	PROPN
ma-80	285	10	z	z	PROPN
ma-80	285	11	ln=	ln=	NOUN
ma-80	286	1	figure	figure	NOUN
ma-80	286	2	12	12	NUM
ma-80	286	3	.	.	PUNCT
ma-80	287	1	illustration	illustration	NOUN
ma-80	287	2	of	of	ADP
ma-80	287	3	the	the	DET
ma-80	287	4	geometry	geometry	NOUN
ma-80	287	5	underpinning	underpin	VERB
ma-80	287	6	the	the	DET
ma-80	287	7	iterative	iterative	NOUN
ma-80	287	8	relationship	relationship	NOUN
ma-80	287	9	to	to	PART
ma-80	287	10	find	find	VERB
ma-80	287	11	approximations	approximation	NOUN
ma-80	287	12	to	to	PART
ma-80	287	13	which	which	PRON
ma-80	287	14	is	be	AUX
ma-80	287	15	the	the	DET
ma-80	287	16	solution	solution	NOUN
ma-80	287	17	of	of	ADP
ma-80	287	18	for	for	ADP
ma-80	287	19	fixed.zo	fixed.zo	X
ma-80	287	20	z	z	X
ma-80	287	21	z	z	PROPN
ma-80	288	1	ln	ln	PROPN
ma-80	288	2	y=	y=	NUM
ma-80	289	1	y	y	PROPN
ma-80	289	2	1	1	NUM
ma-80	289	3	z	z	NOUN
ma-80	289	4	y	y	PROPN
ma-80	289	5	zo	zo	PROPN
ma-80	289	6	z	z	PROPN
ma-80	289	7	z	z	PROPN
ma-80	289	8	ln	ln	PROPN
ma-80	290	1	z2z1	z2z1	PROPN
ma-80	290	2	z	z	NOUN
ma-80	290	3	1	1	NUM
ma-80	290	4	–	–	PUNCT
ma-80	290	5	z1	z1	ADJ
ma-80	290	6	z1	z1	PROPN
ma-80	291	1	ln	ln	PUNCT
ma-80	292	1	z	z	NOUN
ma-80	292	2	z1–	z1–	NUM
ma-80	292	3			X
ma-80	292	4	z1	z1	PROPN
ma-80	293	1	ln	ln	PRON
ma-80	293	2	1+	1+	NUM
ma-80	293	3	+	+	NOUN
ma-80	293	4	y2	y2	PROPN
ma-80	293	5	y1	y1	NOUN
ma-80	293	6	z1	z1	VERB
ma-80	293	7	1	1	NUM
ma-80	293	8	y+=	y+=	PROPN
ma-80	293	9	y	y	NOUN
ma-80	293	10	y	y	PROPN
ma-80	293	11	0	0	NUM
ma-80	293	12	zi	zi	PROPN
ma-80	293	13	zi	zi	PROPN
ma-80	293	14	1	1	NUM
ma-80	293	15	–	–	PUNCT
ma-80	293	16	zi	zi	NOUN
ma-80	293	17	1	1	NUM
ma-80	293	18	–	–	PUNCT
ma-80	293	19	zi	zi	NOUN
ma-80	293	20	1–	1–	NUM
ma-80	293	21	ln	ln	PROPN
ma-80	293	22	y	y	PROPN
ma-80	293	23	–	–	PUNCT
ma-80	293	24	zi	zi	NOUN
ma-80	293	25	1–	1–	NUM
ma-80	293	26	ln	ln	NOUN
ma-80	293	27	1	1	NUM
ma-80	293	28	+	+	CCONJ
ma-80	293	29	-----------------------------------------	-----------------------------------------	ADJ
ma-80	293	30	–	–	PUNCT
ma-80	293	31	=	=	NOUN
ma-80	293	32	z1	z1	NOUN
ma-80	293	33	1	1	NUM
ma-80	293	34	y+	y+	NUM
ma-80	293	35	=	=	PROPN
ma-80	293	36	xi	xi	ADP
ma-80	293	37	zi	zi	PROPN
ma-80	293	38	ln	ln	DET
ma-80	293	39	=	=	PROPN
ma-80	293	40	xi	xi	NUM
ma-80	293	41	wui	wui	PROPN
ma-80	293	42	y	y	PROPN
ma-80	293	43	=	=	NOUN
ma-80	294	1	y	y	PROPN
ma-80	294	2	zo	zo	PROPN
ma-80	294	3	y	y	PROPN
ma-80	294	4	z	z	PROPN
ma-80	294	5	z	z	PROPN
ma-80	294	6	ln=	ln=	PUNCT
ma-80	295	1	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	PROPN
ma-80	295	2	tial	tial	ADJ
ma-80	295	3	value	value	NOUN
ma-80	295	4	is	be	AUX
ma-80	295	5	established	establish	VERB
ma-80	295	6	by	by	ADP
ma-80	295	7	the	the	DET
ma-80	295	8	intersection	intersection	NOUN
ma-80	295	9	of	of	ADP
ma-80	295	10	a	a	DET
ma-80	295	11	first	first	ADJ
ma-80	295	12	order	order	NOUN
ma-80	295	13	taylor	taylor	PROPN
ma-80	295	14	series	series	PROPN
ma-80	295	15	for	for	ADP
ma-80	295	16	at	at	ADP
ma-80	295	17	the	the	DET
ma-80	295	18	point	point	NOUN
ma-80	295	19	,	,	PUNCT
ma-80	295	20	which	which	PRON
ma-80	295	21	is	be	AUX
ma-80	295	22	,	,	PUNCT
ma-80	295	23	and	and	CCONJ
ma-80	295	24	the	the	DET
ma-80	295	25	level	level	NOUN
ma-80	295	26	.	.	PUNCT
ma-80	296	1	the	the	DET
ma-80	296	2	solution	solution	NOUN
ma-80	296	3	is	be	AUX
ma-80	296	4	.	.	PUNCT
ma-80	297	1	a	a	DET
ma-80	297	2	first	first	ADJ
ma-80	297	3	order	order	NOUN
ma-80	297	4	taylor	taylor	PROPN
ma-80	297	5	series	series	PROPN
ma-80	297	6	for	for	ADP
ma-80	297	7	at	at	ADP
ma-80	297	8	this	this	DET
ma-80	297	9	point	point	NOUN
ma-80	297	10	is	be	AUX
ma-80	297	11	and	and	CCONJ
ma-80	297	12	the	the	DET
ma-80	297	13	intersection	intersection	NOUN
ma-80	297	14	of	of	ADP
ma-80	297	15	this	this	DET
ma-80	297	16	approximation	approximation	NOUN
ma-80	297	17	with	with	ADP
ma-80	297	18	the	the	DET
ma-80	297	19	level	level	NOUN
ma-80	297	20	is	be	AUX
ma-80	297	21	the	the	DET
ma-80	297	22	point	point	NOUN
ma-80	297	23	defined	define	VERB
ma-80	297	24	according	accord	VERB
ma-80	297	25	to	to	ADP
ma-80	297	26	(	(	PUNCT
ma-80	297	27	48	48	NUM
ma-80	297	28	)	)	PUNCT
ma-80	297	29	iteration	iteration	NOUN
ma-80	297	30	in	in	ADP
ma-80	297	31	this	this	DET
ma-80	297	32	manner	manner	NOUN
ma-80	297	33	leads	lead	VERB
ma-80	297	34	to	to	ADP
ma-80	297	35	the	the	DET
ma-80	297	36	stated	state	VERB
ma-80	297	37	general	general	ADJ
ma-80	297	38	iteration	iteration	NOUN
ma-80	297	39	formulas	formula	NOUN
ma-80	297	40	.	.	PUNCT
ma-80	298	1	3.3.1	3.3.1	X
ma-80	298	2	.	.	PUNCT
ma-80	298	3	explicit	explicit	ADJ
ma-80	298	4	formulas	formula	NOUN
ma-80	298	5	.	.	PUNCT
ma-80	299	1	approximations	approximation	NOUN
ma-80	299	2	,	,	PUNCT
ma-80	299	3	of	of	ADP
ma-80	299	4	orders	order	NOUN
ma-80	299	5	one	one	NUM
ma-80	299	6	to	to	ADP
ma-80	299	7	three	three	NUM
ma-80	299	8	,	,	PUNCT
ma-80	299	9	are	be	AUX
ma-80	299	10	:	:	PUNCT
ma-80	299	11	(	(	PUNCT
ma-80	299	12	49	49	NUM
ma-80	299	13	)	)	PUNCT
ma-80	299	14	(	(	PUNCT
ma-80	299	15	50	50	NUM
ma-80	299	16	)	)	PUNCT
ma-80	299	17	(	(	PUNCT
ma-80	299	18	51	51	NUM
ma-80	299	19	)	)	PUNCT
ma-80	299	20	3.4	3.4	NUM
ma-80	299	21	.	.	PUNCT
ma-80	299	22	iterative	iterative	ADJ
ma-80	299	23	algorithm	algorithm	NOUN
ma-80	299	24	for	for	ADP
ma-80	299	25	(	(	PUNCT
ma-80	299	26	-1	-1	ADJ
ma-80	299	27	/	/	SYM
ma-80	299	28	e,0	e,0	NOUN
ma-80	299	29	]	]	PUNCT
ma-80	299	30	.	.	PUNCT
ma-80	300	1	for	for	ADP
ma-80	300	2	the	the	DET
ma-80	300	3	case	case	NOUN
ma-80	300	4	of	of	ADP
ma-80	300	5	,	,	PUNCT
ma-80	300	6	the	the	DET
ma-80	300	7	geometric	geometric	ADJ
ma-80	300	8	approach	approach	NOUN
ma-80	300	9	,	,	PUNCT
ma-80	300	10	illustrated	illustrate	VERB
ma-80	300	11	in	in	ADP
ma-80	300	12	figure	figure	NOUN
ma-80	300	13	13	13	NUM
ma-80	300	14	,	,	PUNCT
ma-80	300	15	can	can	AUX
ma-80	300	16	be	be	AUX
ma-80	300	17	utilized	utilize	VERB
ma-80	300	18	to	to	PART
ma-80	300	19	establish	establish	VERB
ma-80	300	20	an	an	DET
ma-80	300	21	algorithm	algorithm	NOUN
ma-80	300	22	for	for	ADP
ma-80	300	23	determining	determine	VERB
ma-80	300	24	approximations	approximation	NOUN
ma-80	300	25	to	to	ADP
ma-80	300	26	the	the	DET
ma-80	300	27	lambert	lambert	PROPN
ma-80	300	28	w	w	PROPN
ma-80	300	29	function	function	PROPN
ma-80	300	30	.	.	PUNCT
ma-80	301	1	theorem	theorem	VERB
ma-80	301	2	3.4	3.4	NUM
ma-80	301	3	.	.	PUNCT
ma-80	301	4	iterative	iterative	ADJ
ma-80	301	5	algorithm	algorithm	NOUN
ma-80	301	6	for	for	ADP
ma-80	301	7	(	(	PUNCT
ma-80	301	8	-1	-1	ADJ
ma-80	301	9	/	/	SYM
ma-80	301	10	e,0	e,0	NOUN
ma-80	301	11	]	]	PUNCT
ma-80	301	12	.	.	PUNCT
ma-80	302	1	an	an	DET
ma-80	302	2	iterative	iterative	NOUN
ma-80	302	3	algorithm	algorithm	NOUN
ma-80	302	4	for	for	ADP
ma-80	302	5	defining	define	VERB
ma-80	302	6	approximations	approximation	NOUN
ma-80	302	7	to	to	ADP
ma-80	302	8	,	,	PUNCT
ma-80	302	9	for	for	ADP
ma-80	302	10	,	,	PUNCT
ma-80	302	11	is	be	AUX
ma-80	302	12	:	:	PUNCT
ma-80	302	13	(	(	PUNCT
ma-80	302	14	52	52	NUM
ma-80	302	15	)	)	PUNCT
ma-80	302	16	proof	proof	NOUN
ma-80	302	17	.	.	PUNCT
ma-80	303	1	consider	consider	VERB
ma-80	303	2	the	the	DET
ma-80	303	3	illustration	illustration	NOUN
ma-80	303	4	shown	show	VERB
ma-80	303	5	in	in	ADP
ma-80	303	6	figure	figure	NOUN
ma-80	303	7	13	13	NUM
ma-80	303	8	.	.	PUNCT
ma-80	304	1	with	with	ADP
ma-80	304	2	an	an	DET
ma-80	304	3	initial	initial	ADJ
ma-80	304	4	approximation	approximation	NOUN
ma-80	304	5	for	for	ADP
ma-80	304	6	of	of	ADP
ma-80	304	7	,	,	PUNCT
ma-80	304	8	a	a	DET
ma-80	304	9	first	first	ADJ
ma-80	304	10	order	order	NOUN
ma-80	304	11	taylor	taylor	PROPN
ma-80	304	12	series	series	PROPN
ma-80	304	13	for	for	ADP
ma-80	304	14	,	,	PUNCT
ma-80	304	15	based	base	VERB
ma-80	304	16	on	on	ADP
ma-80	304	17	the	the	DET
ma-80	304	18	point	point	NOUN
ma-80	304	19	,	,	PUNCT
ma-80	304	20	with	with	SCONJ
ma-80	304	21	,	,	PUNCT
ma-80	304	22	is	be	AUX
ma-80	304	23	.	.	PUNCT
ma-80	305	1	the	the	DET
ma-80	305	2	intersection	intersection	NOUN
ma-80	305	3	of	of	ADP
ma-80	305	4	this	this	DET
ma-80	305	5	taylor	taylor	PROPN
ma-80	305	6	series	series	PROPN
ma-80	305	7	with	with	ADP
ma-80	305	8	,	,	PUNCT
ma-80	305	9	at	at	ADP
ma-80	305	10	the	the	DET
ma-80	305	11	point	point	NOUN
ma-80	305	12	,	,	PUNCT
ma-80	305	13	leads	lead	VERB
ma-80	305	14	to	to	ADP
ma-80	305	15	(	(	PUNCT
ma-80	305	16	53	53	NUM
ma-80	305	17	)	)	PUNCT
ma-80	305	18	the	the	DET
ma-80	305	19	value	value	NOUN
ma-80	305	20	of	of	ADP
ma-80	305	21	associated	associate	VERB
ma-80	305	22	with	with	ADP
ma-80	305	23	is	be	AUX
ma-80	305	24	.	.	PUNCT
ma-80	306	1	a	a	DET
ma-80	306	2	first	first	ADJ
ma-80	306	3	order	order	NOUN
ma-80	306	4	taylor	taylor	PROPN
ma-80	306	5	series	series	PROPN
ma-80	306	6	approximation	approximation	NOUN
ma-80	306	7	for	for	ADP
ma-80	306	8	at	at	ADP
ma-80	306	9	the	the	DET
ma-80	306	10	point	point	NOUN
ma-80	306	11	is	be	AUX
ma-80	306	12	and	and	CCONJ
ma-80	306	13	the	the	DET
ma-80	306	14	intersection	intersection	NOUN
ma-80	306	15	of	of	ADP
ma-80	306	16	this	this	DET
ma-80	306	17	approximation	approximation	NOUN
ma-80	306	18	with	with	ADP
ma-80	306	19	,	,	PUNCT
ma-80	306	20	at	at	ADP
ma-80	306	21	the	the	DET
ma-80	306	22	point	point	NOUN
ma-80	306	23	,	,	PUNCT
ma-80	306	24	leads	lead	VERB
ma-80	306	25	to	to	ADP
ma-80	306	26	z	z	PROPN
ma-80	306	27	z	z	PROPN
ma-80	306	28	ln	ln	PROPN
ma-80	306	29	z	z	NOUN
ma-80	306	30	1=	1=	X
ma-80	306	31	z	z	NOUN
ma-80	306	32	1	1	NUM
ma-80	306	33	–	–	PUNCT
ma-80	306	34	y	y	PROPN
ma-80	306	35	z1	z1	PROPN
ma-80	306	36	1	1	NUM
ma-80	306	37	y+=	y+=	PROPN
ma-80	307	1	z	z	NOUN
ma-80	307	2	z	z	PROPN
ma-80	308	1	ln	ln	PROPN
ma-80	308	2	z1	z1	ADJ
ma-80	308	3	z1	z1	PROPN
ma-80	308	4	ln	ln	PUNCT
ma-80	309	1	z	z	NOUN
ma-80	309	2	z1–	z1–	NUM
ma-80	309	3			X
ma-80	309	4	z1	z1	PROPN
ma-80	310	1	ln	ln	PRON
ma-80	310	2	1+	1+	NUM
ma-80	310	3	+	+	NOUN
ma-80	310	4	y	y	PROPN
ma-80	310	5	z2	z2	PROPN
ma-80	310	6	z2	z2	PROPN
ma-80	310	7	z1	z1	VERB
ma-80	310	8	z1	z1	PROPN
ma-80	310	9	z1	z1	PROPN
ma-80	310	10	ln	ln	PROPN
ma-80	310	11	y	y	PROPN
ma-80	310	12	–	–	PUNCT
ma-80	310	13	z1	z1	PROPN
ma-80	310	14	ln	ln	NOUN
ma-80	310	15	1	1	NUM
ma-80	310	16	+	+	NUM
ma-80	310	17	-----------------------------.–=	-----------------------------.–=	NOUN
ma-80	310	18	z1	z1	VERB
ma-80	310	19	y	y	NOUN
ma-80	310	20			PROPN
ma-80	310	21	1	1	NUM
ma-80	310	22	y+	y+	NUM
ma-80	310	23	=	=	NOUN
ma-80	310	24	x1	x1	NOUN
ma-80	310	25	wu1	wu1	ADJ
ma-80	310	26	y	y	NOUN
ma-80	310	27			PROPN
ma-80	310	28	1	1	NUM
ma-80	310	29	y+	y+	NOUN
ma-80	310	30	ln	ln	PROPN
ma-80	310	31	=	=	PROPN
ma-80	310	32	=	=	SYM
ma-80	310	33	z2	z2	PROPN
ma-80	310	34	y	y	NOUN
ma-80	310	35			PROPN
ma-80	310	36	1	1	NUM
ma-80	310	37	2y+	2y+	NUM
ma-80	310	38	1	1	NUM
ma-80	310	39	1	1	NUM
ma-80	310	40	y+	y+	NOUN
ma-80	310	41	ln+	ln+	PROPN
ma-80	311	1	-------------------------------=	-------------------------------=	PROPN
ma-80	311	2	x2	x2	PROPN
ma-80	311	3	wu2	wu2	VERB
ma-80	311	4	y	y	NOUN
ma-80	311	5			PROPN
ma-80	311	6	1	1	NUM
ma-80	311	7	2y+	2y+	NUM
ma-80	311	8	1	1	NUM
ma-80	311	9	1	1	NUM
ma-80	311	10	y+	y+	NOUN
ma-80	311	11	ln+	ln+	PROPN
ma-80	311	12	-------------------------------ln	-------------------------------ln	NOUN
ma-80	311	13	=	=	PROPN
ma-80	311	14	=	=	SYM
ma-80	311	15	z3	z3	PROPN
ma-80	311	16	y	y	NOUN
ma-80	311	17			PROPN
ma-80	311	18	1	1	NUM
ma-80	311	19	3y	3y	NUM
ma-80	311	20	y	y	PROPN
ma-80	311	21	1	1	NUM
ma-80	311	22	y+	y+	NOUN
ma-80	311	23	ln+	ln+	PROPN
ma-80	312	1	+	+	CCONJ
ma-80	312	2	1	1	NUM
ma-80	312	3	1	1	NUM
ma-80	312	4	y+	y+	NOUN
ma-80	312	5	ln+	ln+	PUNCT
ma-80	312	6			NOUN
ma-80	312	7	1	1	NUM
ma-80	312	8	1	1	NUM
ma-80	312	9	2y+	2y+	NUM
ma-80	312	10	1	1	NUM
ma-80	312	11	1	1	NUM
ma-80	312	12	y+	y+	NOUN
ma-80	312	13	ln+	ln+	PROPN
ma-80	312	14	-------------------------------ln+	-------------------------------ln+	PUNCT
ma-80	312	15	-----------------------------------------------------------------------------------------------=	-----------------------------------------------------------------------------------------------=	PROPN
ma-80	313	1	x3	x3	PROPN
ma-80	313	2	wu3	wu3	VERB
ma-80	313	3	y	y	NOUN
ma-80	313	4			PROPN
ma-80	313	5	1	1	NUM
ma-80	313	6	3y	3y	NUM
ma-80	313	7	y	y	PROPN
ma-80	313	8	1	1	NUM
ma-80	313	9	y+	y+	NOUN
ma-80	313	10	ln+	ln+	PROPN
ma-80	314	1	+	+	CCONJ
ma-80	314	2	1	1	NUM
ma-80	314	3	1	1	NUM
ma-80	314	4	y+	y+	NOUN
ma-80	314	5	ln+	ln+	PUNCT
ma-80	314	6			NOUN
ma-80	314	7	1	1	NUM
ma-80	314	8	1	1	NUM
ma-80	314	9	2y+	2y+	NUM
ma-80	314	10	1	1	NUM
ma-80	314	11	1	1	NUM
ma-80	314	12	y+	y+	NOUN
ma-80	314	13	ln+	ln+	NOUN
ma-80	314	14	-------------------------------ln+	-------------------------------ln+	PUNCT
ma-80	315	1	----------------------------------------------------------------------------------------------.ln=	----------------------------------------------------------------------------------------------.ln=	PROPN
ma-80	315	2	=	=	SYM
ma-80	315	3	y	y	PROPN
ma-80	315	4	1	1	NUM
ma-80	315	5	–	–	PUNCT
ma-80	315	6	e	e	ADV
ma-80	315	7	0	0	NUM
ma-80	316	1			PROPN
ma-80	316	2	x	x	SYM
ma-80	316	3	w	w	PRON
ma-80	316	4	y	y	NOUN
ma-80	316	5	=	=	NOUN
ma-80	316	6	y	y	NOUN
ma-80	316	7	1	1	NUM
ma-80	316	8	e	e	ADV
ma-80	316	9	–	–	PUNCT
ma-80	316	10	0	0	ADJ
ma-80	316	11			NOUN
ma-80	316	12	xi	xi	X
ma-80	316	13	yi	yi	PROPN
ma-80	316	14	1	1	NUM
ma-80	316	15	–	–	PUNCT
ma-80	316	16	1	1	NUM
ma-80	316	17	xi	xi	ADP
ma-80	316	18	1–+	1–+	NUM
ma-80	316	19			PROPN
ma-80	316	20	1	1	NUM
ma-80	316	21	yi	yi	NOUN
ma-80	316	22	1–+	1–+	NUM
ma-80	316	23	-------------------------------------=	-------------------------------------=	NOUN
ma-80	317	1	x0	x0	PROPN
ma-80	317	2	0=	0=	NUM
ma-80	318	1	y0	y0	PROPN
ma-80	318	2	y=	y=	VERB
ma-80	318	3	yi	yi	INTJ
ma-80	319	1	ye	ye	INTJ
ma-80	319	2	xi	xi	PROPN
ma-80	319	3	–	–	PUNCT
ma-80	319	4	.=	.=	NOUN
ma-80	320	1	xo	xo	PROPN
ma-80	321	1	x0	x0	PROPN
ma-80	321	2	0=	0=	NOUN
ma-80	322	1	ye	ye	NUM
ma-80	322	2	x	x	PROPN
ma-80	322	3	–	–	PUNCT
ma-80	322	4	x0	x0	PROPN
ma-80	322	5	y0	y0	PROPN
ma-80	323	1			PUNCT
ma-80	323	2	y0	y0	NOUN
ma-80	323	3	y=	y=	NUM
ma-80	324	1	y0	y0	NOUN
ma-80	324	2	1	1	NUM
ma-80	324	3	x	x	SYM
ma-80	324	4	x0–	x0–	NUM
ma-80	325	1	–	–	PROPN
ma-80	325	2			NOUN
ma-80	326	1	x	x	PUNCT
ma-80	326	2	x1	x1	NUM
ma-80	327	1	x1	x1	NUM
ma-80	327	2	y0	y0	NOUN
ma-80	327	3	1	1	NUM
ma-80	327	4	x0+	x0+	X
ma-80	327	5			PROPN
ma-80	327	6	1	1	NUM
ma-80	327	7	y0	y0	NUM
ma-80	327	8	+	+	CCONJ
ma-80	327	9	-------------------------.=	-------------------------.=	ADJ
ma-80	327	10	ye	ye	NOUN
ma-80	327	11	x	x	PROPN
ma-80	327	12	–	–	PUNCT
ma-80	327	13	x1	x1	VERB
ma-80	327	14	y1	y1	NOUN
ma-80	327	15	ye	ye	NUM
ma-80	327	16	x1	x1	PROPN
ma-80	327	17	–	–	PUNCT
ma-80	327	18	=	=	PUNCT
ma-80	327	19	ye	ye	NUM
ma-80	327	20	x	x	PROPN
ma-80	327	21	–	–	PUNCT
ma-80	327	22	x1	x1	PROPN
ma-80	328	1	y1	y1	NOUN
ma-80	328	2			PUNCT
ma-80	328	3	y1	y1	NOUN
ma-80	328	4	1	1	NUM
ma-80	328	5	x	x	SYM
ma-80	328	6	x1–	x1–	PUNCT
ma-80	329	1	–	–	PROPN
ma-80	329	2			NOUN
ma-80	329	3	x	x	SYM
ma-80	329	4	x2	x2	PROPN
ma-80	329	5	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	PROPN
ma-80	329	6	(	(	PUNCT
ma-80	329	7	54	54	NUM
ma-80	329	8	)	)	PUNCT
ma-80	329	9	the	the	DET
ma-80	329	10	value	value	NOUN
ma-80	329	11	of	of	ADP
ma-80	329	12	associated	associate	VERB
ma-80	329	13	with	with	ADP
ma-80	329	14	this	this	DET
ma-80	329	15	value	value	NOUN
ma-80	329	16	is	be	AUX
ma-80	329	17	.	.	PUNCT
ma-80	330	1	iteration	iteration	NOUN
ma-80	330	2	in	in	ADP
ma-80	330	3	this	this	DET
ma-80	330	4	manner	manner	NOUN
ma-80	330	5	leads	lead	VERB
ma-80	330	6	to	to	ADP
ma-80	330	7	the	the	DET
ma-80	330	8	general	general	ADJ
ma-80	330	9	formula	formula	NOUN
ma-80	330	10	as	as	SCONJ
ma-80	330	11	stated	state	VERB
ma-80	330	12	in	in	ADP
ma-80	330	13	the	the	DET
ma-80	330	14	theorem	theorem	NOUN
ma-80	330	15	.	.	PROPN
ma-80	331	1	3.4.1	3.4.1	X
ma-80	331	2	.	.	PUNCT
ma-80	331	3	explicit	explicit	ADJ
ma-80	331	4	approximations	approximation	NOUN
ma-80	331	5	.	.	PUNCT
ma-80	332	1	approximations	approximation	NOUN
ma-80	332	2	,	,	PUNCT
ma-80	332	3	for	for	ADP
ma-80	332	4	orders	order	NOUN
ma-80	332	5	one	one	NUM
ma-80	332	6	to	to	ADP
ma-80	332	7	four	four	NUM
ma-80	332	8	,	,	PUNCT
ma-80	332	9	are	be	AUX
ma-80	332	10	:	:	PUNCT
ma-80	332	11	(	(	PUNCT
ma-80	332	12	55	55	NUM
ma-80	332	13	)	)	PUNCT
ma-80	332	14	(	(	PUNCT
ma-80	332	15	56	56	NUM
ma-80	332	16	)	)	PUNCT
ma-80	332	17	3.4.2	3.4.2	NUM
ma-80	332	18	.	.	PUNCT
ma-80	333	1	results	result	NOUN
ma-80	333	2	.	.	PUNCT
ma-80	334	1	the	the	DET
ma-80	334	2	relative	relative	ADJ
ma-80	334	3	error	error	NOUN
ma-80	334	4	in	in	ADP
ma-80	334	5	the	the	DET
ma-80	334	6	iterative	iterative	NOUN
ma-80	334	7	approximations	approximation	NOUN
ma-80	334	8	specified	specify	VERB
ma-80	334	9	in	in	ADP
ma-80	334	10	theorem	theorem	ADJ
ma-80	334	11	3.4	3.4	NUM
ma-80	334	12	are	be	AUX
ma-80	334	13	shown	show	VERB
ma-80	334	14	in	in	ADP
ma-80	334	15	figure	figure	NOUN
ma-80	334	16	14	14	NUM
ma-80	334	17	.	.	PUNCT
ma-80	335	1	for	for	ADP
ma-80	335	2	orders	order	NOUN
ma-80	335	3	two	two	NUM
ma-80	335	4	,	,	PUNCT
ma-80	335	5	and	and	CCONJ
ma-80	335	6	higher	high	ADJ
ma-80	335	7	,	,	PUNCT
ma-80	335	8	the	the	DET
ma-80	335	9	approximation	approximation	NOUN
ma-80	335	10	are	be	AUX
ma-80	335	11	more	more	ADV
ma-80	335	12	accurate	accurate	ADJ
ma-80	335	13	than	than	ADP
ma-80	335	14	the	the	DET
ma-80	335	15	approximations	approximation	NOUN
ma-80	335	16	detailed	detail	VERB
ma-80	335	17	in	in	ADP
ma-80	335	18	theorem	theorem	ADJ
ma-80	335	19	3.1	3.1	NUM
ma-80	335	20	.	.	NOUN
ma-80	335	21	3.5	3.5	NUM
ma-80	335	22	.	.	PUNCT
ma-80	336	1	improved	improve	VERB
ma-80	336	2	approximations	approximation	NOUN
ma-80	336	3	for	for	ADP
ma-80	336	4	[	[	X
ma-80	336	5	0,∞	0,∞	NOUN
ma-80	336	6	)	)	PUNCT
ma-80	336	7	.	.	PUNCT
ma-80	337	1	improved	improved	ADJ
ma-80	337	2	approximations	approximation	NOUN
ma-80	337	3	,	,	PUNCT
ma-80	337	4	for	for	ADP
ma-80	337	5	the	the	DET
ma-80	337	6	interval	interval	NOUN
ma-80	337	7	,	,	PUNCT
ma-80	337	8	can	can	AUX
ma-80	337	9	be	be	AUX
ma-80	337	10	established	establish	VERB
ma-80	337	11	by	by	ADP
ma-80	337	12	using	use	VERB
ma-80	337	13	the	the	DET
ma-80	337	14	iteration	iteration	NOUN
ma-80	337	15	formula	formula	NOUN
ma-80	337	16	specified	specify	VERB
ma-80	337	17	in	in	ADP
ma-80	337	18	theorem	theorem	ADJ
ma-80	337	19	3.3	3.3	NUM
ma-80	337	20	and	and	CCONJ
ma-80	337	21	by	by	ADP
ma-80	337	22	using	use	VERB
ma-80	337	23	figure	figure	NOUN
ma-80	337	24	13	13	NUM
ma-80	337	25	.	.	PUNCT
ma-80	338	1	illustration	illustration	NOUN
ma-80	338	2	of	of	ADP
ma-80	338	3	the	the	DET
ma-80	338	4	geometry	geometry	NOUN
ma-80	338	5	underpinning	underpin	VERB
ma-80	338	6	the	the	DET
ma-80	338	7	iterative	iterative	NOUN
ma-80	338	8	relationship	relationship	NOUN
ma-80	338	9	to	to	PART
ma-80	338	10	find	find	VERB
ma-80	338	11	approximations	approximation	NOUN
ma-80	338	12	to	to	ADP
ma-80	338	13	,	,	PUNCT
ma-80	338	14	the	the	DET
ma-80	338	15	solution	solution	NOUN
ma-80	338	16	of	of	ADP
ma-80	338	17	,	,	PUNCT
ma-80	338	18	for	for	ADP
ma-80	338	19	the	the	DET
ma-80	338	20	case	case	NOUN
ma-80	338	21	of	of	ADP
ma-80	338	22	fixed	fix	VERB
ma-80	338	23	and	and	CCONJ
ma-80	338	24	.	.	PUNCT
ma-80	339	1	xo	xo	PROPN
ma-80	340	1	x	x	PUNCT
ma-80	340	2	ye	ye	NUM
ma-80	340	3	x	x	NOUN
ma-80	340	4	–	–	PUNCT
ma-80	340	5	=	=	SYM
ma-80	340	6	y	y	SYM
ma-80	340	7	y	y	PROPN
ma-80	340	8	1	1	NUM
ma-80	340	9	e–	e–	NOUN
ma-80	340	10	0	0	NUM
ma-80	341	1			PROPN
ma-80	341	2	x1	x1	PROPN
ma-80	342	1	x	x	PUNCT
ma-80	342	2	y	y	NOUN
ma-80	342	3	x	x	SYM
ma-80	342	4	x2	x2	NOUN
ma-80	342	5	y1	y1	INTJ
ma-80	342	6	ye	ye	NUM
ma-80	342	7	x	x	SYM
ma-80	342	8	–	–	PUNCT
ma-80	342	9	1=	1=	NUM
ma-80	342	10	xo	xo	NOUN
ma-80	343	1	y1	y1	NOUN
ma-80	343	2	1	1	NUM
ma-80	343	3	x	x	SYM
ma-80	343	4	x1–	x1–	PROPN
ma-80	344	1	–	–	PROPN
ma-80	344	2			NOUN
ma-80	344	3	ye	ye	NUM
ma-80	344	4	x	x	PROPN
ma-80	344	5	–	–	PUNCT
ma-80	344	6	y2	y2	NOUN
ma-80	344	7	ye	ye	NUM
ma-80	344	8	x	x	SYM
ma-80	344	9	–	–	PUNCT
ma-80	344	10	2=	2=	NUM
ma-80	344	11	y	y	PROPN
ma-80	344	12	1	1	NUM
ma-80	344	13	x	x	SYM
ma-80	344	14	x0–	x0–	NUM
ma-80	345	1	–	–	PROPN
ma-80	345	2			NOUN
ma-80	346	1	x0	x0	PROPN
ma-80	346	2	x2	x2	PROPN
ma-80	346	3	y1	y1	PROPN
ma-80	346	4	1	1	NUM
ma-80	346	5	x1+	x1+	PROPN
ma-80	346	6			PROPN
ma-80	346	7	1	1	NUM
ma-80	346	8	y1	y1	NOUN
ma-80	346	9	+	+	X
ma-80	346	10	-------------------------.=	-------------------------.=	ADJ
ma-80	346	11	ye	ye	NOUN
ma-80	346	12	x	x	NOUN
ma-80	346	13	–	–	PUNCT
ma-80	346	14	y2	y2	NOUN
ma-80	346	15	ye	ye	NUM
ma-80	346	16	x2	x2	PROPN
ma-80	346	17	–	–	PUNCT
ma-80	346	18	=	=	SYM
ma-80	347	1	we1	we1	X
ma-80	347	2	y	y	NOUN
ma-80	347	3			PUNCT
ma-80	347	4	y	y	PROPN
ma-80	347	5	1	1	NUM
ma-80	347	6	y+	y+	NUM
ma-80	347	7	------------=	------------=	PROPN
ma-80	347	8	we2	we2	ADJ
ma-80	347	9	y	y	NOUN
ma-80	347	10			PUNCT
ma-80	347	11	y	y	PROPN
ma-80	347	12	1	1	NUM
ma-80	347	13	2y+	2y+	NOUN
ma-80	347	14			PROPN
ma-80	347	15	1	1	NUM
ma-80	347	16	y+	y+	NOUN
ma-80	347	17			PROPN
ma-80	347	18	y	y	PROPN
ma-80	347	19	e	e	PROPN
ma-80	347	20	y	y	PROPN
ma-80	347	21	1	1	NUM
ma-80	347	22	y+	y+	NOUN
ma-80	347	23			PROPN
ma-80	348	1	+	+	NOUN
ma-80	348	2			ADJ
ma-80	348	3			ADP
ma-80	348	4	----------------------------------------------------=	----------------------------------------------------=	PUNCT
ma-80	348	5	we3	we3	VERB
ma-80	348	6	y	y	NOUN
ma-80	348	7			PUNCT
ma-80	348	8	y	y	PROPN
ma-80	348	9	y	y	PROPN
ma-80	348	10	2	2	NUM
ma-80	348	11	3y+	3y+	NOUN
ma-80	348	12			PROPN
ma-80	348	13	1	1	NUM
ma-80	348	14	y+	y+	NOUN
ma-80	348	15	ey	ey	PROPN
ma-80	349	1	1	1	NUM
ma-80	349	2	y+	y+	NOUN
ma-80	349	3			PROPN
ma-80	350	1	+	+	CCONJ
ma-80	350	2	1	1	NUM
ma-80	350	3	y+	y+	NOUN
ma-80	350	4			PROPN
ma-80	350	5	y	y	PROPN
ma-80	350	6	e	e	PROPN
ma-80	350	7	y	y	PROPN
ma-80	350	8	1	1	NUM
ma-80	350	9	y+	y+	NOUN
ma-80	350	10			PROPN
ma-80	351	1	+	+	NOUN
ma-80	351	2			ADJ
ma-80	351	3			PROPN
ma-80	351	4	y	y	PROPN
ma-80	351	5	y	y	PROPN
ma-80	351	6	1	1	NUM
ma-80	351	7	2y+	2y+	NOUN
ma-80	351	8			PROPN
ma-80	351	9	1	1	NUM
ma-80	351	10	y+	y+	NOUN
ma-80	351	11			PROPN
ma-80	351	12	y	y	PROPN
ma-80	351	13	e	e	PROPN
ma-80	351	14	y	y	PROPN
ma-80	351	15	1	1	NUM
ma-80	351	16	y+	y+	NOUN
ma-80	351	17			PROPN
ma-80	352	1	+	+	NOUN
ma-80	352	2			ADJ
ma-80	352	3			NOUN
ma-80	352	4	----------------------------------------------------exp+	----------------------------------------------------exp+	ADJ
ma-80	352	5	----------------------------------------------------------------------------------------------------------------------------------------=	----------------------------------------------------------------------------------------------------------------------------------------=	PROPN
ma-80	352	6	0	0	NUM
ma-80	353	1			NUM
ma-80	353	2			X
ma-80	353	3	(	(	PUNCT
ma-80	353	4	57)we4	57)we4	NUM
ma-80	353	5	y	y	NOUN
ma-80	353	6			PROPN
ma-80	353	7	y	y	PROPN
ma-80	353	8	y	y	PROPN
ma-80	353	9	2	2	NUM
ma-80	353	10	3	3	NUM
ma-80	353	11	4y+	4y+	NOUN
ma-80	353	12			PROPN
ma-80	353	13	2y	2y	NUM
ma-80	353	14	1	1	NUM
ma-80	353	15	y+	y+	NOUN
ma-80	353	16	ey	ey	PROPN
ma-80	354	1	1	1	NUM
ma-80	354	2	y+	y+	NOUN
ma-80	354	3			PROPN
ma-80	354	4	y	y	PROPN
ma-80	354	5	1	1	NUM
ma-80	354	6	y+	y+	NOUN
ma-80	354	7			PROPN
ma-80	354	8	y	y	PROPN
ma-80	354	9	1	1	NUM
ma-80	354	10	2y+	2y+	NOUN
ma-80	354	11			PROPN
ma-80	354	12	1	1	NUM
ma-80	354	13	y+	y+	NOUN
ma-80	354	14			PROPN
ma-80	354	15	y	y	PROPN
ma-80	354	16	e	e	PROPN
ma-80	354	17	y	y	PROPN
ma-80	354	18	1	1	NUM
ma-80	354	19	y+	y+	NOUN
ma-80	354	20			PROPN
ma-80	355	1	+	+	NOUN
ma-80	355	2			ADJ
ma-80	355	3			NOUN
ma-80	355	4	----------------------------------------------------exp+	----------------------------------------------------exp+	NOUN
ma-80	355	5	+	+	CCONJ
ma-80	355	6	+	+	CCONJ
ma-80	355	7	1	1	NUM
ma-80	355	8	y+	y+	NOUN
ma-80	355	9			PROPN
ma-80	355	10	y	y	PROPN
ma-80	355	11	1	1	NUM
ma-80	355	12	3y	3y	NUM
ma-80	355	13	e	e	NOUN
ma-80	355	14	y	y	PROPN
ma-80	355	15	1	1	NUM
ma-80	355	16	y+	y+	NOUN
ma-80	355	17			PROPN
ma-80	356	1	+	+	CCONJ
ma-80	356	2	+	+	ADJ
ma-80	356	3			ADJ
ma-80	356	4			NOUN
ma-80	356	5	1	1	NUM
ma-80	356	6	y+	y+	NOUN
ma-80	356	7			PROPN
ma-80	356	8	y	y	PROPN
ma-80	356	9	e	e	PROPN
ma-80	356	10	y	y	PROPN
ma-80	356	11	1	1	NUM
ma-80	356	12	y+	y+	NOUN
ma-80	356	13			PROPN
ma-80	357	1	+	+	NOUN
ma-80	357	2			ADJ
ma-80	357	3			NOUN
ma-80	357	4	----------------------------------------------------exp	----------------------------------------------------exp	PROPN
ma-80	357	5	1	1	NUM
ma-80	357	6	y+	y+	NOUN
ma-80	357	7			PROPN
ma-80	357	8	y	y	PROPN
ma-80	357	9	e	e	PROPN
ma-80	357	10	y	y	PROPN
ma-80	357	11	1	1	NUM
ma-80	357	12	y+	y+	NOUN
ma-80	357	13			PROPN
ma-80	358	1	+	+	NOUN
ma-80	358	2			ADJ
ma-80	358	3			PROPN
ma-80	358	4	y	y	PROPN
ma-80	358	5	y	y	PROPN
ma-80	358	6	1	1	NUM
ma-80	358	7	2y+	2y+	NOUN
ma-80	358	8			PROPN
ma-80	358	9	1	1	NUM
ma-80	358	10	y+	y+	NOUN
ma-80	358	11			PROPN
ma-80	358	12	y	y	PROPN
ma-80	358	13	e	e	PROPN
ma-80	358	14	y	y	PROPN
ma-80	358	15	1	1	NUM
ma-80	358	16	y+	y+	NOUN
ma-80	358	17			PROPN
ma-80	359	1	+	+	NOUN
ma-80	359	2			ADJ
ma-80	359	3			ADP
ma-80	359	4	----------------------------------------------------exp+	----------------------------------------------------exp+	ADJ
ma-80	359	5			PROPN
ma-80	359	6	y	y	PROPN
ma-80	359	7	y	y	PROPN
ma-80	359	8	y	y	PROPN
ma-80	359	9	2	2	NUM
ma-80	359	10	3y+	3y+	NOUN
ma-80	359	11			PROPN
ma-80	359	12	1	1	NUM
ma-80	359	13	y+	y+	NOUN
ma-80	359	14	ey	ey	PROPN
ma-80	359	15	1	1	NUM
ma-80	359	16	y+	y+	NOUN
ma-80	359	17			PROPN
ma-80	360	1	+	+	NOUN
ma-80	360	2			ADJ
ma-80	360	3			ADP
ma-80	360	4	1	1	NUM
ma-80	360	5	y+	y+	NOUN
ma-80	360	6			PROPN
ma-80	360	7	y	y	PROPN
ma-80	360	8	e	e	PROPN
ma-80	360	9	y	y	PROPN
ma-80	360	10	1	1	NUM
ma-80	360	11	y+	y+	NOUN
ma-80	360	12			PROPN
ma-80	361	1	+	+	NOUN
ma-80	361	2			ADJ
ma-80	361	3			PROPN
ma-80	361	4	y	y	PROPN
ma-80	361	5	y	y	PROPN
ma-80	361	6	1	1	NUM
ma-80	361	7	2y+	2y+	NOUN
ma-80	361	8			PROPN
ma-80	361	9	1	1	NUM
ma-80	361	10	y+	y+	NOUN
ma-80	361	11			PROPN
ma-80	361	12	y	y	PROPN
ma-80	361	13	e	e	PROPN
ma-80	361	14	y	y	PROPN
ma-80	361	15	1	1	NUM
ma-80	361	16	y+	y+	NOUN
ma-80	361	17			PROPN
ma-80	362	1	+	+	NOUN
ma-80	362	2			ADJ
ma-80	362	3			ADP
ma-80	362	4	----------------------------------------------------exp+	----------------------------------------------------exp+	ADJ
ma-80	362	5	----------------------------------------------------------------------------------------------------------------------------------------exp+	----------------------------------------------------------------------------------------------------------------------------------------exp+	PROPN
ma-80	362	6	----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------=	----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------=	PUNCT
ma-80	362	7	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	PROPN
ma-80	362	8	an	an	DET
ma-80	362	9	initial	initial	ADJ
ma-80	362	10	approximation	approximation	NOUN
ma-80	362	11	of	of	ADP
ma-80	362	12	rather	rather	ADV
ma-80	362	13	than	than	ADP
ma-80	362	14	.	.	PUNCT
ma-80	363	1	the	the	DET
ma-80	363	2	resulting	result	VERB
ma-80	363	3	approximations	approximation	NOUN
ma-80	363	4	,	,	PUNCT
ma-80	363	5	of	of	ADP
ma-80	363	6	orders	order	NOUN
ma-80	363	7	one	one	NUM
ma-80	363	8	to	to	ADP
ma-80	363	9	four	four	NUM
ma-80	363	10	,	,	PUNCT
ma-80	363	11	are	be	AUX
ma-80	363	12	:	:	PUNCT
ma-80	363	13	(	(	PUNCT
ma-80	363	14	58	58	NUM
ma-80	363	15	)	)	PUNCT
ma-80	363	16	(	(	PUNCT
ma-80	363	17	59	59	NUM
ma-80	363	18	)	)	PUNCT
ma-80	363	19	(	(	PUNCT
ma-80	363	20	60	60	NUM
ma-80	363	21	)	)	PUNCT
ma-80	363	22	(	(	PUNCT
ma-80	363	23	61	61	NUM
ma-80	363	24	)	)	PUNCT
ma-80	363	25	the	the	DET
ma-80	363	26	improvement	improvement	NOUN
ma-80	363	27	in	in	ADP
ma-80	363	28	the	the	DET
ma-80	363	29	relative	relative	ADJ
ma-80	363	30	error	error	NOUN
ma-80	363	31	bounds	bound	NOUN
ma-80	363	32	for	for	ADP
ma-80	363	33	the	the	DET
ma-80	363	34	interval	interval	NOUN
ma-80	363	35	,	,	PUNCT
ma-80	363	36	for	for	ADP
ma-80	363	37	values	value	NOUN
ma-80	363	38	of	of	ADP
ma-80	363	39	close	close	ADJ
ma-80	363	40	to	to	PART
ma-80	363	41	optimum	optimum	ADV
ma-80	363	42	,	,	PUNCT
ma-80	363	43	are	be	AUX
ma-80	363	44	detailed	detail	VERB
ma-80	363	45	in	in	ADP
ma-80	363	46	table	table	NOUN
ma-80	363	47	2	2	NUM
ma-80	363	48	.	.	PUNCT
ma-80	364	1	for	for	ADP
ma-80	364	2	the	the	DET
ma-80	364	3	case	case	NOUN
ma-80	364	4	of	of	ADP
ma-80	364	5	a	a	DET
ma-80	364	6	third	third	ADJ
ma-80	364	7	order	order	NOUN
ma-80	364	8	approximation	approximation	NOUN
ma-80	364	9	,	,	PUNCT
ma-80	364	10	and	and	CCONJ
ma-80	364	11	for	for	ADP
ma-80	364	12	,	,	PUNCT
ma-80	364	13	the	the	DET
ma-80	364	14	maximum	maximum	ADJ
ma-80	364	15	relative	relative	ADJ
ma-80	364	16	error	error	NOUN
ma-80	364	17	is	be	AUX
ma-80	364	18	.	.	PUNCT
ma-80	365	1	thus	thus	ADV
ma-80	365	2	,	,	PUNCT
ma-80	365	3	the	the	DET
ma-80	365	4	approximation	approximation	NOUN
ma-80	365	5	(	(	PUNCT
ma-80	365	6	62	62	NUM
ma-80	365	7	)	)	PUNCT
ma-80	365	8	figure	figure	NOUN
ma-80	365	9	14	14	NUM
ma-80	365	10	.	.	PUNCT
ma-80	365	11	graph	graph	NOUN
ma-80	365	12	of	of	ADP
ma-80	365	13	the	the	DET
ma-80	365	14	relative	relative	ADJ
ma-80	365	15	error	error	NOUN
ma-80	365	16	in	in	ADP
ma-80	365	17	approximations	approximation	NOUN
ma-80	365	18	to	to	ADP
ma-80	365	19	,	,	PUNCT
ma-80	365	20	for	for	ADP
ma-80	365	21	the	the	DET
ma-80	365	22	interval	interval	NOUN
ma-80	365	23	,	,	PUNCT
ma-80	365	24	based	base	VERB
ma-80	365	25	on	on	ADP
ma-80	365	26	the	the	DET
ma-80	365	27	iterative	iterative	NOUN
ma-80	365	28	algorithms	algorithm	NOUN
ma-80	365	29	specified	specify	VERB
ma-80	365	30	in	in	ADP
ma-80	365	31	theorem	theorem	ADJ
ma-80	365	32	3.4	3.4	NUM
ma-80	365	33	and	and	CCONJ
ma-80	365	34	theorem	theorem	VERB
ma-80	365	35	3.1	3.1	NUM
ma-80	365	36	.	.	PUNCT
ma-80	366	1	w	w	NOUN
ma-80	366	2	y	y	NOUN
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ma-80	366	5	e	e	ADP
ma-80	366	6	–	–	PUNCT
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ma-80	366	9	y	y	PROPN
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ma-80	366	11	y	y	NOUN
ma-80	366	12			PROPN
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ma-80	366	15			PUNCT
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ma-80	366	17	y	y	NOUN
ma-80	366	18			PROPN
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ma-80	367	1			PUNCT
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ma-80	367	7			PROPN
ma-80	367	8	wl2	wl2	PROPN
ma-80	367	9	y	y	PROPN
ma-80	367	10			PROPN
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ma-80	367	12	y	y	NOUN
ma-80	367	13			NOUN
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ma-80	367	15	y	y	NOUN
ma-80	367	16			NOUN
ma-80	367	17	wl3	wl3	NOUN
ma-80	367	18	y	y	NOUN
ma-80	367	19			PROPN
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ma-80	367	21	y	y	NOUN
ma-80	367	22			PROPN
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ma-80	367	25			PUNCT
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ma-80	367	27	y	y	NOUN
ma-80	367	28			PROPN
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ma-80	369	1			PROPN
ma-80	369	2	1	1	NUM
ma-80	369	3	ky+=	ky+=	PROPN
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ma-80	369	5	y	y	NOUN
ma-80	369	6			PROPN
ma-80	369	7	1	1	NUM
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ma-80	369	10	y	y	NOUN
ma-80	369	11			PROPN
ma-80	369	12	1	1	NUM
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ma-80	369	14	=	=	PROPN
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ma-80	371	1	1	1	NUM
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ma-80	371	4	=	=	PROPN
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ma-80	371	8	1	1	NUM
ma-80	371	9	1	1	NUM
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ma-80	371	12	1	1	NUM
ma-80	371	13	1	1	NUM
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ma-80	371	16	----------------------------------=	----------------------------------=	PUNCT
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ma-80	371	25	1	1	NUM
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ma-80	371	28	----------------------------------ln	----------------------------------ln	PROPN
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ma-80	371	40	ln+	ln+	PROPN
ma-80	372	1	+	+	NOUN
ma-80	372	2	1	1	NUM
ma-80	372	3	1	1	NUM
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ma-80	372	7	1	1	NUM
ma-80	372	8	1	1	NUM
ma-80	372	9	1	1	NUM
ma-80	372	10	k+	k+	PROPN
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ma-80	372	12	1	1	NUM
ma-80	372	13	1	1	NUM
ma-80	372	14	ky+	ky+	PROPN
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ma-80	372	16	----------------------------------ln+	----------------------------------ln+	PROPN
ma-80	372	17	-----------------------------------------------------------------------------------------------------=	-----------------------------------------------------------------------------------------------------=	X
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ma-80	372	19	y	y	NOUN
ma-80	372	20			PROPN
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ma-80	372	22	y	y	NOUN
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ma-80	372	24	ln	ln	NOUN
ma-80	372	25	=	=	NOUN
ma-80	372	26	z4	z4	VERB
ma-80	372	27	y	y	NOUN
ma-80	372	28			PUNCT
ma-80	373	1	=	=	SYM
ma-80	374	1	1	1	NUM
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ma-80	374	7	1	1	NUM
ma-80	374	8	k+	k+	PROPN
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ma-80	374	11	1	1	NUM
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ma-80	374	14	----------------------------------ln	----------------------------------ln	NOUN
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ma-80	374	20	1	1	NUM
ma-80	374	21	1	1	NUM
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ma-80	374	24	1	1	NUM
ma-80	374	25	1	1	NUM
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ma-80	374	28	----------------------------------ln++	----------------------------------ln++	PROPN
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ma-80	375	1	+	+	CCONJ
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ma-80	375	3	1	1	NUM
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ma-80	375	7	1	1	NUM
ma-80	375	8	1	1	NUM
ma-80	375	9	1	1	NUM
ma-80	375	10	k+	k+	PROPN
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ma-80	375	13	1	1	NUM
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ma-80	375	15	ln+	ln+	PROPN
ma-80	375	16	----------------------------------ln+	----------------------------------ln+	PROPN
ma-80	375	17	1	1	NUM
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ma-80	375	20	k+	k+	PROPN
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ma-80	375	22	y	y	PROPN
ma-80	375	23	1	1	NUM
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ma-80	375	25	ln+	ln+	PROPN
ma-80	376	1	+	+	NOUN
ma-80	376	2	1	1	NUM
ma-80	376	3	1	1	NUM
ma-80	376	4	ky+	ky+	NOUN
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ma-80	376	7	1	1	NUM
ma-80	376	8	1	1	NUM
ma-80	376	9	1	1	NUM
ma-80	376	10	k+	k+	PROPN
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ma-80	376	12	1	1	NUM
ma-80	376	13	1	1	NUM
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ma-80	376	16	----------------------------------ln+	----------------------------------ln+	PROPN
ma-80	376	17	-----------------------------------------------------------------------------------------------------ln+	-----------------------------------------------------------------------------------------------------ln+	PROPN
ma-80	376	18	------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------wk4	------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------wk4	PUNCT
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ma-80	376	22	y	y	NOUN
ma-80	376	23			NOUN
ma-80	376	24	.ln=	.ln=	NOUN
ma-80	376	25	0	0	NUM
ma-80	376	26			NUM
ma-80	376	27			X
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ma-80	376	32	---------------=	---------------=	PUNCT
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ma-80	376	34	10	10	NUM
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ma-80	376	36	wk3	wk3	VERB
ma-80	376	37	y	y	NOUN
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ma-80	376	43	y	y	PROPN
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ma-80	376	46	ln+	ln+	PROPN
ma-80	377	1	+	+	NOUN
ma-80	377	2	1	1	NUM
ma-80	377	3	1	1	NUM
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ma-80	377	7	1	1	NUM
ma-80	377	8	1	1	NUM
ma-80	377	9	1	1	NUM
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ma-80	377	15	ln+	ln+	PROPN
ma-80	377	16	----------------------------------ln+	----------------------------------ln+	PROPN
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ma-80	377	18	=	=	PROPN
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ma-80	377	21	10000	10000	NUM
ma-80	377	22	---------------=	---------------=	PUNCT
ma-80	377	23	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	NOUN
ma-80	377	24	1	1	NUM
ma-80	377	25	0.381	0.381	NUM
ma-80	377	26	0.570	0.570	NUM
ma-80	377	27	0.518	0.518	NUM
ma-80	377	28	0.465	0.465	NUM
ma-80	377	29	represents	represent	VERB
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ma-80	377	31	good	good	ADJ
ma-80	377	32	compromise	compromise	NOUN
ma-80	377	33	between	between	ADP
ma-80	377	34	accuracy	accuracy	NOUN
ma-80	377	35	and	and	CCONJ
ma-80	377	36	complexity	complexity	NOUN
ma-80	377	37	for	for	ADP
ma-80	377	38	the	the	DET
ma-80	377	39	interval	interval	NOUN
ma-80	377	40	with	with	ADP
ma-80	377	41	a	a	DET
ma-80	377	42	relative	relative	ADJ
ma-80	377	43	error	error	NOUN
ma-80	377	44	bound	bind	VERB
ma-80	377	45	of	of	ADP
ma-80	377	46	close	close	ADJ
ma-80	377	47	to	to	ADP
ma-80	377	48	.	.	PUNCT
ma-80	378	1	3.6	3.6	NUM
ma-80	378	2	.	.	PUNCT
ma-80	378	3	higher	high	ADJ
ma-80	378	4	accuracy	accuracy	NOUN
ma-80	378	5	via	via	ADP
ma-80	378	6	iterative	iterative	ADJ
ma-80	378	7	quadratic	quadratic	ADJ
ma-80	378	8	approximations	approximation	NOUN
ma-80	378	9	.	.	PUNCT
ma-80	379	1	the	the	DET
ma-80	379	2	iterative	iterative	NOUN
ma-80	379	3	approximation	approximation	NOUN
ma-80	379	4	detailed	detail	VERB
ma-80	379	5	in	in	ADP
ma-80	379	6	theorem	theorem	NOUN
ma-80	379	7	3.1	3.1	NUM
ma-80	379	8	can	can	AUX
ma-80	379	9	be	be	AUX
ma-80	379	10	improved	improve	VERB
ma-80	379	11	upon	upon	SCONJ
ma-80	379	12	by	by	ADP
ma-80	379	13	utilizing	utilize	VERB
ma-80	379	14	quadratic	quadratic	ADJ
ma-80	379	15	,	,	PUNCT
ma-80	379	16	rather	rather	ADV
ma-80	379	17	than	than	ADP
ma-80	379	18	affine	affine	NOUN
ma-80	379	19	,	,	PUNCT
ma-80	379	20	approximations	approximation	NOUN
ma-80	379	21	as	as	SCONJ
ma-80	379	22	illustrated	illustrate	VERB
ma-80	379	23	in	in	ADP
ma-80	379	24	figure	figure	NOUN
ma-80	379	25	15	15	NUM
ma-80	379	26	.	.	PUNCT
ma-80	380	1	theorem	theorem	VERB
ma-80	380	2	3.5	3.5	NUM
ma-80	380	3	.	.	PUNCT
ma-80	381	1	iterative	iterative	ADJ
ma-80	381	2	quadratic	quadratic	ADJ
ma-80	381	3	approximations	approximation	NOUN
ma-80	381	4	for	for	ADP
ma-80	381	5	lambert	lambert	PROPN
ma-80	381	6	w	w	PROPN
ma-80	381	7	function	function	PROPN
ma-80	381	8	.	.	PUNCT
ma-80	382	1	an	an	DET
ma-80	382	2	iterative	iterative	NOUN
ma-80	382	3	formula	formula	NOUN
ma-80	382	4	,	,	PUNCT
ma-80	382	5	based	base	VERB
ma-80	382	6	on	on	ADP
ma-80	382	7	quadratic	quadratic	ADJ
ma-80	382	8	approximations	approximation	NOUN
ma-80	382	9	,	,	PUNCT
ma-80	382	10	for	for	ADP
ma-80	382	11	the	the	DET
ma-80	382	12	lambert	lambert	PROPN
ma-80	382	13	w	w	PROPN
ma-80	382	14	function	function	NOUN
ma-80	382	15	,	,	PUNCT
ma-80	382	16	and	and	CCONJ
ma-80	382	17	valid	valid	ADJ
ma-80	382	18	for	for	ADP
ma-80	382	19	,	,	PUNCT
ma-80	382	20	is	be	AUX
ma-80	382	21	(	(	PUNCT
ma-80	382	22	63	63	NUM
ma-80	382	23	)	)	PUNCT
ma-80	382	24	proof	proof	NOUN
ma-80	382	25	.	.	PUNCT
ma-80	383	1	the	the	DET
ma-80	383	2	proof	proof	NOUN
ma-80	383	3	is	be	AUX
ma-80	383	4	detailed	detail	VERB
ma-80	383	5	in	in	ADP
ma-80	383	6	appendix	appendix	PROPN
ma-80	383	7	c.	c.	PROPN
ma-80	383	8	3.6.1	3.6.1	NUM
ma-80	383	9	.	.	PUNCT
ma-80	384	1	explicit	explicit	ADJ
ma-80	384	2	approximations	approximation	NOUN
ma-80	384	3	.	.	PUNCT
ma-80	385	1	approximations	approximation	NOUN
ma-80	385	2	,	,	PUNCT
ma-80	385	3	of	of	ADP
ma-80	385	4	orders	order	NOUN
ma-80	385	5	one	one	NUM
ma-80	385	6	to	to	ADP
ma-80	385	7	three	three	NUM
ma-80	385	8	,	,	PUNCT
ma-80	385	9	are	be	AUX
ma-80	385	10	:	:	PUNCT
ma-80	385	11	(	(	PUNCT
ma-80	385	12	64	64	NUM
ma-80	385	13	)	)	PUNCT
ma-80	385	14	table	table	NOUN
ma-80	385	15	2	2	NUM
ma-80	385	16	.	.	PUNCT
ma-80	385	17	relative	relative	ADJ
ma-80	385	18	error	error	NOUN
ma-80	385	19	bounds	bound	NOUN
ma-80	385	20	,	,	PUNCT
ma-80	385	21	over	over	ADP
ma-80	385	22	the	the	DET
ma-80	385	23	interval	interval	NOUN
ma-80	385	24	,	,	PUNCT
ma-80	385	25	in	in	ADP
ma-80	385	26	the	the	DET
ma-80	385	27	approximations	approximation	NOUN
ma-80	385	28	,	,	PUNCT
ma-80	385	29	,	,	PUNCT
ma-80	385	30	to	to	ADP
ma-80	385	31	the	the	DET
ma-80	385	32	lambert	lambert	PROPN
ma-80	385	33	w	w	PROPN
ma-80	385	34	function	function	PROPN
ma-80	385	35	.	.	PUNCT
ma-80	386	1	iteration	iteration	NOUN
ma-80	386	2	order	order	NOUN
ma-80	386	3	:	:	PUNCT
ma-80	387	1	i	i	PRON
ma-80	387	2	relative	relative	ADJ
ma-80	387	3	error	error	NOUN
ma-80	387	4	bound	bind	VERB
ma-80	387	5	:	:	PUNCT
ma-80	387	6	k	k	PROPN
ma-80	387	7	=	=	SYM
ma-80	387	8	1	1	NUM
ma-80	387	9	relative	relative	ADJ
ma-80	387	10	error	error	NOUN
ma-80	387	11	bound	bind	VERB
ma-80	387	12	:	:	PUNCT
ma-80	387	13	k	k	X
ma-80	387	14	=	=	SYM
ma-80	387	15	0.4	0.4	NUM
ma-80	387	16	relative	relative	ADJ
ma-80	387	17	error	error	NOUN
ma-80	387	18	bound	bind	VERB
ma-80	387	19	:	:	PUNCT
ma-80	387	20	k	k	X
ma-80	387	21	=	=	PUNCT
ma-80	387	22	0.45	0.45	NUM
ma-80	387	23	relative	relative	ADJ
ma-80	387	24	error	error	NOUN
ma-80	387	25	bound	bind	VERB
ma-80	387	26	:	:	PUNCT
ma-80	388	1	k	k	X
ma-80	388	2	=	=	SYM
ma-80	388	3	0.5	0.5	NUM
ma-80	388	4	2	2	NUM
ma-80	388	5	0.0569	0.0569	NUM
ma-80	388	6	0.0335	0.0335	NUM
ma-80	388	7	0.0250	0.0250	NUM
ma-80	388	8	0.0184	0.0184	NUM
ma-80	388	9	3	3	NUM
ma-80	388	10	4	4	NUM
ma-80	388	11	5	5	NUM
ma-80	388	12	6	6	NUM
ma-80	388	13	0	0	NUM
ma-80	388	14			NUM
ma-80	388	15			NOUN
ma-80	388	16	10	10	NUM
ma-80	388	17	4	4	NUM
ma-80	388	18	–	–	PUNCT
ma-80	388	19	0	0	NUM
ma-80	388	20			NUM
ma-80	388	21			X
ma-80	388	22	wki	wki	PROPN
ma-80	388	23	y	y	PROPN
ma-80	389	1			PUNCT
ma-80	390	1	i	i	NOUN
ma-80	390	2	1	1	NUM
ma-80	390	3	2	2	NUM
ma-80	390	4			NOUN
ma-80	390	5	6	6	PROPN
ma-80	390	6			NUM
ma-80	390	7			NOUN
ma-80	391	1			VERB
ma-80	392	1	1.33	1.33	NUM
ma-80	392	2	10	10	NUM
ma-80	392	3	3–	3–	NUM
ma-80	392	4	1.87	1.87	NUM
ma-80	392	5	10	10	NUM
ma-80	392	6	4–	4–	NOUN
ma-80	392	7	1.05	1.05	NUM
ma-80	392	8	10	10	NUM
ma-80	392	9	4–	4–	PROPN
ma-80	392	10	1.50	1.50	NUM
ma-80	392	11	10	10	NUM
ma-80	393	1	4–	4–	PROPN
ma-80	393	2	7.23	7.23	NUM
ma-80	393	3	10	10	NUM
ma-80	394	1	7–	7–	NOUN
ma-80	394	2	6.46	6.46	NUM
ma-80	394	3	10	10	NUM
ma-80	394	4	9–	9–	PROPN
ma-80	394	5	4.96	4.96	NUM
ma-80	394	6	10	10	NUM
ma-80	394	7	9–	9–	PROPN
ma-80	394	8	9.97	9.97	NUM
ma-80	394	9	10	10	NUM
ma-80	394	10	9–	9–	PROPN
ma-80	394	11	2.15	2.15	NUM
ma-80	394	12	10	10	NUM
ma-80	394	13	13–	13–	NUM
ma-80	394	14	7.98	7.98	NUM
ma-80	394	15	10	10	NUM
ma-80	394	16	18–	18–	NUM
ma-80	394	17	1.11	1.11	NUM
ma-80	394	18	10	10	NUM
ma-80	394	19	17–	17–	NUM
ma-80	394	20	4.43	4.43	NUM
ma-80	394	21	10	10	NUM
ma-80	394	22	17–	17–	NUM
ma-80	394	23	1.90	1.90	NUM
ma-80	394	24	10	10	NUM
ma-80	394	25	26–	26–	NUM
ma-80	394	26	1.24	1.24	NUM
ma-80	394	27	10	10	NUM
ma-80	394	28	35–	35–	NUM
ma-80	394	29	5.53	5.53	NUM
ma-80	394	30	10	10	NUM
ma-80	394	31	35–	35–	NUM
ma-80	394	32	8.78	8.78	NUM
ma-80	394	33	10	10	NUM
ma-80	394	34	34–	34–	NUM
ma-80	394	35	figure	figure	NOUN
ma-80	394	36	15	15	NUM
ma-80	394	37	.	.	PUNCT
ma-80	395	1	illustration	illustration	NOUN
ma-80	395	2	of	of	ADP
ma-80	395	3	the	the	DET
ma-80	395	4	geometry	geometry	NOUN
ma-80	395	5	underpinning	underpin	VERB
ma-80	395	6	an	an	DET
ma-80	395	7	iterative	iterative	NOUN
ma-80	395	8	relationship	relationship	NOUN
ma-80	395	9	,	,	PUNCT
ma-80	395	10	based	base	VERB
ma-80	395	11	on	on	ADP
ma-80	395	12	quadratic	quadratic	ADJ
ma-80	395	13	approximations	approximation	NOUN
ma-80	395	14	,	,	PUNCT
ma-80	395	15	to	to	PART
ma-80	395	16	find	find	VERB
ma-80	395	17	an	an	DET
ma-80	395	18	approximation	approximation	NOUN
ma-80	395	19	to	to	ADP
ma-80	395	20	which	which	PRON
ma-80	395	21	is	be	AUX
ma-80	395	22	the	the	DET
ma-80	395	23	solution	solution	NOUN
ma-80	395	24	of	of	ADP
ma-80	395	25	for	for	ADP
ma-80	395	26	fixed	fix	VERB
ma-80	395	27	,	,	PUNCT
ma-80	395	28	.	.	PUNCT
ma-80	396	1	xo	xo	PROPN
ma-80	397	1	x	x	PUNCT
ma-80	397	2	y	y	PROPN
ma-80	397	3	x–	x–	PUNCT
ma-80	398	1	exp=	exp=	PROPN
ma-80	398	2	y	y	NOUN
ma-80	398	3	y	y	NOUN
ma-80	398	4	0	0	NUM
ma-80	399	1	wl1	wl1	PROPN
ma-80	399	2	wl2	wl2	PROPN
ma-80	399	3	wl2	wl2	PROPN
ma-80	399	4	x	x	PROPN
ma-80	400	1	wl1	wl1	PROPN
ma-80	400	2	xo	xo	PROPN
ma-80	401	1	x	x	X
ma-80	401	2	wu1	wu1	NOUN
ma-80	401	3	ye	ye	NOUN
ma-80	401	4	x	x	PROPN
ma-80	401	5	–	–	PUNCT
ma-80	401	6	xo	xo	PROPN
ma-80	401	7	wu2	wu2	VERB
ma-80	401	8	y	y	PROPN
ma-80	401	9	1	1	NUM
ma-80	401	10	x	x	NOUN
ma-80	401	11	–	–	PUNCT
ma-80	401	12	x	x	SYM
ma-80	401	13	2	2	NUM
ma-80	401	14	2	2	NUM
ma-80	402	1	-----+	-----+	ADJ
ma-80	402	2	wl1	wl1	NOUN
ma-80	402	3	x	x	X
ma-80	402	4	wu1	wu1	NOUN
ma-80	402	5	–	–	PUNCT
ma-80	402	6			ADJ
ma-80	402	7	wl1	wl1	PUNCT
ma-80	403	1	x	x	X
ma-80	403	2	wu1	wu1	ADJ
ma-80	403	3	–	–	PUNCT
ma-80	403	4			NOUN
ma-80	403	5	2	2	ADJ
ma-80	403	6	2	2	NUM
ma-80	403	7	--------------------------wl1	--------------------------wl1	NOUN
ma-80	403	8	+	+	NOUN
ma-80	403	9	–	–	PUNCT
ma-80	403	10	y	y	PROPN
ma-80	403	11	y	y	PROPN
ma-80	403	12	1	1	NUM
ma-80	403	13	e–	e–	NUM
ma-80	403	14	wli	wli	NOUN
ma-80	403	15	1	1	NUM
ma-80	403	16	wli	wli	PROPN
ma-80	403	17	1	1	NUM
ma-80	403	18	–	–	PUNCT
ma-80	403	19	-------------1	-------------1	PROPN
ma-80	403	20	wli	wli	PROPN
ma-80	403	21	1	1	NUM
ma-80	403	22	–	–	SYM
ma-80	403	23	1	1	NUM
ma-80	403	24	wui	wui	NOUN
ma-80	403	25	1	1	NUM
ma-80	403	26	–	–	PUNCT
ma-80	403	27	+	+	NOUN
ma-80	403	28			ADJ
ma-80	403	29			NOUN
ma-80	403	30	1	1	NUM
ma-80	403	31	wli	wli	PROPN
ma-80	403	32	1	1	NUM
ma-80	403	33	–	–	SYM
ma-80	403	34	2	2	NUM
ma-80	403	35	–	–	PUNCT
ma-80	403	36	2wli	2wli	NUM
ma-80	403	37	1	1	NUM
ma-80	403	38	–	–	SYM
ma-80	403	39	1	1	NUM
ma-80	403	40	wui	wui	NOUN
ma-80	403	41	1	1	NUM
ma-80	403	42	–	–	PUNCT
ma-80	403	43	+	+	NUM
ma-80	403	44			ADJ
ma-80	403	45	+–+	+–+	NOUN
ma-80	403	46	=	=	AUX
ma-80	403	47	wui	wui	NOUN
ma-80	403	48	y	y	PROPN
ma-80	403	49	wli	wli	PROPN
ma-80	403	50	---------ln	---------ln	PROPN
ma-80	404	1	=	=	PROPN
ma-80	405	1	wl1	wl1	PROPN
ma-80	405	2	y	y	PROPN
ma-80	405	3	1	1	NUM
ma-80	405	4	y+	y+	NUM
ma-80	405	5	------------=	------------=	X
ma-80	405	6	wu1	wu1	PROPN
ma-80	405	7	1	1	NUM
ma-80	405	8	y+	y+	NOUN
ma-80	405	9	.ln=	.ln=	NOUN
ma-80	406	1	wl1	wl1	PROPN
ma-80	407	1	y	y	NOUN
ma-80	407	2			PUNCT
ma-80	407	3	y	y	PROPN
ma-80	407	4	1	1	NUM
ma-80	407	5	y+	y+	NUM
ma-80	407	6	------------=	------------=	X
ma-80	407	7	wu1	wu1	NOUN
ma-80	407	8	y	y	NOUN
ma-80	407	9			PROPN
ma-80	407	10	1	1	NUM
ma-80	407	11	y+	y+	NOUN
ma-80	407	12	ln=	ln=	PUNCT
ma-80	408	1	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	PROPN
ma-80	408	2	(	(	PUNCT
ma-80	408	3	65	65	NUM
ma-80	408	4	)	)	PUNCT
ma-80	408	5	(	(	PUNCT
ma-80	408	6	66	66	NUM
ma-80	408	7	)	)	PUNCT
ma-80	408	8	(	(	PUNCT
ma-80	408	9	67	67	NUM
ma-80	408	10	)	)	PUNCT
ma-80	408	11	3.6.2	3.6.2	NUM
ma-80	408	12	.	.	PUNCT
ma-80	408	13	results	result	NOUN
ma-80	408	14	.	.	PUNCT
ma-80	409	1	the	the	DET
ma-80	409	2	relative	relative	ADJ
ma-80	409	3	errors	error	NOUN
ma-80	409	4	in	in	ADP
ma-80	409	5	the	the	DET
ma-80	409	6	approximations	approximation	NOUN
ma-80	409	7	specified	specify	VERB
ma-80	409	8	in	in	ADP
ma-80	409	9	theorem	theorem	ADJ
ma-80	409	10	3.5	3.5	NUM
ma-80	409	11	are	be	AUX
ma-80	409	12	shown	show	VERB
ma-80	409	13	in	in	ADP
ma-80	409	14	figure	figure	NOUN
ma-80	409	15	16	16	NUM
ma-80	409	16	and	and	CCONJ
ma-80	409	17	figure	figure	VERB
ma-80	409	18	17	17	NUM
ma-80	409	19	.	.	PUNCT
ma-80	410	1	the	the	DET
ma-80	410	2	relative	relative	ADJ
ma-80	410	3	error	error	NOUN
ma-80	410	4	bounds	bound	NOUN
ma-80	410	5	,	,	PUNCT
ma-80	410	6	for	for	ADP
ma-80	410	7	the	the	DET
ma-80	410	8	interval	interval	NOUN
ma-80	410	9	,	,	PUNCT
ma-80	410	10	are	be	AUX
ma-80	410	11	detailed	detail	VERB
ma-80	410	12	in	in	ADP
ma-80	410	13	table	table	NOUN
ma-80	410	14	3	3	NUM
ma-80	410	15	and	and	CCONJ
ma-80	410	16	the	the	DET
ma-80	410	17	convergence	convergence	NOUN
ma-80	410	18	is	be	AUX
ma-80	410	19	cubic	cubic	ADJ
ma-80	410	20	in	in	ADP
ma-80	410	21	nature	nature	NOUN
ma-80	410	22	.	.	PUNCT
ma-80	411	1	the	the	DET
ma-80	411	2	approximation	approximation	NOUN
ma-80	411	3	has	have	VERB
ma-80	411	4	a	a	DET
ma-80	411	5	relative	relative	ADJ
ma-80	411	6	error	error	NOUN
ma-80	411	7	bound	bind	VERB
ma-80	411	8	for	for	ADP
ma-80	411	9	the	the	DET
ma-80	411	10	interval	interval	NOUN
ma-80	411	11	of	of	ADP
ma-80	411	12	.	.	PUNCT
ma-80	412	1	4	4	X
ma-80	412	2	.	.	X
ma-80	412	3	convergence	convergence	NOUN
ma-80	412	4	consider	consider	VERB
ma-80	412	5	the	the	DET
ma-80	412	6	case	case	NOUN
ma-80	412	7	of	of	ADP
ma-80	412	8	,	,	PUNCT
ma-80	412	9	,	,	PUNCT
ma-80	412	10	and	and	CCONJ
ma-80	412	11	the	the	DET
ma-80	412	12	error	error	NOUN
ma-80	412	13	definitions	definition	NOUN
ma-80	412	14	(	(	PUNCT
ma-80	412	15	68	68	NUM
ma-80	412	16	)	)	PUNCT
ma-80	412	17	associated	associate	VERB
ma-80	412	18	with	with	ADP
ma-80	412	19	the	the	DET
ma-80	412	20	upper	upper	ADJ
ma-80	412	21	and	and	CCONJ
ma-80	412	22	lower	low	ADJ
ma-80	412	23	approximations	approximation	NOUN
ma-80	412	24	detailed	detail	VERB
ma-80	412	25	in	in	ADP
ma-80	412	26	theorem	theorem	ADJ
ma-80	412	27	3.1	3.1	NUM
ma-80	412	28	and	and	CCONJ
ma-80	412	29	as	as	SCONJ
ma-80	412	30	illustrated	illustrate	VERB
ma-80	412	31	in	in	ADP
ma-80	412	32	figure	figure	NOUN
ma-80	412	33	18	18	NUM
ma-80	412	34	.	.	PUNCT
ma-80	413	1	the	the	DET
ma-80	413	2	following	follow	VERB
ma-80	413	3	results	result	NOUN
ma-80	413	4	hold	hold	VERB
ma-80	413	5	:	:	PUNCT
ma-80	413	6	table	table	NOUN
ma-80	413	7	3	3	NUM
ma-80	413	8	.	.	PUNCT
ma-80	413	9	relative	relative	ADJ
ma-80	413	10	error	error	NOUN
ma-80	413	11	bounds	bound	NOUN
ma-80	413	12	,	,	PUNCT
ma-80	413	13	over	over	ADP
ma-80	413	14	the	the	DET
ma-80	413	15	interval	interval	NOUN
ma-80	413	16	,	,	PUNCT
ma-80	413	17	for	for	ADP
ma-80	413	18	the	the	DET
ma-80	413	19	approximations	approximation	NOUN
ma-80	413	20	to	to	ADP
ma-80	413	21	the	the	DET
ma-80	413	22	lambert	lambert	PROPN
ma-80	413	23	w	w	PROPN
ma-80	413	24	function	function	PROPN
ma-80	413	25	detailed	detail	VERB
ma-80	413	26	in	in	ADP
ma-80	413	27	theorem	theorem	ADJ
ma-80	413	28	3.5	3.5	NUM
ma-80	413	29	.	.	PUNCT
ma-80	414	1	iteration	iteration	NOUN
ma-80	414	2	order	order	NOUN
ma-80	415	1	i	i	PRON
ma-80	415	2	maximum	maximum	VERB
ma-80	415	3	relative	relative	ADJ
ma-80	415	4	error	error	NOUN
ma-80	415	5	in	in	ADP
ma-80	415	6	maximum	maximum	ADJ
ma-80	415	7	relative	relative	ADJ
ma-80	415	8	error	error	NOUN
ma-80	415	9	in	in	ADP
ma-80	415	10	1	1	NUM
ma-80	415	11	increasing	increase	VERB
ma-80	415	12	0.381	0.381	NUM
ma-80	415	13	2	2	NUM
ma-80	415	14	increasing	increase	VERB
ma-80	415	15	0.0122	0.0122	NUM
ma-80	415	16	3	3	NUM
ma-80	415	17	4	4	NUM
ma-80	415	18	5	5	NUM
ma-80	415	19	wl2	wl2	PROPN
ma-80	415	20	y	y	PROPN
ma-80	415	21			PROPN
ma-80	415	22	1	1	NUM
ma-80	415	23	y	y	PROPN
ma-80	415	24	--1	--1	NOUN
ma-80	415	25	2y	2y	PROPN
ma-80	415	26	y	y	PROPN
ma-80	415	27	1	1	NUM
ma-80	415	28	y+	y+	NOUN
ma-80	415	29	ln	ln	PROPN
ma-80	415	30	1	1	NUM
ma-80	415	31	4y	4y	PRON
ma-80	415	32	2y	2y	NUM
ma-80	415	33	2	2	NUM
ma-80	415	34	2y	2y	NUM
ma-80	415	35	1	1	NUM
ma-80	415	36	y+	y+	NOUN
ma-80	415	37			PROPN
ma-80	415	38	1	1	NUM
ma-80	415	39	y+	y+	NOUN
ma-80	415	40	ln+	ln+	PROPN
ma-80	416	1	+	+	CCONJ
ma-80	416	2	+	+	ADJ
ma-80	416	3	–	–	PUNCT
ma-80	416	4	+	+	X
ma-80	417	1	+	+	ADJ
ma-80	417	2	=	=	NOUN
ma-80	417	3	wu2	wu2	VERB
ma-80	417	4	y	y	NOUN
ma-80	417	5			PUNCT
ma-80	417	6	y	y	PROPN
ma-80	417	7	2	2	NUM
ma-80	417	8	1	1	NUM
ma-80	417	9	2y	2y	NUM
ma-80	417	10	y	y	PROPN
ma-80	417	11	1	1	NUM
ma-80	417	12	y+	y+	NOUN
ma-80	417	13	ln	ln	PROPN
ma-80	417	14	1	1	NUM
ma-80	417	15	4y	4y	PRON
ma-80	417	16	2y	2y	NUM
ma-80	417	17	2	2	NUM
ma-80	417	18	2y	2y	NUM
ma-80	417	19	1	1	NUM
ma-80	417	20	y+	y+	NOUN
ma-80	417	21			PROPN
ma-80	417	22	1	1	NUM
ma-80	417	23	y+	y+	NOUN
ma-80	417	24	ln+	ln+	PROPN
ma-80	418	1	+	+	CCONJ
ma-80	418	2	+	+	ADJ
ma-80	418	3	–	–	PUNCT
ma-80	418	4	+	+	ADJ
ma-80	418	5	+	+	NUM
ma-80	418	6	-----------------------------------------------------------------------------------------------------------------------------------------------ln=	-----------------------------------------------------------------------------------------------------------------------------------------------ln=	NOUN
ma-80	418	7	wl3	wl3	NOUN
ma-80	418	8	y	y	NOUN
ma-80	418	9			NOUN
ma-80	418	10	1	1	NUM
ma-80	418	11	1	1	NUM
ma-80	418	12	2y	2y	NUM
ma-80	418	13	y	y	PROPN
ma-80	418	14	1	1	NUM
ma-80	418	15	y+	y+	NOUN
ma-80	418	16	ln	ln	PROPN
ma-80	418	17	q2	q2	NOUN
ma-80	418	18	y	y	NOUN
ma-80	418	19	–+	–+	PUNCT
ma-80	419	1	+	+	CCONJ
ma-80	419	2	-----------------------------------------------------------------=	-----------------------------------------------------------------=	PROPN
ma-80	419	3	y	y	PROPN
ma-80	419	4	1	1	NUM
ma-80	419	5	2y	2y	NUM
ma-80	419	6	y	y	PROPN
ma-80	419	7	1	1	NUM
ma-80	419	8	y+	y+	NOUN
ma-80	419	9	ln	ln	PROPN
ma-80	419	10	q2	q2	NOUN
ma-80	419	11	y	y	NOUN
ma-80	419	12	–+	–+	PUNCT
ma-80	420	1	+	+	CCONJ
ma-80	420	2	1	1	NUM
ma-80	420	3	y	y	SYM
ma-80	420	4	2	2	NUM
ma-80	420	5	1	1	NUM
ma-80	420	6	2y	2y	NUM
ma-80	420	7	y	y	PROPN
ma-80	420	8	1	1	NUM
ma-80	420	9	y+	y+	NOUN
ma-80	420	10	ln	ln	PROPN
ma-80	420	11	q2	q2	NOUN
ma-80	420	12	y	y	NOUN
ma-80	420	13	–+	–+	PUNCT
ma-80	421	1	+	+	CCONJ
ma-80	421	2	------------------------------------------------------------------ln+	------------------------------------------------------------------ln+	PUNCT
ma-80	422	1	–	–	PUNCT
ma-80	422	2	+	+	NUM
ma-80	422	3	y	y	SYM
ma-80	422	4	2	2	NUM
ma-80	422	5	1	1	NUM
ma-80	422	6	2y	2y	NUM
ma-80	422	7	y	y	PROPN
ma-80	422	8	1	1	NUM
ma-80	422	9	y+	y+	NOUN
ma-80	422	10	ln	ln	PROPN
ma-80	422	11	q2	q2	NOUN
ma-80	422	12	y	y	NOUN
ma-80	422	13	–+	–+	PUNCT
ma-80	423	1	+	+	ADP
ma-80	423	2			ADJ
ma-80	423	3	2	2	NOUN
ma-80	423	4	–	–	PUNCT
ma-80	423	5	+	+	NUM
ma-80	423	6	2y	2y	SYM
ma-80	423	7	1	1	NUM
ma-80	423	8	2y	2y	NUM
ma-80	423	9	y	y	PROPN
ma-80	423	10	1	1	NUM
ma-80	423	11	y+	y+	NOUN
ma-80	423	12	ln	ln	PROPN
ma-80	423	13	q2	q2	NOUN
ma-80	423	14	y	y	NOUN
ma-80	423	15	–+	–+	PUNCT
ma-80	424	1	+	+	CCONJ
ma-80	424	2	1	1	NUM
ma-80	424	3	y	y	SYM
ma-80	424	4	2	2	NUM
ma-80	424	5	1	1	NUM
ma-80	424	6	2y	2y	NUM
ma-80	424	7	y	y	PROPN
ma-80	424	8	1	1	NUM
ma-80	424	9	y+	y+	NOUN
ma-80	424	10	ln	ln	PROPN
ma-80	424	11	q2	q2	NOUN
ma-80	424	12	y	y	NOUN
ma-80	424	13	–+	–+	PUNCT
ma-80	425	1	+	+	CCONJ
ma-80	425	2	------------------------------------------------------------------ln+	------------------------------------------------------------------ln+	PUNCT
ma-80	425	3	q2	q2	X
ma-80	425	4	y	y	PROPN
ma-80	425	5			PROPN
ma-80	425	6	1	1	NUM
ma-80	425	7	4y	4y	NUM
ma-80	425	8	2y	2y	NUM
ma-80	426	1	2	2	NUM
ma-80	426	2	2y	2y	NUM
ma-80	426	3	1	1	NUM
ma-80	426	4	y+	y+	NOUN
ma-80	426	5			PROPN
ma-80	426	6	1	1	NUM
ma-80	426	7	y+	y+	NOUN
ma-80	426	8	ln+	ln+	PROPN
ma-80	426	9	+	+	CCONJ
ma-80	427	1	+	+	PUNCT
ma-80	427	2	=	=	NOUN
ma-80	427	3	wu3	wu3	VERB
ma-80	427	4	y	y	NOUN
ma-80	427	5			PROPN
ma-80	427	6	y	y	PROPN
ma-80	427	7	wl3	wl3	PROPN
ma-80	427	8	i	i	NOUN
ma-80	427	9			NOUN
ma-80	427	10	---------------.ln=	---------------.ln=	ADP
ma-80	427	11	0	0	NUM
ma-80	427	12			NOUN
ma-80	427	13			NOUN
ma-80	427	14	wu3	wu3	NOUN
ma-80	427	15	0	0	NUM
ma-80	427	16			NOUN
ma-80	427	17			NOUN
ma-80	427	18	1.26	1.26	NUM
ma-80	427	19	10	10	NUM
ma-80	427	20	6–	6–	NUM
ma-80	427	21	0	0	NUM
ma-80	427	22			NOUN
ma-80	427	23			PROPN
ma-80	427	24	wli	wli	PROPN
ma-80	427	25	wui	wui	PROPN
ma-80	427	26	1.02	1.02	NUM
ma-80	427	27	10	10	NUM
ma-80	427	28	5–	5–	PROPN
ma-80	427	29	1.26	1.26	NUM
ma-80	427	30	10	10	NUM
ma-80	427	31	6–	6–	PROPN
ma-80	427	32	1.66	1.66	NUM
ma-80	427	33	10	10	NUM
ma-80	427	34	17–	17–	NUM
ma-80	427	35	2.04	2.04	NUM
ma-80	427	36	10	10	NUM
ma-80	427	37	18–	18–	NUM
ma-80	427	38	7.88	7.88	NUM
ma-80	427	39	10	10	NUM
ma-80	427	40	53–	53–	NUM
ma-80	427	41	9.63	9.63	NUM
ma-80	427	42	10	10	NUM
ma-80	427	43	54–	54–	NUM
ma-80	427	44	y	y	PROPN
ma-80	427	45	0	0	NUM
ma-80	427	46	xo	xo	PROPN
ma-80	427	47	w	w	PROPN
ma-80	427	48	y	y	PROPN
ma-80	427	49	=	=	NOUN
ma-80	427	50	li	li	VERB
ma-80	427	51	xo	xo	PROPN
ma-80	427	52	wli	wli	PROPN
ma-80	427	53	–	–	PUNCT
ma-80	427	54	=	=	NUM
ma-80	427	55	ui	ui	PROPN
ma-80	427	56	wui	wui	PROPN
ma-80	427	57	xo	xo	PROPN
ma-80	427	58	–	–	PUNCT
ma-80	427	59	=	=	NUM
ma-80	427	60	ith	ith	PROPN
ma-80	427	61	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	PROPN
ma-80	427	62	theorem	theorem	VERB
ma-80	427	63	4.1	4.1	NUM
ma-80	427	64	.	.	PUNCT
ma-80	428	1	convergence	convergence	NOUN
ma-80	428	2	of	of	ADP
ma-80	428	3	iterative	iterative	ADJ
ma-80	428	4	algorithm	algorithm	NOUN
ma-80	428	5	.	.	PUNCT
ma-80	429	1	for	for	ADP
ma-80	429	2	the	the	DET
ma-80	429	3	case	case	NOUN
ma-80	429	4	of	of	ADP
ma-80	429	5	fixed	fix	VERB
ma-80	429	6	and	and	CCONJ
ma-80	429	7	,	,	PUNCT
ma-80	429	8	the	the	DET
ma-80	429	9	errors	error	NOUN
ma-80	429	10	associated	associate	VERB
ma-80	429	11	with	with	ADP
ma-80	429	12	the	the	DET
ma-80	429	13	lower	low	ADJ
ma-80	429	14	approximations	approximation	NOUN
ma-80	429	15	,	,	PUNCT
ma-80	429	16	,	,	PUNCT
ma-80	429	17	detailed	detail	VERB
ma-80	429	18	in	in	ADP
ma-80	429	19	theorem	theorem	NOUN
ma-80	429	20	3.1	3.1	NUM
ma-80	429	21	,	,	PUNCT
ma-80	429	22	are	be	AUX
ma-80	429	23	(	(	PUNCT
ma-80	429	24	69	69	NUM
ma-80	429	25	)	)	PUNCT
ma-80	429	26	figure	figure	NOUN
ma-80	429	27	16	16	NUM
ma-80	429	28	.	.	PUNCT
ma-80	430	1	graph	graph	NOUN
ma-80	430	2	of	of	ADP
ma-80	430	3	the	the	DET
ma-80	430	4	relative	relative	ADJ
ma-80	430	5	errors	error	NOUN
ma-80	430	6	in	in	ADP
ma-80	430	7	approximations	approximation	NOUN
ma-80	430	8	to	to	PART
ma-80	430	9	as	as	SCONJ
ma-80	430	10	specified	specify	VERB
ma-80	430	11	in	in	ADP
ma-80	430	12	theorem	theorem	ADJ
ma-80	430	13	3.5.w	3.5.w	NUM
ma-80	430	14	y	y	NOUN
ma-80	430	15			PROPN
ma-80	430	16	y	y	PROPN
ma-80	430	17	wl2	wl2	PROPN
ma-80	430	18	y	y	PROPN
ma-80	430	19			PROPN
ma-80	430	20	re	re	ADP
ma-80	430	21	y	y	NOUN
ma-80	430	22			PUNCT
ma-80	431	1	wl1	wl1	PROPN
ma-80	431	2	y	y	NOUN
ma-80	431	3			NOUN
ma-80	431	4	wu1	wu1	NOUN
ma-80	431	5	y	y	NOUN
ma-80	431	6			NOUN
ma-80	431	7	wu2	wu2	VERB
ma-80	431	8	y	y	NOUN
ma-80	431	9			PROPN
ma-80	431	10	wu3	wu3	VERB
ma-80	431	11	y	y	NOUN
ma-80	431	12			PROPN
ma-80	431	13	figure	figure	NOUN
ma-80	431	14	17	17	NUM
ma-80	431	15	.	.	PUNCT
ma-80	432	1	graph	graph	NOUN
ma-80	432	2	of	of	ADP
ma-80	432	3	the	the	DET
ma-80	432	4	relative	relative	ADJ
ma-80	432	5	errors	error	NOUN
ma-80	432	6	in	in	ADP
ma-80	432	7	approximations	approximation	NOUN
ma-80	432	8	to	to	PART
ma-80	432	9	as	as	SCONJ
ma-80	432	10	specified	specify	VERB
ma-80	432	11	in	in	ADP
ma-80	432	12	theorem	theorem	ADJ
ma-80	432	13	3.5	3.5	NUM
ma-80	432	14	.	.	PUNCT
ma-80	433	1	w	w	NOUN
ma-80	433	2	y	y	NOUN
ma-80	433	3			PUNCT
ma-80	434	1	y	y	PRON
ma-80	434	2	wl1	wl1	PROPN
ma-80	434	3	y	y	PROPN
ma-80	434	4	re	re	X
ma-80	434	5	y	y	NOUN
ma-80	434	6			PROPN
ma-80	434	7	wl2	wl2	PROPN
ma-80	434	8	y	y	PROPN
ma-80	434	9			PROPN
ma-80	434	10	wu1	wu1	NOUN
ma-80	434	11	y	y	NOUN
ma-80	434	12			NOUN
ma-80	434	13	wu2	wu2	VERB
ma-80	434	14	y	y	NOUN
ma-80	434	15			NOUN
ma-80	434	16	wl3	wl3	NOUN
ma-80	434	17	y	y	NOUN
ma-80	434	18			PROPN
ma-80	434	19	wu3	wu3	VERB
ma-80	434	20	y	y	NOUN
ma-80	434	21			PROPN
ma-80	434	22	figure	figure	NOUN
ma-80	434	23	18	18	NUM
ma-80	434	24	.	.	PUNCT
ma-80	435	1	error	error	NOUN
ma-80	435	2	definitions	definition	NOUN
ma-80	435	3	associated	associate	VERB
ma-80	435	4	with	with	ADP
ma-80	435	5	the	the	DET
ma-80	435	6	upper	upper	ADJ
ma-80	435	7	and	and	CCONJ
ma-80	435	8	lower	low	ADJ
ma-80	435	9	approximations	approximation	NOUN
ma-80	435	10	to	to	ADP
ma-80	435	11	.	.	PUNCT
ma-80	436	1	ith	ith	PROPN
ma-80	436	2	xo	xo	PROPN
ma-80	436	3	w	w	PROPN
ma-80	436	4	y	y	PROPN
ma-80	436	5	=	=	PROPN
ma-80	436	6	wli	wli	PROPN
ma-80	436	7	wli	wli	PROPN
ma-80	436	8	1	1	NUM
ma-80	436	9	+	+	CCONJ
ma-80	436	10	x	x	PUNCT
ma-80	436	11	xo	xo	PROPN
ma-80	436	12	y	y	PROPN
ma-80	436	13	x	x	PROPN
ma-80	436	14	wui	wui	PROPN
ma-80	436	15	ye	ye	PROPN
ma-80	436	16	x	x	PROPN
ma-80	436	17	–	–	PUNCT
ma-80	436	18	xo	xo	PROPN
ma-80	436	19	wui	wui	PROPN
ma-80	436	20	1	1	NUM
ma-80	436	21	+	+	CCONJ
ma-80	436	22	uili	uili	VERB
ma-80	436	23	y	y	PROPN
ma-80	436	24	xo	xo	PROPN
ma-80	437	1	w	w	PROPN
ma-80	437	2	y	y	PROPN
ma-80	437	3	=	=	NOUN
ma-80	437	4	wli	wli	NOUN
ma-80	437	5	i	i	NOUN
ma-80	437	6	1	1	NUM
ma-80	437	7	2	2	NUM
ma-80	437	8			NOUN
ma-80	437	9			X
ma-80	437	10			NUM
ma-80	437	11	li	li	VERB
ma-80	437	12	li	li	VERB
ma-80	437	13	1	1	NUM
ma-80	437	14	–	–	PUNCT
ma-80	437	15	wli	wli	NOUN
ma-80	437	16	1	1	NUM
ma-80	437	17	–	–	PUNCT
ma-80	437	18	wui	wui	PROPN
ma-80	437	19	1	1	NUM
ma-80	437	20	–	–	PUNCT
ma-80	437	21	wli	wli	NOUN
ma-80	437	22	1	1	NUM
ma-80	437	23	–	–	PUNCT
ma-80	437	24	–	–	PUNCT
ma-80	437	25			NOUN
ma-80	437	26			NOUN
ma-80	437	27	1	1	NUM
ma-80	437	28	wli	wli	NOUN
ma-80	437	29	1	1	NUM
ma-80	437	30	–	–	PUNCT
ma-80	437	31	+	+	NUM
ma-80	437	32	-------------------------------------------------------	-------------------------------------------------------	PUNCT
ma-80	437	33	–	–	PUNCT
ma-80	437	34	li	li	ADJ
ma-80	437	35	1	1	NUM
ma-80	437	36	–	–	PUNCT
ma-80	437	37	wli	wli	NOUN
ma-80	437	38	1	1	NUM
ma-80	437	39	–	–	PUNCT
ma-80	437	40	li	li	ADJ
ma-80	437	41	1	1	NUM
ma-80	437	42	–	–	PUNCT
ma-80	437	43	ui	ui	PROPN
ma-80	437	44	1	1	NUM
ma-80	437	45	–	–	PUNCT
ma-80	437	46	+	+	NOUN
ma-80	437	47			ADJ
ma-80	437	48			NOUN
ma-80	437	49	1	1	NUM
ma-80	437	50	wli	wli	NOUN
ma-80	437	51	1	1	NUM
ma-80	437	52	–	–	PUNCT
ma-80	437	53	+	+	NUM
ma-80	437	54	---------------------------------------------------–=	---------------------------------------------------–=	NOUN
ma-80	437	55	=	=	PUNCT
ma-80	437	56	l1	l1	PROPN
ma-80	437	57	xo	xo	PROPN
ma-80	437	58	y	y	PROPN
ma-80	437	59	1	1	NUM
ma-80	437	60	y+	y+	NUM
ma-80	437	61	------------	------------	PUNCT
ma-80	437	62	–	–	PUNCT
ma-80	437	63	.=	.=	VERB
ma-80	438	1	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	NOUN
ma-80	438	2	the	the	DET
ma-80	438	3	following	follow	VERB
ma-80	438	4	results	result	NOUN
ma-80	438	5	hold	hold	VERB
ma-80	438	6	:	:	PUNCT
ma-80	438	7	first	first	ADV
ma-80	438	8	,	,	PUNCT
ma-80	438	9	the	the	DET
ma-80	438	10	sequence	sequence	NOUN
ma-80	438	11	is	be	AUX
ma-80	438	12	a	a	DET
ma-80	438	13	monotonically	monotonically	ADV
ma-80	438	14	increasing	increase	VERB
ma-80	438	15	sequence	sequence	NOUN
ma-80	438	16	,	,	PUNCT
ma-80	438	17	i.e.	i.e.	X
ma-80	438	18	.	.	PUNCT
ma-80	439	1	second	second	ADV
ma-80	439	2	,	,	PUNCT
ma-80	439	3	the	the	DET
ma-80	439	4	errors	error	NOUN
ma-80	439	5	,	,	PUNCT
ma-80	439	6	,	,	PUNCT
ma-80	439	7	define	define	VERB
ma-80	439	8	a	a	DET
ma-80	439	9	monotonically	monotonically	ADV
ma-80	439	10	decreasing	decrease	VERB
ma-80	439	11	sequence	sequence	NOUN
ma-80	439	12	,	,	PUNCT
ma-80	439	13	i.e.	i.e.	X
ma-80	439	14	.	.	PUNCT
ma-80	440	1	third	third	ADJ
ma-80	440	2	,	,	PUNCT
ma-80	440	3	convergence	convergence	NOUN
ma-80	440	4	is	be	AUX
ma-80	440	5	guaranteed	guarantee	VERB
ma-80	440	6	,	,	PUNCT
ma-80	440	7	i.e.	i.e.	X
ma-80	440	8	,	,	PUNCT
ma-80	440	9	and	and	CCONJ
ma-80	440	10	.	.	PUNCT
ma-80	441	1	proof	proof	NOUN
ma-80	441	2	.	.	PUNCT
ma-80	442	1	the	the	DET
ma-80	442	2	proof	proof	NOUN
ma-80	442	3	of	of	ADP
ma-80	442	4	these	these	DET
ma-80	442	5	results	result	NOUN
ma-80	442	6	is	be	AUX
ma-80	442	7	detailed	detail	VERB
ma-80	442	8	in	in	ADP
ma-80	442	9	appendix	appendix	PROPN
ma-80	442	10	d.	d.	PROPN
ma-80	442	11	5	5	NUM
ma-80	442	12	.	.	PUNCT
ma-80	442	13	spline	spline	PROPN
ma-80	442	14	based	base	VERB
ma-80	442	15	approximation	approximation	NOUN
ma-80	442	16	for	for	ADP
ma-80	442	17	[	[	X
ma-80	442	18	-1	-1	ADJ
ma-80	442	19	/	/	SYM
ma-80	442	20	e,0	e,0	NOUN
ma-80	442	21	]	]	PUNCT
ma-80	442	22	the	the	DET
ma-80	442	23	approximations	approximation	NOUN
ma-80	442	24	,	,	PUNCT
ma-80	442	25	detailed	detail	VERB
ma-80	442	26	above	above	ADV
ma-80	442	27	in	in	ADP
ma-80	442	28	theorem	theorem	ADJ
ma-80	442	29	3.1	3.1	NUM
ma-80	442	30	and	and	CCONJ
ma-80	442	31	theorem	theorem	VERB
ma-80	442	32	3.4	3.4	NUM
ma-80	442	33	,	,	PUNCT
ma-80	442	34	are	be	AUX
ma-80	442	35	sharp	sharp	ADJ
ma-80	442	36	at	at	ADP
ma-80	442	37	the	the	DET
ma-80	442	38	origin	origin	NOUN
ma-80	442	39	but	but	CCONJ
ma-80	442	40	not	not	PART
ma-80	442	41	at	at	ADP
ma-80	442	42	the	the	DET
ma-80	442	43	point	point	NOUN
ma-80	442	44	.	.	PUNCT
ma-80	443	1	it	it	PRON
ma-80	443	2	is	be	AUX
ma-80	443	3	useful	useful	ADJ
ma-80	443	4	to	to	PART
ma-80	443	5	have	have	VERB
ma-80	443	6	approximations	approximation	NOUN
ma-80	443	7	that	that	PRON
ma-80	443	8	are	be	AUX
ma-80	443	9	sharp	sharp	ADJ
ma-80	443	10	at	at	ADP
ma-80	443	11	both	both	DET
ma-80	443	12	points	point	NOUN
ma-80	443	13	and	and	CCONJ
ma-80	443	14	which	which	PRON
ma-80	443	15	converge	converge	VERB
ma-80	443	16	throughout	throughout	ADP
ma-80	443	17	the	the	DET
ma-80	443	18	interval	interval	NOUN
ma-80	443	19	,	,	PUNCT
ma-80	443	20	e.	e.	PROPN
ma-80	443	21	g.	g.	PROPN
ma-80	444	1	[	[	X
ma-80	444	2	3	3	NUM
ma-80	444	3	]	]	PUNCT
ma-80	444	4	,	,	PUNCT
ma-80	444	5	eqn	eqn	NOUN
ma-80	444	6	.	.	PROPN
ma-80	444	7	7	7	NUM
ma-80	445	1	and	and	CCONJ
ma-80	445	2	[	[	X
ma-80	445	3	17	17	NUM
ma-80	445	4	]	]	PUNCT
ma-80	445	5	,	,	PUNCT
ma-80	445	6	eqn	eqn	PROPN
ma-80	445	7	.	.	PUNCT
ma-80	446	1	20	20	NUM
ma-80	446	2	.	.	PUNCT
ma-80	447	1	the	the	DET
ma-80	447	2	latter	latter	ADJ
ma-80	447	3	approximation	approximation	NOUN
ma-80	447	4	is	be	AUX
ma-80	447	5	sharp	sharp	ADJ
ma-80	447	6	at	at	ADP
ma-80	447	7	but	but	CCONJ
ma-80	447	8	not	not	PART
ma-80	447	9	at	at	ADP
ma-80	447	10	the	the	DET
ma-80	447	11	origin	origin	NOUN
ma-80	447	12	.	.	PUNCT
ma-80	448	1	one	one	NUM
ma-80	448	2	approach	approach	NOUN
ma-80	448	3	,	,	PUNCT
ma-80	448	4	with	with	ADP
ma-80	448	5	potential	potential	NOUN
ma-80	448	6	,	,	PUNCT
ma-80	448	7	is	be	AUX
ma-80	448	8	to	to	PART
ma-80	448	9	utilize	utilize	VERB
ma-80	448	10	the	the	DET
ma-80	448	11	two	two	NUM
ma-80	448	12	point	point	NOUN
ma-80	448	13	spline	spline	NOUN
ma-80	448	14	approximation	approximation	NOUN
ma-80	448	15	for	for	ADP
ma-80	448	16	a	a	DET
ma-80	448	17	function	function	NOUN
ma-80	448	18	as	as	SCONJ
ma-80	448	19	specified	specify	VERB
ma-80	448	20	by	by	ADP
ma-80	448	21	howard	howard	PROPN
ma-80	448	22	,	,	PUNCT
ma-80	448	23	[	[	X
ma-80	448	24	16	16	NUM
ma-80	448	25	]	]	PUNCT
ma-80	448	26	,	,	PUNCT
ma-80	448	27	eqn	eqn	PROPN
ma-80	448	28	.	.	PUNCT
ma-80	448	29	40	40	NUM
ma-80	448	30	.	.	PUNCT
ma-80	449	1	for	for	ADP
ma-80	449	2	an	an	DET
ma-80	449	3	interval	interval	NOUN
ma-80	449	4	,	,	PUNCT
ma-80	449	5	the	the	DET
ma-80	449	6	order	order	NOUN
ma-80	449	7	approximation	approximation	NOUN
ma-80	449	8	can	can	AUX
ma-80	449	9	be	be	AUX
ma-80	449	10	written	write	VERB
ma-80	449	11	in	in	ADP
ma-80	449	12	the	the	DET
ma-80	449	13	form	form	NOUN
ma-80	449	14	(	(	PUNCT
ma-80	449	15	see	see	VERB
ma-80	449	16	appendix	appendix	NOUN
ma-80	449	17	e	e	NOUN
ma-80	449	18	)	)	PUNCT
ma-80	449	19	(	(	PUNCT
ma-80	449	20	70	70	NUM
ma-80	449	21	)	)	PUNCT
ma-80	450	1	where	where	SCONJ
ma-80	450	2	(	(	PUNCT
ma-80	450	3	71	71	NUM
ma-80	450	4	)	)	PUNCT
ma-80	450	5	5.1	5.1	NUM
ma-80	450	6	.	.	PUNCT
ma-80	451	1	spline	spline	NOUN
ma-80	451	2	based	base	VERB
ma-80	451	3	approximations	approximation	NOUN
ma-80	451	4	for	for	ADP
ma-80	451	5	[	[	X
ma-80	451	6	-1	-1	X
ma-80	451	7	/	/	SYM
ma-80	451	8	e,0	e,0	NOUN
ma-80	451	9	]	]	PUNCT
ma-80	451	10	.	.	PUNCT
ma-80	452	1	the	the	DET
ma-80	452	2	spline	spline	PROPN
ma-80	452	3	approximation	approximation	NOUN
ma-80	452	4	detailed	detail	VERB
ma-80	452	5	in	in	ADP
ma-80	452	6	equation	equation	NOUN
ma-80	452	7	70	70	NUM
ma-80	452	8	has	have	VERB
ma-80	452	9	the	the	DET
ma-80	452	10	potential	potential	NOUN
ma-80	452	11	to	to	PART
ma-80	452	12	provide	provide	VERB
ma-80	452	13	approximations	approximation	NOUN
ma-80	452	14	for	for	ADP
ma-80	452	15	the	the	DET
ma-80	452	16	lambert	lambert	PROPN
ma-80	452	17	w	w	PROPN
ma-80	452	18	function	function	NOUN
ma-80	452	19	in	in	ADP
ma-80	452	20	the	the	DET
ma-80	452	21	interval	interval	NOUN
ma-80	452	22	with	with	ADP
ma-80	452	23	exact	exact	ADJ
ma-80	452	24	values	value	NOUN
ma-80	452	25	at	at	ADP
ma-80	452	26	the	the	DET
ma-80	452	27	end	end	NOUN
ma-80	452	28	points	point	NOUN
ma-80	452	29	of	of	ADP
ma-80	452	30	this	this	DET
ma-80	452	31	interval	interval	NOUN
ma-80	452	32	.	.	PUNCT
ma-80	453	1	however	however	ADV
ma-80	453	2	,	,	PUNCT
ma-80	453	3	an	an	DET
ma-80	453	4	initial	initial	ADJ
ma-80	453	5	problem	problem	NOUN
ma-80	453	6	is	be	AUX
ma-80	453	7	that	that	SCONJ
ma-80	453	8	the	the	DET
ma-80	453	9	derivatives	derivative	NOUN
ma-80	453	10	of	of	ADP
ma-80	453	11	the	the	DET
ma-80	453	12	lambert	lambert	PROPN
ma-80	453	13	w	w	PROPN
ma-80	453	14	function	function	NOUN
ma-80	453	15	are	be	AUX
ma-80	453	16	undefined	undefined	ADJ
ma-80	453	17	at	at	ADP
ma-80	453	18	the	the	DET
ma-80	453	19	point	point	NOUN
ma-80	453	20	.	.	PUNCT
ma-80	454	1	this	this	DET
ma-80	454	2	problem	problem	NOUN
ma-80	454	3	can	can	AUX
ma-80	454	4	be	be	AUX
ma-80	454	5	overcome	overcome	VERB
ma-80	454	6	by	by	ADP
ma-80	454	7	utilizing	utilize	VERB
ma-80	454	8	two	two	NUM
ma-80	454	9	suitable	suitable	ADJ
ma-80	454	10	transformations	transformation	NOUN
ma-80	454	11	.	.	PUNCT
ma-80	455	1	lemma	lemma	PROPN
ma-80	455	2	1	1	NUM
ma-80	455	3	.	.	PUNCT
ma-80	455	4	transformations	transformation	NOUN
ma-80	455	5	.	.	PUNCT
ma-80	456	1	with	with	ADP
ma-80	456	2	,	,	PUNCT
ma-80	456	3	,	,	PUNCT
ma-80	456	4	the	the	DET
ma-80	456	5	first	first	ADJ
ma-80	456	6	transformation	transformation	NOUN
ma-80	456	7	(	(	PUNCT
ma-80	456	8	72	72	NUM
ma-80	456	9	)	)	PUNCT
ma-80	456	10	with	with	ADP
ma-80	456	11	,	,	PUNCT
ma-80	456	12	and	and	CCONJ
ma-80	456	13	,	,	PUNCT
ma-80	456	14	,	,	PUNCT
ma-80	456	15	yields	yield	NOUN
ma-80	456	16	(	(	PUNCT
ma-80	456	17	73	73	NUM
ma-80	456	18	)	)	PUNCT
ma-80	456	19	(	(	PUNCT
ma-80	456	20	74	74	X
ma-80	456	21	)	)	PUNCT
ma-80	456	22	wli	wli	PROPN
ma-80	456	23	wli	wli	PROPN
ma-80	456	24	wli	wli	PROPN
ma-80	456	25	1	1	NUM
ma-80	456	26	–	–	PUNCT
ma-80	456	27			VERB
ma-80	456	28	li	li	VERB
ma-80	456	29	i	i	PRON
ma-80	456	30	1	1	NUM
ma-80	456	31	2	2	NUM
ma-80	456	32			NOUN
ma-80	456	33			X
ma-80	456	34			VERB
ma-80	456	35	li	li	VERB
ma-80	456	36	1	1	NUM
ma-80	456	37	+	+	NUM
ma-80	457	1	li	li	NOUN
ma-80	457	2	lii	lii	ADJ
ma-80	457	3			NOUN
ma-80	457	4	lim	lim	PROPN
ma-80	457	5	0=	0=	NUM
ma-80	457	6	wlii	wlii	PROPN
ma-80	457	7			PROPN
ma-80	457	8	lim	lim	PROPN
ma-80	457	9	xo=	xo=	PROPN
ma-80	457	10	wuii	wuii	PROPN
ma-80	457	11			PROPN
ma-80	457	12	lim	lim	PROPN
ma-80	457	13	xo=	xo=	PROPN
ma-80	457	14	1	1	NUM
ma-80	457	15	e	e	ADV
ma-80	457	16	–	–	PUNCT
ma-80	457	17	1	1	NUM
ma-80	457	18	–	–	PUNCT
ma-80	457	19	e	e	NOUN
ma-80	457	20	0	0	NUM
ma-80	457	21			NOUN
ma-80	457	22	1	1	NUM
ma-80	457	23	–	–	PUNCT
ma-80	457	24	e	e	ADV
ma-80	457	25	f	f	PROPN
ma-80	457	26			PROPN
ma-80	457	27			NOUN
ma-80	457	28			PROPN
ma-80	458	1	nth	nth	NOUN
ma-80	458	2	fn	fn	PROPN
ma-80	458	3	x	x	PROPN
ma-80	459	1			PROPN
ma-80	459	2			NOUN
ma-80	459	3	x–	x–	NOUN
ma-80	459	4	n	n	PROPN
ma-80	460	1	1	1	NUM
ma-80	460	2	+	+	ADP
ma-80	460	3	an	an	DET
ma-80	460	4	r	r	ADJ
ma-80	460	5	x	x	NOUN
ma-80	460	6	–	–	NOUN
ma-80	460	7	r	r	NOUN
ma-80	460	8	r	r	NOUN
ma-80	460	9	0=	0=	NOUN
ma-80	461	1	n	n	NOUN
ma-80	461	2			X
ma-80	462	1	x	x	PUNCT
ma-80	462	2	–	–	NOUN
ma-80	462	3	n	n	PROPN
ma-80	462	4	1	1	NUM
ma-80	462	5	+	+	NUM
ma-80	462	6	bn	bn	NUM
ma-80	462	7	r	r	ADJ
ma-80	462	8			NOUN
ma-80	462	9	x–	x–	PUNCT
ma-80	463	1	r	r	X
ma-80	463	2	r	r	NOUN
ma-80	463	3	0=	0=	NUM
ma-80	463	4	n	n	NOUN
ma-80	463	5	+	+	NUM
ma-80	463	6	=	=	PROPN
ma-80	463	7	x	x	SYM
ma-80	463	8			X
ma-80	463	9			NOUN
ma-80	463	10	,	,	PROPN
ma-80	463	11	an	an	DET
ma-80	463	12	r	r	PROPN
ma-80	463	13	1	1	NUM
ma-80	463	14			NOUN
ma-80	463	15	–	–	NOUN
ma-80	463	16	n	n	PROPN
ma-80	463	17	1	1	NUM
ma-80	463	18	+	+	NUM
ma-80	463	19	---------------------------f	---------------------------f	NOUN
ma-80	463	20	r	r	NOUN
ma-80	463	21	u–	u–	NOUN
ma-80	463	22			PUNCT
ma-80	463	23			NOUN
ma-80	463	24			NOUN
ma-80	463	25	r	r	NOUN
ma-80	463	26	u–	u–	NOUN
ma-80	463	27			PROPN
ma-80	463	28	!	!	PUNCT
ma-80	463	29	----------------------n	----------------------n	PUNCT
ma-80	464	1	u+	u+	PROPN
ma-80	464	2			PROPN
ma-80	464	3	!	!	PUNCT
ma-80	465	1	u!n	u!n	PROPN
ma-80	465	2	!	!	PUNCT
ma-80	465	3	-------------------	-------------------	PROPN
ma-80	465	4	u	u	NOUN
ma-80	466	1	0=	0=	NOUN
ma-80	466	2	r	r	NOUN
ma-80	466	3			X
ma-80	466	4	1	1	NUM
ma-80	466	5			NOUN
ma-80	466	6	–	–	NOUN
ma-80	466	7	u	u	PROPN
ma-80	466	8	--------------------	--------------------	PUNCT
ma-80	466	9			NUM
ma-80	466	10	=	=	NOUN
ma-80	466	11	bn	bn	NOUN
ma-80	466	12	r	r	ADJ
ma-80	466	13	1	1	NUM
ma-80	466	14			NOUN
ma-80	466	15	–	–	NOUN
ma-80	466	16	n	n	PROPN
ma-80	466	17	1	1	NUM
ma-80	466	18	+	+	CCONJ
ma-80	466	19	---------------------------1–	---------------------------1–	PROPN
ma-80	466	20	r	r	DET
ma-80	466	21	u	u	NOUN
ma-80	466	22	–	–	PUNCT
ma-80	466	23	f	f	PROPN
ma-80	466	24	r	r	NOUN
ma-80	466	25	u–	u–	NOUN
ma-80	466	26			NUM
ma-80	466	27			NOUN
ma-80	467	1			PUNCT
ma-80	467	2	r	r	NOUN
ma-80	467	3	u–	u–	NOUN
ma-80	467	4			PROPN
ma-80	467	5	!	!	PUNCT
ma-80	467	6	-------------------------------------------n	-------------------------------------------n	PUNCT
ma-80	467	7	u+	u+	PROPN
ma-80	467	8			PROPN
ma-80	467	9	!	!	PUNCT
ma-80	467	10	u!n	u!n	PROPN
ma-80	467	11	!	!	PUNCT
ma-80	467	12	-------------------	-------------------	PROPN
ma-80	467	13	u	u	NOUN
ma-80	467	14	0=	0=	NOUN
ma-80	467	15	r	r	NOUN
ma-80	467	16			X
ma-80	467	17	1	1	NUM
ma-80	467	18			NOUN
ma-80	467	19	–	–	NOUN
ma-80	467	20	u	u	PROPN
ma-80	468	1	--------------------.	--------------------.	PUNCT
ma-80	468	2	=	=	NOUN
ma-80	468	3	1	1	NUM
ma-80	468	4	e	e	ADV
ma-80	468	5	–	–	PUNCT
ma-80	468	6	0	0	NUM
ma-80	468	7			NOUN
ma-80	468	8	1	1	NUM
ma-80	468	9	e	e	ADV
ma-80	468	10	–	–	PUNCT
ma-80	468	11	f	f	X
ma-80	468	12	x	x	PUNCT
ma-80	468	13			PROPN
ma-80	468	14	xe	xe	PROPN
ma-80	468	15	x	x	X
ma-80	469	1	=	=	SYM
ma-80	469	2	x	x	SYM
ma-80	469	3	1–	1–	NUM
ma-80	469	4	y1	y1	NOUN
ma-80	469	5	g1	g1	NOUN
ma-80	469	6	x1	x1	PUNCT
ma-80	470	1			PROPN
ma-80	470	2	1	1	NUM
ma-80	470	3	e	e	PROPN
ma-80	470	4	--f	--f	NOUN
ma-80	470	5	x1	x1	PROPN
ma-80	471	1	1–	1–	NUM
ma-80	471	2	+	+	NUM
ma-80	471	3	==	==	NOUN
ma-80	471	4	x	x	PUNCT
ma-80	471	5	x1	x1	PROPN
ma-80	472	1	1–=	1–=	NUM
ma-80	472	2	x1	x1	NUM
ma-80	472	3	0	0	NOUN
ma-80	473	1	y	y	PROPN
ma-80	473	2	y1	y1	PROPN
ma-80	473	3	1	1	NUM
ma-80	473	4	e	e	X
ma-80	473	5	---–=	---–=	PROPN
ma-80	473	6	y	y	PROPN
ma-80	473	7	1	1	NUM
ma-80	473	8	–	–	PUNCT
ma-80	473	9	e	e	X
ma-80	473	10	------	------	X
ma-80	473	11	y1	y1	NOUN
ma-80	473	12	0	0	NOUN
ma-80	473	13	g1	g1	PROPN
ma-80	473	14	x1	x1	PUNCT
ma-80	474	1			PROPN
ma-80	474	2	1	1	NUM
ma-80	474	3	e	e	NOUN
ma-80	474	4	--1	--1	NOUN
ma-80	474	5	x1	x1	PROPN
ma-80	474	6	1–	1–	NUM
ma-80	474	7	e	e	PROPN
ma-80	474	8	x1+	x1+	PROPN
ma-80	474	9			PROPN
ma-80	474	10	=	=	NOUN
ma-80	474	11	x1	x1	NUM
ma-80	474	12	0	0	NOUN
ma-80	474	13			NUM
ma-80	474	14	w	w	PROPN
ma-80	474	15	y	y	NOUN
ma-80	474	16			PUNCT
ma-80	474	17	f	f	PROPN
ma-80	474	18	1	1	NUM
ma-80	474	19	–	–	PUNCT
ma-80	474	20	y	y	NOUN
ma-80	474	21			PROPN
ma-80	474	22	g1	g1	NOUN
ma-80	474	23	1	1	NUM
ma-80	474	24	–	–	PUNCT
ma-80	474	25	y	y	NOUN
ma-80	474	26	1	1	NUM
ma-80	474	27	e	e	NOUN
ma-80	474	28	---+	---+	NUM
ma-80	474	29	1	1	NUM
ma-80	474	30	–	–	PUNCT
ma-80	474	31	=	=	NOUN
ma-80	474	32	y	y	NOUN
ma-80	474	33	1	1	NUM
ma-80	474	34	–	–	PUNCT
ma-80	474	35	e	e	X
ma-80	474	36	------.=	------.=	NOUN
ma-80	474	37	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	NOUN
ma-80	474	38	with	with	ADP
ma-80	474	39	the	the	DET
ma-80	474	40	second	second	ADJ
ma-80	474	41	transformation	transformation	NOUN
ma-80	474	42	of	of	ADP
ma-80	474	43	,	,	PUNCT
ma-80	474	44	it	it	PRON
ma-80	474	45	follows	follow	VERB
ma-80	474	46	that	that	SCONJ
ma-80	474	47	(	(	PUNCT
ma-80	474	48	75	75	NUM
ma-80	474	49	)	)	PUNCT
ma-80	474	50	(	(	PUNCT
ma-80	474	51	76	76	NUM
ma-80	474	52	)	)	PUNCT
ma-80	474	53	proof	proof	NOUN
ma-80	474	54	.	.	PUNCT
ma-80	475	1	the	the	DET
ma-80	475	2	proofs	proof	NOUN
ma-80	475	3	for	for	ADP
ma-80	475	4	these	these	DET
ma-80	475	5	results	result	NOUN
ma-80	475	6	are	be	AUX
ma-80	475	7	detailed	detail	VERB
ma-80	475	8	in	in	ADP
ma-80	475	9	appendix	appendix	PROPN
ma-80	475	10	f.	f.	PROPN
ma-80	475	11	5.1.1	5.1.1	PROPN
ma-80	475	12	.	.	PUNCT
ma-80	476	1	graphs	graph	NOUN
ma-80	476	2	and	and	CCONJ
ma-80	476	3	values	value	NOUN
ma-80	476	4	.	.	PUNCT
ma-80	477	1	consistent	consistent	ADJ
ma-80	477	2	with	with	ADP
ma-80	477	3	equation	equation	NOUN
ma-80	477	4	76	76	NUM
ma-80	477	5	,	,	PUNCT
ma-80	477	6	the	the	DET
ma-80	477	7	lambert	lambert	PROPN
ma-80	477	8	w	w	PROPN
ma-80	477	9	function	function	PROPN
ma-80	477	10	is	be	AUX
ma-80	477	11	defined	define	VERB
ma-80	477	12	in	in	ADP
ma-80	477	13	terms	term	NOUN
ma-80	477	14	of	of	ADP
ma-80	477	15	for	for	ADP
ma-80	477	16	.	.	PUNCT
ma-80	478	1	relevant	relevant	ADJ
ma-80	478	2	values	value	NOUN
ma-80	478	3	associated	associate	VERB
ma-80	478	4	with	with	ADP
ma-80	478	5	the	the	DET
ma-80	478	6	points	point	NOUN
ma-80	478	7	and	and	CCONJ
ma-80	478	8	are	be	AUX
ma-80	478	9	specified	specify	VERB
ma-80	478	10	in	in	ADP
ma-80	478	11	table	table	NOUN
ma-80	478	12	4	4	NUM
ma-80	478	13	.	.	PUNCT
ma-80	479	1	the	the	DET
ma-80	479	2	graph	graph	NOUN
ma-80	479	3	of	of	ADP
ma-80	479	4	,	,	PUNCT
ma-80	479	5	and	and	CCONJ
ma-80	479	6	its	its	PRON
ma-80	479	7	inverse	inverse	NOUN
ma-80	479	8	,	,	PUNCT
ma-80	479	9	are	be	AUX
ma-80	479	10	shown	show	VERB
ma-80	479	11	in	in	ADP
ma-80	479	12	figure	figure	NOUN
ma-80	479	13	19	19	NUM
ma-80	479	14	.	.	PUNCT
ma-80	480	1	5.1.2	5.1.2	NUM
ma-80	480	2	.	.	PUNCT
ma-80	480	3	spline	spline	NOUN
ma-80	480	4	based	base	VERB
ma-80	480	5	approximations	approximation	NOUN
ma-80	480	6	.	.	PUNCT
ma-80	481	1	consistent	consistent	ADJ
ma-80	481	2	with	with	ADP
ma-80	481	3	equation	equation	NOUN
ma-80	481	4	76	76	NUM
ma-80	481	5	,	,	PUNCT
ma-80	481	6	and	and	CCONJ
ma-80	481	7	the	the	DET
ma-80	481	8	values	value	NOUN
ma-80	481	9	tabulated	tabulate	VERB
ma-80	481	10	in	in	ADP
ma-80	481	11	table	table	NOUN
ma-80	481	12	4	4	NUM
ma-80	481	13	,	,	PUNCT
ma-80	481	14	an	an	DET
ma-80	481	15	approximation	approximation	NOUN
ma-80	481	16	for	for	ADP
ma-80	481	17	the	the	DET
ma-80	481	18	lambert	lambert	NOUN
ma-80	481	19	,	,	PUNCT
ma-80	481	20	over	over	ADP
ma-80	481	21	the	the	DET
ma-80	481	22	interval	interval	NOUN
ma-80	481	23	,	,	PUNCT
ma-80	481	24	requires	require	VERB
ma-80	481	25	an	an	DET
ma-80	481	26	approximation	approximation	NOUN
ma-80	481	27	to	to	ADP
ma-80	481	28	the	the	DET
ma-80	481	29	inverse	inverse	NOUN
ma-80	481	30	of	of	ADP
ma-80	481	31	,	,	PUNCT
ma-80	481	32	,	,	PUNCT
ma-80	481	33	i.e.	i.e.	X
ma-80	481	34	,	,	PUNCT
ma-80	481	35	,	,	PUNCT
ma-80	481	36	to	to	PART
ma-80	481	37	be	be	AUX
ma-80	481	38	determined	determine	VERB
ma-80	481	39	.	.	PUNCT
ma-80	482	1	a	a	DET
ma-80	482	2	spline	spline	NOUN
ma-80	482	3	approximation	approximation	NOUN
ma-80	482	4	for	for	ADP
ma-80	482	5	,	,	PUNCT
ma-80	482	6	of	of	ADP
ma-80	482	7	order	order	NOUN
ma-80	482	8	,	,	PUNCT
ma-80	482	9	requires	require	VERB
ma-80	482	10	derivatives	derivative	NOUN
ma-80	482	11	,	,	PUNCT
ma-80	482	12	of	of	ADP
ma-80	482	13	orders	order	NOUN
ma-80	482	14	zero	zero	NUM
ma-80	482	15	to	to	ADP
ma-80	482	16	,	,	PUNCT
ma-80	482	17	at	at	ADP
ma-80	482	18	the	the	DET
ma-80	482	19	points	point	NOUN
ma-80	482	20	and	and	CCONJ
ma-80	482	21	to	to	PART
ma-80	482	22	be	be	AUX
ma-80	482	23	determined	determine	VERB
ma-80	482	24	.	.	PUNCT
ma-80	483	1	such	such	ADJ
ma-80	483	2	values	value	NOUN
ma-80	483	3	can	can	AUX
ma-80	483	4	be	be	AUX
ma-80	483	5	determined	determine	VERB
ma-80	483	6	from	from	ADP
ma-80	483	7	the	the	DET
ma-80	483	8	derivatives	derivative	NOUN
ma-80	483	9	of	of	ADP
ma-80	483	10	at	at	ADP
ma-80	483	11	the	the	DET
ma-80	483	12	points	point	NOUN
ma-80	483	13	and	and	CCONJ
ma-80	483	14	as	as	SCONJ
ma-80	483	15	detailed	detailed	ADJ
ma-80	483	16	in	in	ADP
ma-80	483	17	appendix	appendix	PROPN
ma-80	483	18	g.	g.	NOUN
ma-80	483	19	the	the	DET
ma-80	483	20	following	follow	VERB
ma-80	483	21	approximations	approximation	NOUN
ma-80	483	22	result	result	VERB
ma-80	483	23	.	.	PUNCT
ma-80	484	1	theorem	theorem	VERB
ma-80	484	2	5.1	5.1	NUM
ma-80	484	3	.	.	PUNCT
ma-80	485	1	spline	spline	NOUN
ma-80	485	2	based	base	VERB
ma-80	485	3	approximations	approximation	NOUN
ma-80	485	4	for	for	ADP
ma-80	485	5	the	the	DET
ma-80	485	6	lambert	lambert	PROPN
ma-80	485	7	w	w	PROPN
ma-80	485	8	function	function	PROPN
ma-80	485	9	.	.	PUNCT
ma-80	486	1	the	the	DET
ma-80	486	2	order	order	NOUN
ma-80	486	3	spline	spline	NOUN
ma-80	486	4	based	base	VERB
ma-80	486	5	approximation	approximation	NOUN
ma-80	486	6	for	for	ADP
ma-80	486	7	the	the	DET
ma-80	486	8	lambert	lambert	PROPN
ma-80	486	9	w	w	PROPN
ma-80	486	10	function	function	PROPN
ma-80	486	11	,	,	PUNCT
ma-80	486	12	based	base	VERB
ma-80	486	13	on	on	ADP
ma-80	486	14	the	the	DET
ma-80	486	15	transformation	transformation	NOUN
ma-80	486	16	and	and	CCONJ
ma-80	486	17	the	the	DET
ma-80	486	18	points	point	NOUN
ma-80	486	19	and	and	CCONJ
ma-80	486	20	,	,	PUNCT
ma-80	486	21	is	be	AUX
ma-80	486	22	(	(	PUNCT
ma-80	486	23	77	77	NUM
ma-80	486	24	)	)	PUNCT
ma-80	486	25	table	table	NOUN
ma-80	486	26	4	4	NUM
ma-80	486	27	.	.	PUNCT
ma-80	487	1	values	value	NOUN
ma-80	487	2	associated	associate	VERB
ma-80	487	3	with	with	ADP
ma-80	487	4	the	the	DET
ma-80	487	5	points	point	NOUN
ma-80	487	6	and	and	CCONJ
ma-80	487	7	.	.	PUNCT
ma-80	488	1	g	g	NOUN
ma-80	488	2	x1	x1	PROPN
ma-80	489	1			PROPN
ma-80	489	2	g1	g1	PROPN
ma-80	489	3	x1	x1	PROPN
ma-80	490	1	=	=	NOUN
ma-80	490	2	g	g	NOUN
ma-80	490	3	x1	x1	PROPN
ma-80	491	1			PROPN
ma-80	491	2	1	1	NUM
ma-80	491	3	e	e	NOUN
ma-80	491	4	--1	--1	NOUN
ma-80	491	5	x1	x1	PROPN
ma-80	491	6	1–	1–	NUM
ma-80	491	7	e	e	PROPN
ma-80	491	8	x1+	x1+	PROPN
ma-80	491	9			PROPN
ma-80	491	10	=	=	NOUN
ma-80	491	11	x1	x1	NUM
ma-80	491	12	0	0	NOUN
ma-80	491	13			NUM
ma-80	491	14	w	w	ADP
ma-80	491	15	y	y	NOUN
ma-80	491	16			PROPN
ma-80	491	17	g	g	PROPN
ma-80	491	18	1	1	NUM
ma-80	491	19	–	–	PUNCT
ma-80	491	20	y	y	NOUN
ma-80	491	21	1	1	NUM
ma-80	491	22	e	e	NOUN
ma-80	491	23	---+	---+	NUM
ma-80	491	24	1	1	NUM
ma-80	491	25	–	–	PUNCT
ma-80	491	26	=	=	NOUN
ma-80	491	27	y	y	NOUN
ma-80	491	28	1	1	NUM
ma-80	491	29	e	e	NOUN
ma-80	491	30	---	---	PUNCT
ma-80	491	31	–	–	PUNCT
ma-80	491	32	.	.	PUNCT
ma-80	491	33	g	g	PROPN
ma-80	491	34	1	1	NUM
ma-80	491	35	–	–	PUNCT
ma-80	491	36	y	y	PROPN
ma-80	491	37	1	1	NUM
ma-80	491	38	e	e	ADV
ma-80	491	39	–	–	PUNCT
ma-80	491	40	0	0	NUM
ma-80	491	41			PROPN
ma-80	491	42	y	y	PROPN
ma-80	491	43	1	1	NUM
ma-80	491	44	e–=	e–=	NOUN
ma-80	491	45	y	y	NOUN
ma-80	491	46	0=	0=	NOUN
ma-80	492	1	g	g	NOUN
ma-80	492	2	x1	x1	PROPN
ma-80	493	1			PROPN
ma-80	493	2	g	g	PROPN
ma-80	493	3	1	1	NUM
ma-80	493	4	–	–	PUNCT
ma-80	493	5	y2	y2	ADJ
ma-80	493	6			PROPN
ma-80	493	7	figure	figure	NOUN
ma-80	493	8	19	19	NUM
ma-80	493	9	.	.	PUNCT
ma-80	493	10	graph	graph	NOUN
ma-80	493	11	of	of	ADP
ma-80	493	12	and	and	CCONJ
ma-80	493	13	its	its	PRON
ma-80	493	14	inverse	inverse	NOUN
ma-80	493	15	.	.	PUNCT
ma-80	494	1	y2	y2	INTJ
ma-80	494	2	g	g	PROPN
ma-80	494	3	x1	x1	PROPN
ma-80	495	1	=	=	PROPN
ma-80	495	2	g	g	PROPN
ma-80	495	3	1	1	NUM
ma-80	495	4	–	–	PUNCT
ma-80	495	5	y2	y2	ADV
ma-80	495	6			PUNCT
ma-80	495	7	x1	x1	NUM
ma-80	495	8	y2	y2	PROPN
ma-80	496	1	g	g	NOUN
ma-80	496	2	1	1	NUM
ma-80	496	3	–	–	PUNCT
ma-80	496	4	y2	y2	ADJ
ma-80	496	5			PROPN
ma-80	496	6	g	g	NOUN
ma-80	496	7	x1	x1	PROPN
ma-80	497	1			PROPN
ma-80	497	2	1	1	NUM
ma-80	497	3	e	e	ADV
ma-80	497	4	y	y	PROPN
ma-80	497	5	1	1	NUM
ma-80	497	6	e–=	e–=	NOUN
ma-80	497	7	y	y	PROPN
ma-80	497	8	0=	0=	PUNCT
ma-80	498	1	y	y	PROPN
ma-80	498	2	y1	y1	PROPN
ma-80	498	3	y	y	PROPN
ma-80	498	4	1	1	NUM
ma-80	498	5	e+=	e+=	VERB
ma-80	498	6	x	x	X
ma-80	498	7	w	w	NOUN
ma-80	498	8	y	y	NOUN
ma-80	498	9	=	=	NOUN
ma-80	499	1	x1	x1	NUM
ma-80	499	2	x	x	SYM
ma-80	499	3	1+=	1+=	NUM
ma-80	499	4	y2	y2	NOUN
ma-80	499	5	g	g	PROPN
ma-80	499	6	x1	x1	PROPN
ma-80	499	7	=	=	PROPN
ma-80	499	8	1	1	NUM
ma-80	499	9	–	–	PUNCT
ma-80	499	10	e	e	ADV
ma-80	499	11	0	0	NUM
ma-80	499	12	1	1	NUM
ma-80	499	13	–	–	PUNCT
ma-80	499	14	0	0	NUM
ma-80	499	15	0	0	NUM
ma-80	499	16	0	0	NUM
ma-80	499	17	1	1	NUM
ma-80	499	18	e	e	CCONJ
ma-80	499	19	0	0	NUM
ma-80	499	20	1	1	NUM
ma-80	499	21	1	1	NUM
ma-80	499	22	e	e	ADV
ma-80	499	23	w	w	PROPN
ma-80	499	24	1	1	NUM
ma-80	499	25	e	e	NOUN
ma-80	499	26	–	–	PUNCT
ma-80	499	27	0	0	NUM
ma-80	499	28			NOUN
ma-80	499	29	g	g	NOUN
ma-80	499	30	x1	x1	PROPN
ma-80	500	1			PUNCT
ma-80	501	1	x1	x1	PRON
ma-80	501	2	0	0	NUM
ma-80	501	3	1	1	NUM
ma-80	501	4			PROPN
ma-80	501	5	g	g	PROPN
ma-80	501	6	1	1	NUM
ma-80	501	7	–	–	PUNCT
ma-80	501	8	y2	y2	ADV
ma-80	501	9			VERB
ma-80	501	10	y2	y2	NOUN
ma-80	501	11	0	0	NUM
ma-80	501	12	1	1	NUM
ma-80	501	13	e	e	PROPN
ma-80	501	14			PROPN
ma-80	501	15	g	g	PROPN
ma-80	501	16	1	1	NUM
ma-80	501	17	–	–	PUNCT
ma-80	501	18	n	n	CCONJ
ma-80	501	19	n	n	NOUN
ma-80	501	20	0	0	NUM
ma-80	501	21	1	1	NUM
ma-80	501	22	e	e	ADP
ma-80	501	23	g	g	PROPN
ma-80	501	24	0	0	NUM
ma-80	501	25	1	1	NUM
ma-80	501	26	kth	kth	NOUN
ma-80	501	27	g	g	PROPN
ma-80	501	28	1	1	NUM
ma-80	501	29	e–	e–	NOUN
ma-80	501	30			NOUN
ma-80	501	31	0	0	NUM
ma-80	502	1	w	w	PROPN
ma-80	502	2	k	k	X
ma-80	503	1	y	y	PROPN
ma-80	503	2			PROPN
ma-80	503	3	1	1	NUM
ma-80	503	4	–	–	PUNCT
ma-80	503	5	2e	2e	NOUN
ma-80	503	6	y	y	NOUN
ma-80	503	7	1	1	NUM
ma-80	503	8	e	e	NOUN
ma-80	503	9	---+	---+	PROPN
ma-80	503	10	1	1	NUM
ma-80	503	11	1	1	SYM
ma-80	503	12	y	y	PROPN
ma-80	503	13	1	1	NUM
ma-80	503	14	e	e	PROPN
ma-80	503	15	---+	---+	PROPN
ma-80	503	16	2	2	ADJ
ma-80	503	17	y	y	NOUN
ma-80	503	18	1	1	NUM
ma-80	503	19	e	e	NOUN
ma-80	503	20	---+	---+	NUM
ma-80	503	21	3	3	NUM
ma-80	503	22	y	y	NOUN
ma-80	503	23	1	1	NUM
ma-80	503	24	e	e	NOUN
ma-80	503	25	---+	---+	NUM
ma-80	503	26	3	3	NUM
ma-80	503	27	2	2	NUM
ma-80	503	28	+	+	PROPN
ma-80	504	1	+	+	CCONJ
ma-80	504	2	+	+	CCONJ
ma-80	504	3	+	+	CCONJ
ma-80	504	4	2k	2k	VERB
ma-80	504	5	y	y	PROPN
ma-80	504	6	1	1	NUM
ma-80	504	7	e	e	NOUN
ma-80	504	8	---+	---+	NUM
ma-80	504	9	k	k	PROPN
ma-80	505	1	+	+	ADJ
ma-80	505	2	+	+	NUM
ma-80	505	3	=	=	NOUN
ma-80	505	4	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	NOUN
ma-80	505	5	for	for	ADP
ma-80	505	6	and	and	CCONJ
ma-80	505	7	for	for	ADP
ma-80	505	8	appropriately	appropriately	ADV
ma-80	505	9	defined	define	VERB
ma-80	505	10	constants	constant	NOUN
ma-80	505	11	.	.	PUNCT
ma-80	506	1	proof	proof	NOUN
ma-80	506	2	.	.	PUNCT
ma-80	507	1	the	the	DET
ma-80	507	2	proof	proof	NOUN
ma-80	507	3	is	be	AUX
ma-80	507	4	detailed	detail	VERB
ma-80	507	5	in	in	ADP
ma-80	507	6	appendix	appendix	PROPN
ma-80	507	7	g.	g.	PROPN
ma-80	508	1	5.1.3	5.1.3	NUM
ma-80	508	2	.	.	PUNCT
ma-80	508	3	explicit	explicit	ADJ
ma-80	508	4	approximations	approximation	NOUN
ma-80	508	5	.	.	PUNCT
ma-80	509	1	explicit	explicit	ADJ
ma-80	509	2	approximations	approximation	NOUN
ma-80	509	3	,	,	PUNCT
ma-80	509	4	of	of	ADP
ma-80	509	5	orders	order	NOUN
ma-80	509	6	one	one	NUM
ma-80	509	7	to	to	ADP
ma-80	509	8	four	four	NUM
ma-80	509	9	,	,	PUNCT
ma-80	509	10	are	be	AUX
ma-80	509	11	:	:	PUNCT
ma-80	509	12	(	(	PUNCT
ma-80	509	13	78	78	NUM
ma-80	509	14	)	)	PUNCT
ma-80	509	15	(	(	PUNCT
ma-80	509	16	79	79	NUM
ma-80	509	17	)	)	PUNCT
ma-80	509	18	(	(	PUNCT
ma-80	509	19	80	80	NUM
ma-80	509	20	)	)	PUNCT
ma-80	509	21	(	(	PUNCT
ma-80	509	22	81	81	NUM
ma-80	509	23	)	)	PUNCT
ma-80	509	24	k	k	NOUN
ma-80	509	25	1	1	NUM
ma-80	509	26	2	2	NUM
ma-80	509	27			NOUN
ma-80	509	28			X
ma-80	510	1			NUM
ma-80	510	2	w	w	NOUN
ma-80	510	3	1	1	NUM
ma-80	510	4	y	y	NOUN
ma-80	510	5			PROPN
ma-80	510	6	1	1	NUM
ma-80	510	7	–	–	PUNCT
ma-80	510	8	2e	2e	NOUN
ma-80	510	9	y	y	NOUN
ma-80	510	10	1	1	NUM
ma-80	510	11	e	e	NOUN
ma-80	510	12	---+	---+	NUM
ma-80	510	13	1	1	NUM
ma-80	510	14	2	2	NUM
ma-80	510	15	e	e	NOUN
ma-80	510	16	1	1	NUM
ma-80	510	17	1	1	NUM
ma-80	510	18	2e	2e	NUM
ma-80	510	19	---------3	---------3	NOUN
ma-80	510	20	2	2	NUM
ma-80	510	21	2	2	NUM
ma-80	510	22	----------–+	----------–+	NOUN
ma-80	510	23	y	y	NOUN
ma-80	510	24	1	1	NUM
ma-80	510	25	e	e	PROPN
ma-80	510	26	---+	---+	NUM
ma-80	510	27	–	–	PUNCT
ma-80	510	28	e	e	NOUN
ma-80	510	29	1	1	NUM
ma-80	510	30	2	2	NUM
ma-80	510	31	–	–	PUNCT
ma-80	510	32	2	2	NUM
ma-80	510	33	e	e	NOUN
ma-80	510	34	-------+	-------+	NOUN
ma-80	510	35	y	y	PROPN
ma-80	510	36	1	1	NUM
ma-80	510	37	e	e	X
ma-80	510	38	---+++=	---+++=	X
ma-80	510	39	w	w	PROPN
ma-80	510	40	2	2	NUM
ma-80	510	41	y	y	NOUN
ma-80	510	42			PROPN
ma-80	510	43	1	1	NUM
ma-80	510	44	–	–	PUNCT
ma-80	510	45	2e	2e	NOUN
ma-80	510	46	y	y	NOUN
ma-80	510	47	1	1	NUM
ma-80	510	48	e	e	NOUN
ma-80	510	49	---+	---+	NUM
ma-80	510	50	1	1	NUM
ma-80	510	51	2e	2e	PROPN
ma-80	510	52	3	3	NUM
ma-80	510	53	---------y	---------y	NUM
ma-80	510	54	1	1	NUM
ma-80	510	55	e	e	NOUN
ma-80	510	56	---+	---+	NUM
ma-80	510	57	–	–	PUNCT
ma-80	510	58	6e	6e	NUM
ma-80	510	59	2	2	NUM
ma-80	510	60	1–	1–	NUM
ma-80	510	61			PROPN
ma-80	510	62	7	7	NUM
ma-80	510	63	2	2	NUM
ma-80	510	64	-------	-------	PUNCT
ma-80	510	65	–	–	PUNCT
ma-80	510	66	2	2	NUM
ma-80	510	67	2	2	NUM
ma-80	510	68	e	e	NOUN
ma-80	510	69	----------	----------	PROPN
ma-80	510	70	–	–	PUNCT
ma-80	510	71	y	y	PROPN
ma-80	510	72	1	1	NUM
ma-80	510	73	e	e	NOUN
ma-80	510	74	---+	---+	NUM
ma-80	510	75	–	–	PUNCT
ma-80	510	76	+	+	NUM
ma-80	510	77	e	e	X
ma-80	510	78	3	3	NUM
ma-80	510	79	2	2	NUM
ma-80	510	80	17	17	NUM
ma-80	510	81	2	2	NUM
ma-80	510	82	------8	------8	PROPN
ma-80	510	83	–	–	PUNCT
ma-80	510	84	6	6	NUM
ma-80	510	85	2e	2e	NUM
ma-80	510	86	–	–	PUNCT
ma-80	510	87	4	4	NUM
ma-80	510	88	2	2	NUM
ma-80	510	89	e	e	NOUN
ma-80	510	90	----------	----------	PUNCT
ma-80	510	91	–	–	PUNCT
ma-80	510	92	y	y	PROPN
ma-80	510	93	1	1	NUM
ma-80	510	94	e	e	NOUN
ma-80	510	95	---+	---+	NUM
ma-80	510	96	3	3	NUM
ma-80	510	97	2	2	NUM
ma-80	510	98	+	+	CCONJ
ma-80	510	99	e	e	NOUN
ma-80	510	100	2	2	NUM
ma-80	510	101	10	10	NUM
ma-80	510	102	2	2	NUM
ma-80	510	103	3	3	NUM
ma-80	510	104	------------3	------------3	NOUN
ma-80	510	105	–	–	PUNCT
ma-80	510	106	5e	5e	NOUN
ma-80	510	107	2	2	NUM
ma-80	510	108	-------	-------	PUNCT
ma-80	510	109	–	–	PUNCT
ma-80	510	110	2	2	NUM
ma-80	510	111	2	2	NUM
ma-80	510	112	–	–	PUNCT
ma-80	510	113	y	y	NOUN
ma-80	510	114	1	1	NUM
ma-80	510	115	e	e	NOUN
ma-80	510	116	---+	---+	NUM
ma-80	510	117	2	2	NUM
ma-80	510	118	+=	+=	NOUN
ma-80	510	119	w	w	NOUN
ma-80	510	120	3	3	NUM
ma-80	510	121	y	y	NOUN
ma-80	510	122			PROPN
ma-80	510	123	1	1	NUM
ma-80	510	124	–	–	PUNCT
ma-80	510	125	2e	2e	NOUN
ma-80	510	126	y	y	NOUN
ma-80	510	127	1	1	NUM
ma-80	510	128	e	e	NOUN
ma-80	510	129	---+	---+	NUM
ma-80	510	130	1	1	NUM
ma-80	510	131	2e	2e	PROPN
ma-80	510	132	3	3	NUM
ma-80	510	133	---------y	---------y	NUM
ma-80	510	134	1	1	NUM
ma-80	510	135	e	e	X
ma-80	510	136	---+	---+	NUM
ma-80	510	137	–	–	PUNCT
ma-80	510	138	11e	11e	NUM
ma-80	510	139	36	36	NUM
ma-80	510	140	--------y	--------y	NUM
ma-80	510	141	1	1	NUM
ma-80	510	142	e	e	NOUN
ma-80	510	143	---+	---+	NUM
ma-80	510	144	–	–	PUNCT
ma-80	511	1	+	+	NUM
ma-80	511	2	e	e	X
ma-80	511	3	3	3	NUM
ma-80	511	4	2	2	NUM
ma-80	511	5	191	191	NUM
ma-80	511	6	9	9	NUM
ma-80	511	7	--------125	--------125	NOUN
ma-80	511	8	3	3	NUM
ma-80	511	9	2	2	NUM
ma-80	511	10	----------	----------	PUNCT
ma-80	511	11	–	–	PUNCT
ma-80	511	12	25	25	NUM
ma-80	511	13	e	e	SYM
ma-80	511	14	2	2	NUM
ma-80	511	15	------------8	------------8	NOUN
ma-80	511	16	2	2	NUM
ma-80	511	17	e	e	NOUN
ma-80	511	18	---------6	---------6	NOUN
ma-80	511	19	2	2	NUM
ma-80	511	20	e	e	NOUN
ma-80	511	21	3	3	NUM
ma-80	511	22	2	2	NUM
ma-80	511	23	----------+	----------+	PUNCT
ma-80	512	1	+	+	PUNCT
ma-80	512	2	+	+	CCONJ
ma-80	512	3	y	y	PROPN
ma-80	512	4	1	1	NUM
ma-80	512	5	e	e	NOUN
ma-80	512	6	---+	---+	NUM
ma-80	512	7	3	3	NUM
ma-80	512	8	2	2	NUM
ma-80	513	1	+	+	CCONJ
ma-80	513	2	e	e	X
ma-80	513	3	2	2	NUM
ma-80	513	4	281	281	NUM
ma-80	513	5	6	6	NUM
ma-80	513	6	--------146	--------146	NOUN
ma-80	513	7	2	2	NUM
ma-80	513	8	3	3	NUM
ma-80	513	9	----------------	----------------	PUNCT
ma-80	513	10	–	–	PUNCT
ma-80	513	11	32	32	NUM
ma-80	513	12	2e	2e	NOUN
ma-80	513	13	22	22	NUM
ma-80	513	14	2	2	NUM
ma-80	513	15	18	18	NUM
ma-80	513	16	2	2	NUM
ma-80	513	17	e	e	NOUN
ma-80	513	18	-------------+	-------------+	NOUN
ma-80	513	19	+	+	CCONJ
ma-80	513	20	+	+	CCONJ
ma-80	513	21	y	y	PROPN
ma-80	513	22	1	1	NUM
ma-80	513	23	e	e	NOUN
ma-80	513	24	---+	---+	PROPN
ma-80	513	25	2	2	NUM
ma-80	513	26	–	–	PUNCT
ma-80	513	27	e	e	X
ma-80	513	28	5	5	NUM
ma-80	513	29	2	2	NUM
ma-80	513	30	335	335	NUM
ma-80	513	31	9	9	NUM
ma-80	513	32	--------40	--------40	PROPN
ma-80	513	33	2	2	NUM
ma-80	513	34	–	–	PUNCT
ma-80	513	35	55e	55e	NUM
ma-80	513	36	3	3	NUM
ma-80	513	37	2	2	NUM
ma-80	513	38	2	2	NUM
ma-80	513	39	----------------20	----------------20	NUM
ma-80	513	40	2	2	NUM
ma-80	513	41	e	e	NOUN
ma-80	513	42	18	18	NUM
ma-80	513	43	2	2	NUM
ma-80	513	44	e	e	NOUN
ma-80	513	45	-------------+	-------------+	NOUN
ma-80	514	1	+	+	CCONJ
ma-80	514	2	+	+	CCONJ
ma-80	514	3	y	y	PROPN
ma-80	514	4	1	1	NUM
ma-80	514	5	e	e	NOUN
ma-80	514	6	---+	---+	NUM
ma-80	514	7	5	5	NUM
ma-80	514	8	2	2	NUM
ma-80	515	1	+	+	CCONJ
ma-80	515	2	e	e	X
ma-80	515	3	3	3	NUM
ma-80	515	4	371	371	NUM
ma-80	515	5	36	36	NUM
ma-80	515	6	--------34	--------34	PROPN
ma-80	515	7	2	2	NUM
ma-80	515	8	3	3	NUM
ma-80	515	9	-------------	-------------	PUNCT
ma-80	515	10	–	–	PUNCT
ma-80	515	11	8	8	NUM
ma-80	515	12	2e	2e	NOUN
ma-80	515	13	2	2	NUM
ma-80	515	14	6	6	NUM
ma-80	515	15	2e	2e	NUM
ma-80	515	16	6	6	NUM
ma-80	515	17	2	2	NUM
ma-80	515	18	+	+	NUM
ma-80	515	19	+	+	CCONJ
ma-80	515	20	+	+	CCONJ
ma-80	515	21	y	y	PROPN
ma-80	515	22	1	1	NUM
ma-80	515	23	e	e	NOUN
ma-80	515	24	---+	---+	NUM
ma-80	515	25	3	3	NUM
ma-80	515	26	+=	+=	NOUN
ma-80	515	27	w	w	NOUN
ma-80	515	28	4	4	NUM
ma-80	515	29	y	y	NOUN
ma-80	515	30			PROPN
ma-80	515	31	1	1	NUM
ma-80	515	32	–	–	PUNCT
ma-80	515	33	+	+	NOUN
ma-80	515	34	=	=	X
ma-80	515	35	2e	2e	PROPN
ma-80	515	36	y	y	NOUN
ma-80	515	37	1	1	NUM
ma-80	515	38	e	e	NOUN
ma-80	515	39	---+	---+	NUM
ma-80	515	40	1	1	NUM
ma-80	515	41	2e	2e	PROPN
ma-80	515	42	3	3	NUM
ma-80	515	43	---------y	---------y	NUM
ma-80	515	44	1	1	NUM
ma-80	515	45	e	e	X
ma-80	515	46	---+	---+	NUM
ma-80	515	47	–	–	PUNCT
ma-80	515	48	11e	11e	NUM
ma-80	515	49	36	36	NUM
ma-80	515	50	--------y	--------y	NUM
ma-80	515	51	1	1	NUM
ma-80	515	52	e	e	NOUN
ma-80	515	53	---+	---+	NUM
ma-80	515	54	43e	43e	NOUN
ma-80	515	55	3	3	NUM
ma-80	515	56	2	2	NUM
ma-80	515	57	135	135	NUM
ma-80	515	58	2	2	NUM
ma-80	515	59	----------------y	----------------y	NUM
ma-80	515	60	1	1	NUM
ma-80	515	61	e	e	NOUN
ma-80	515	62	---+	---+	NUM
ma-80	515	63	3	3	NUM
ma-80	515	64	2	2	NUM
ma-80	515	65	–	–	PUNCT
ma-80	515	66	+	+	PUNCT
ma-80	516	1	+	+	CCONJ
ma-80	516	2	e	e	X
ma-80	516	3	2	2	NUM
ma-80	516	4	4075	4075	NUM
ma-80	516	5	27	27	NUM
ma-80	516	6	2	2	NUM
ma-80	516	7	------------895	------------895	NOUN
ma-80	516	8	12	12	NUM
ma-80	516	9	---------	---------	NUM
ma-80	516	10	–	–	PUNCT
ma-80	516	11	91e	91e	NOUN
ma-80	516	12	2	2	NUM
ma-80	516	13	---------	---------	PUNCT
ma-80	516	14	–	–	PUNCT
ma-80	516	15	61	61	NUM
ma-80	516	16	2	2	NUM
ma-80	516	17	-------	-------	PUNCT
ma-80	516	18	–	–	PUNCT
ma-80	516	19	27	27	NUM
ma-80	516	20	2	2	NUM
ma-80	516	21	e	e	X
ma-80	516	22	-------------	-------------	PUNCT
ma-80	516	23	–	–	PUNCT
ma-80	516	24	64	64	NUM
ma-80	516	25	2	2	NUM
ma-80	516	26	3e	3e	NOUN
ma-80	516	27	2	2	NUM
ma-80	516	28	-------------	-------------	PUNCT
ma-80	516	29	–	–	PUNCT
ma-80	516	30	y	y	PROPN
ma-80	516	31	1	1	NUM
ma-80	516	32	e	e	NOUN
ma-80	516	33	---+	---+	PROPN
ma-80	516	34	2	2	NUM
ma-80	516	35	–	–	PUNCT
ma-80	516	36	e	e	X
ma-80	516	37	5	5	NUM
ma-80	516	38	2	2	NUM
ma-80	516	39	6658	6658	NUM
ma-80	516	40	2	2	NUM
ma-80	516	41	27	27	NUM
ma-80	516	42	------------------2126	------------------2126	NOUN
ma-80	516	43	9	9	NUM
ma-80	516	44	------------	------------	SYM
ma-80	516	45	–	–	PUNCT
ma-80	516	46	315e	315e	NUM
ma-80	516	47	3	3	NUM
ma-80	516	48	2	2	NUM
ma-80	516	49	2	2	NUM
ma-80	516	50	--------------------	--------------------	PUNCT
ma-80	516	51	–	–	PUNCT
ma-80	516	52	110	110	NUM
ma-80	516	53	2e	2e	NUM
ma-80	516	54	–	–	PUNCT
ma-80	516	55	102	102	NUM
ma-80	516	56	2	2	NUM
ma-80	516	57	e	e	X
ma-80	516	58	----------------	----------------	PROPN
ma-80	516	59	–	–	PUNCT
ma-80	516	60	256	256	NUM
ma-80	516	61	2	2	NUM
ma-80	516	62	3e	3e	NOUN
ma-80	516	63	3	3	NUM
ma-80	516	64	2	2	NUM
ma-80	516	65	----------------	----------------	PUNCT
ma-80	516	66	–	–	PUNCT
ma-80	516	67	y	y	PROPN
ma-80	516	68	1	1	NUM
ma-80	516	69	e	e	NOUN
ma-80	516	70	---+	---+	NUM
ma-80	516	71	5	5	NUM
ma-80	516	72	2	2	NUM
ma-80	516	73	+	+	CCONJ
ma-80	516	74	e	e	X
ma-80	516	75	3	3	NUM
ma-80	516	76	8467	8467	NUM
ma-80	516	77	2	2	NUM
ma-80	516	78	27	27	NUM
ma-80	516	79	------------------1175	------------------1175	NUM
ma-80	516	80	4	4	NUM
ma-80	516	81	------------	------------	PUNCT
ma-80	516	82	–	–	PUNCT
ma-80	516	83	207	207	NUM
ma-80	516	84	2e	2e	NUM
ma-80	516	85	2	2	NUM
ma-80	516	86	–	–	PUNCT
ma-80	516	87	149	149	NUM
ma-80	516	88	2e	2e	NUM
ma-80	516	89	–	–	PUNCT
ma-80	516	90	144	144	NUM
ma-80	516	91	2	2	NUM
ma-80	516	92	–	–	PUNCT
ma-80	516	93	128	128	NUM
ma-80	516	94	2	2	NUM
ma-80	516	95	e	e	X
ma-80	516	96	----------------	----------------	PROPN
ma-80	516	97	–	–	PUNCT
ma-80	516	98	y	y	PROPN
ma-80	516	99	1	1	NUM
ma-80	516	100	e	e	NOUN
ma-80	516	101	---+	---+	PROPN
ma-80	516	102	3	3	NUM
ma-80	516	103	–	–	PUNCT
ma-80	516	104	e	e	NOUN
ma-80	516	105	7	7	NUM
ma-80	516	106	2	2	NUM
ma-80	516	107	4904	4904	NUM
ma-80	516	108	2	2	NUM
ma-80	516	109	27	27	NUM
ma-80	516	110	------------------502	------------------502	NOUN
ma-80	516	111	3	3	NUM
ma-80	516	112	---------	---------	NOUN
ma-80	516	113	–	–	PUNCT
ma-80	516	114	245e	245e	NOUN
ma-80	516	115	5	5	NUM
ma-80	516	116	2	2	NUM
ma-80	516	117	2	2	NUM
ma-80	516	118	--------------------	--------------------	PUNCT
ma-80	516	119	–	–	PUNCT
ma-80	516	120	90	90	NUM
ma-80	516	121	2e	2e	NOUN
ma-80	516	122	3	3	NUM
ma-80	516	123	2	2	NUM
ma-80	516	124	–	–	PUNCT
ma-80	516	125	90	90	NUM
ma-80	516	126	2e	2e	NUM
ma-80	516	127	–	–	PUNCT
ma-80	516	128	256	256	NUM
ma-80	516	129	2	2	NUM
ma-80	516	130	3	3	NUM
ma-80	516	131	e	e	X
ma-80	516	132	----------------	----------------	PROPN
ma-80	516	133	–	–	PUNCT
ma-80	516	134	y	y	PROPN
ma-80	516	135	1	1	NUM
ma-80	516	136	e	e	NOUN
ma-80	516	137	---+	---+	NUM
ma-80	516	138	7	7	NUM
ma-80	516	139	2	2	NUM
ma-80	517	1	+	+	CCONJ
ma-80	517	2	e	e	X
ma-80	517	3	4	4	NUM
ma-80	517	4	10843	10843	NUM
ma-80	517	5	135	135	NUM
ma-80	517	6	2	2	NUM
ma-80	517	7	---------------1315	---------------1315	PROPN
ma-80	517	8	36	36	NUM
ma-80	517	9	------------	------------	PUNCT
ma-80	517	10	–	–	PUNCT
ma-80	517	11	55e	55e	NUM
ma-80	517	12	3	3	NUM
ma-80	517	13	2	2	NUM
ma-80	517	14	-----------	-----------	NUM
ma-80	517	15	–	–	PUNCT
ma-80	517	16	41e	41e	X
ma-80	517	17	2	2	NUM
ma-80	517	18	2	2	NUM
ma-80	517	19	-----------	-----------	PUNCT
ma-80	517	20	–	–	PUNCT
ma-80	517	21	21	21	NUM
ma-80	517	22	2e	2e	NUM
ma-80	517	23	–	–	PUNCT
ma-80	517	24	64	64	NUM
ma-80	517	25	2	2	NUM
ma-80	517	26	3	3	NUM
ma-80	517	27	-------------	-------------	PUNCT
ma-80	517	28	–	–	PUNCT
ma-80	517	29	y	y	PROPN
ma-80	517	30	1	1	NUM
ma-80	517	31	e	e	NOUN
ma-80	517	32	---+	---+	NUM
ma-80	517	33	4	4	NUM
ma-80	517	34			PROPN
ma-80	517	35	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	NOUN
ma-80	517	36	5.1.4	5.1.4	PROPN
ma-80	517	37	.	.	PUNCT
ma-80	517	38	results	result	NOUN
ma-80	517	39	.	.	PUNCT
ma-80	518	1	the	the	DET
ma-80	518	2	relative	relative	ADJ
ma-80	518	3	errors	error	NOUN
ma-80	518	4	in	in	ADP
ma-80	518	5	the	the	DET
ma-80	518	6	spline	spline	NOUN
ma-80	518	7	based	base	VERB
ma-80	518	8	approximations	approximation	NOUN
ma-80	518	9	to	to	ADP
ma-80	518	10	the	the	DET
ma-80	518	11	lambert	lambert	PROPN
ma-80	518	12	w	w	PROPN
ma-80	518	13	function	function	PROPN
ma-80	518	14	,	,	PUNCT
ma-80	518	15	as	as	SCONJ
ma-80	518	16	specified	specify	VERB
ma-80	518	17	in	in	ADP
ma-80	518	18	theorem	theorem	ADJ
ma-80	518	19	5.1	5.1	NUM
ma-80	518	20	,	,	PUNCT
ma-80	518	21	of	of	ADP
ma-80	518	22	orders	order	NOUN
ma-80	518	23	one	one	NUM
ma-80	518	24	to	to	ADP
ma-80	518	25	five	five	NUM
ma-80	518	26	,	,	PUNCT
ma-80	518	27	are	be	AUX
ma-80	518	28	shown	show	VERB
ma-80	518	29	in	in	ADP
ma-80	518	30	figure	figure	NOUN
ma-80	518	31	20	20	NUM
ma-80	518	32	.	.	PUNCT
ma-80	519	1	the	the	DET
ma-80	519	2	relative	relative	ADJ
ma-80	519	3	error	error	NOUN
ma-80	519	4	bounds	bound	NOUN
ma-80	519	5	over	over	ADP
ma-80	519	6	the	the	DET
ma-80	519	7	interval	interval	NOUN
ma-80	519	8	,	,	PUNCT
ma-80	519	9	for	for	ADP
ma-80	519	10	first	first	ADV
ma-80	519	11	to	to	PART
ma-80	519	12	fifth	fifth	ADJ
ma-80	519	13	order	order	NOUN
ma-80	519	14	approximations	approximation	NOUN
ma-80	519	15	,	,	PUNCT
ma-80	519	16	respectively	respectively	ADV
ma-80	519	17	,	,	PUNCT
ma-80	519	18	are	be	AUX
ma-80	519	19	:	:	PUNCT
ma-80	519	20	,	,	PUNCT
ma-80	519	21	,	,	PUNCT
ma-80	519	22	,	,	PUNCT
ma-80	519	23	and	and	CCONJ
ma-80	519	24	.	.	PUNCT
ma-80	520	1	by	by	ADP
ma-80	520	2	construction	construction	NOUN
ma-80	520	3	,	,	PUNCT
ma-80	520	4	the	the	DET
ma-80	520	5	approximations	approximation	NOUN
ma-80	520	6	are	be	AUX
ma-80	520	7	sharp	sharp	ADJ
ma-80	520	8	at	at	ADP
ma-80	520	9	the	the	DET
ma-80	520	10	points	point	NOUN
ma-80	520	11	and	and	CCONJ
ma-80	520	12	.	.	PUNCT
ma-80	521	1	the	the	DET
ma-80	521	2	results	result	NOUN
ma-80	521	3	shown	show	VERB
ma-80	521	4	in	in	ADP
ma-80	521	5	figure	figure	NOUN
ma-80	521	6	20	20	NUM
ma-80	521	7	indicate	indicate	VERB
ma-80	521	8	that	that	SCONJ
ma-80	521	9	the	the	DET
ma-80	521	10	sequence	sequence	NOUN
ma-80	521	11	of	of	ADP
ma-80	521	12	approximations	approximation	NOUN
ma-80	521	13	have	have	VERB
ma-80	521	14	good	good	ADJ
ma-80	521	15	convergence	convergence	NOUN
ma-80	521	16	to	to	ADP
ma-80	521	17	the	the	DET
ma-80	521	18	lambert	lambert	PROPN
ma-80	521	19	w	w	PROPN
ma-80	521	20	function	function	NOUN
ma-80	521	21	over	over	ADP
ma-80	521	22	the	the	DET
ma-80	521	23	interval	interval	NOUN
ma-80	521	24	and	and	CCONJ
ma-80	521	25	modest	modest	ADJ
ma-80	521	26	convergence	convergence	NOUN
ma-80	521	27	over	over	ADP
ma-80	521	28	the	the	DET
ma-80	521	29	interval	interval	NOUN
ma-80	521	30	.	.	PUNCT
ma-80	522	1	6	6	X
ma-80	522	2	.	.	NUM
ma-80	522	3	improved	improve	VERB
ma-80	522	4	approximations	approximation	NOUN
ma-80	522	5	via	via	ADP
ma-80	522	6	iteration	iteration	NOUN
ma-80	522	7	iteration	iteration	NOUN
ma-80	522	8	is	be	AUX
ma-80	522	9	,	,	PUNCT
ma-80	522	10	potentially	potentially	ADV
ma-80	522	11	,	,	PUNCT
ma-80	522	12	effective	effective	ADJ
ma-80	522	13	in	in	ADP
ma-80	522	14	improving	improve	VERB
ma-80	522	15	the	the	DET
ma-80	522	16	accuracy	accuracy	NOUN
ma-80	522	17	of	of	ADP
ma-80	522	18	an	an	DET
ma-80	522	19	initial	initial	ADJ
ma-80	522	20	approximation	approximation	NOUN
ma-80	522	21	.	.	PUNCT
ma-80	523	1	one	one	NUM
ma-80	523	2	potential	potential	ADJ
ma-80	523	3	approach	approach	NOUN
ma-80	523	4	is	be	AUX
ma-80	523	5	to	to	PART
ma-80	523	6	utilize	utilize	VERB
ma-80	523	7	the	the	DET
ma-80	523	8	iteration	iteration	NOUN
ma-80	523	9	potential	potential	NOUN
ma-80	523	10	in	in	ADP
ma-80	523	11	the	the	DET
ma-80	523	12	fundamental	fundamental	ADJ
ma-80	523	13	relationship	relationship	NOUN
ma-80	523	14	for	for	ADP
ma-80	523	15	the	the	DET
ma-80	523	16	lambert	lambert	PROPN
ma-80	523	17	w	w	PROPN
ma-80	523	18	function	function	PROPN
ma-80	523	19	as	as	SCONJ
ma-80	523	20	specified	specify	VERB
ma-80	523	21	by	by	ADP
ma-80	523	22	equation	equation	NOUN
ma-80	523	23	116	116	NUM
ma-80	523	24	.	.	PUNCT
ma-80	524	1	an	an	DET
ma-80	524	2	alternative	alternative	ADJ
ma-80	524	3	approach	approach	NOUN
ma-80	524	4	is	be	AUX
ma-80	524	5	to	to	PART
ma-80	524	6	utilized	utilize	VERB
ma-80	524	7	the	the	DET
ma-80	524	8	newton	newton	PROPN
ma-80	524	9	-	-	PUNCT
ma-80	524	10	raphson	raphson	NOUN
ma-80	524	11	method	method	NOUN
ma-80	524	12	.	.	PUNCT
ma-80	525	1	these	these	DET
ma-80	525	2	two	two	NUM
ma-80	525	3	approaches	approach	NOUN
ma-80	525	4	are	be	AUX
ma-80	525	5	detailed	detail	VERB
ma-80	525	6	below	below	ADV
ma-80	525	7	.	.	PUNCT
ma-80	526	1	6.1	6.1	NUM
ma-80	526	2	.	.	PUNCT
ma-80	527	1	inherent	inherent	ADJ
ma-80	527	2	iteration	iteration	NOUN
ma-80	527	3	.	.	PUNCT
ma-80	528	1	the	the	DET
ma-80	528	2	basis	basis	NOUN
ma-80	528	3	for	for	ADP
ma-80	528	4	an	an	DET
ma-80	528	5	iterative	iterative	NOUN
ma-80	528	6	relationship	relationship	NOUN
ma-80	528	7	for	for	ADP
ma-80	528	8	the	the	DET
ma-80	528	9	lambert	lambert	PROPN
ma-80	528	10	w	w	PROPN
ma-80	528	11	function	function	PROPN
ma-80	528	12	is	be	AUX
ma-80	528	13	equation	equation	NOUN
ma-80	528	14	116	116	NUM
ma-80	528	15	,	,	PUNCT
ma-80	528	16	i.e.	i.e.	X
ma-80	528	17	(	(	PUNCT
ma-80	528	18	82	82	NUM
ma-80	528	19	)	)	PUNCT
ma-80	528	20	it	it	PRON
ma-80	528	21	then	then	ADV
ma-80	528	22	follows	follow	VERB
ma-80	528	23	that	that	SCONJ
ma-80	528	24	an	an	DET
ma-80	528	25	approximation	approximation	NOUN
ma-80	528	26	,	,	PUNCT
ma-80	528	27	,	,	PUNCT
ma-80	528	28	for	for	ADP
ma-80	528	29	,	,	PUNCT
ma-80	528	30	can	can	AUX
ma-80	528	31	potentially	potentially	ADV
ma-80	528	32	be	be	AUX
ma-80	528	33	improved	improve	VERB
ma-80	528	34	upon	upon	SCONJ
ma-80	528	35	according	accord	VERB
ma-80	528	36	to	to	ADP
ma-80	528	37	(	(	PUNCT
ma-80	528	38	83	83	NUM
ma-80	528	39	)	)	PUNCT
ma-80	528	40	(	(	PUNCT
ma-80	528	41	84	84	NUM
ma-80	528	42	)	)	PUNCT
ma-80	528	43	1	1	NUM
ma-80	528	44	e	e	NOUN
ma-80	528	45	–	–	PUNCT
ma-80	529	1	0	0	NUM
ma-80	529	2			NOUN
ma-80	529	3	1.27	1.27	NUM
ma-80	529	4	10	10	NUM
ma-80	529	5	2–	2–	NUM
ma-80	529	6	9.68	9.68	NUM
ma-80	529	7	10	10	NUM
ma-80	529	8	4–	4–	PROPN
ma-80	529	9	8.69	8.69	NUM
ma-80	529	10	10	10	NUM
ma-80	529	11	5–	5–	PROPN
ma-80	529	12	8.46	8.46	NUM
ma-80	529	13	10	10	NUM
ma-80	530	1	6–	6–	NUM
ma-80	530	2	8.65	8.65	NUM
ma-80	530	3	10	10	NUM
ma-80	530	4	7–	7–	NOUN
ma-80	530	5	1	1	NUM
ma-80	530	6	e	e	ADV
ma-80	530	7	–	–	PUNCT
ma-80	530	8	0	0	NUM
ma-80	530	9	1	1	NUM
ma-80	530	10	e	e	NOUN
ma-80	530	11	–	–	PUNCT
ma-80	530	12	0	0	NUM
ma-80	530	13			NOUN
ma-80	530	14	0	0	NUM
ma-80	530	15	1	1	NUM
ma-80	530	16			NOUN
ma-80	530	17	figure	figure	NOUN
ma-80	530	18	20	20	NUM
ma-80	530	19	.	.	PUNCT
ma-80	531	1	graph	graph	NOUN
ma-80	531	2	of	of	ADP
ma-80	531	3	the	the	DET
ma-80	531	4	relative	relative	ADJ
ma-80	531	5	errors	error	NOUN
ma-80	531	6	in	in	ADP
ma-80	531	7	the	the	DET
ma-80	531	8	spline	spline	NOUN
ma-80	531	9	based	base	VERB
ma-80	531	10	approximations	approximation	NOUN
ma-80	531	11	,	,	PUNCT
ma-80	531	12	of	of	ADP
ma-80	531	13	orders	order	NOUN
ma-80	531	14	one	one	NUM
ma-80	531	15	to	to	ADP
ma-80	531	16	five	five	NUM
ma-80	531	17	,	,	PUNCT
ma-80	531	18	to	to	ADP
ma-80	531	19	the	the	DET
ma-80	531	20	lambert	lambert	PROPN
ma-80	531	21	w	w	PROPN
ma-80	531	22	function	function	PROPN
ma-80	531	23	as	as	SCONJ
ma-80	531	24	specified	specify	VERB
ma-80	531	25	in	in	ADP
ma-80	531	26	theorem	theorem	ADJ
ma-80	531	27	5.1	5.1	NUM
ma-80	531	28	.	.	PUNCT
ma-80	532	1	y	y	PROPN
ma-80	532	2	order	order	NOUN
ma-80	532	3	1	1	NUM
ma-80	532	4	order	order	NOUN
ma-80	532	5	5	5	NUM
ma-80	532	6	re	re	NOUN
ma-80	532	7	y	y	PROPN
ma-80	532	8			PROPN
ma-80	532	9	1	1	NUM
ma-80	532	10	e	e	ADV
ma-80	532	11	–	–	PUNCT
ma-80	532	12	w	w	NOUN
ma-80	532	13	y	y	NOUN
ma-80	532	14			PROPN
ma-80	532	15	y	y	NOUN
ma-80	532	16	ln	ln	NOUN
ma-80	533	1	w	w	NOUN
ma-80	533	2	y	y	NOUN
ma-80	533	3			X
ma-80	533	4	ln	ln	NOUN
ma-80	533	5	–	–	PUNCT
ma-80	533	6	.=	.=	NOUN
ma-80	533	7	w0	w0	VERB
ma-80	533	8	y	y	NOUN
ma-80	533	9			PROPN
ma-80	533	10	w	w	NOUN
ma-80	533	11	y	y	NOUN
ma-80	533	12			PROPN
ma-80	533	13	w1	w1	NOUN
ma-80	533	14	y	y	NOUN
ma-80	533	15			PROPN
ma-80	533	16	y	y	NOUN
ma-80	533	17	ln	ln	PROPN
ma-80	533	18	w0	w0	PROPN
ma-80	533	19	y	y	NOUN
ma-80	533	20			NOUN
ma-80	534	1	ln–=	ln–=	PRON
ma-80	534	2	w2	w2	NOUN
ma-80	534	3	y	y	PROPN
ma-80	534	4			PROPN
ma-80	535	1	y	y	NOUN
ma-80	536	1	ln	ln	DET
ma-80	536	2	y	y	NOUN
ma-80	537	1	ln	ln	PRON
ma-80	537	2	w0	w0	PROPN
ma-80	537	3	y	y	NOUN
ma-80	537	4			NOUN
ma-80	537	5	ln	ln	NOUN
ma-80	537	6	–	–	PUNCT
ma-80	537	7	ln–=	ln–=	X
ma-80	537	8	w21	w21	PROPN
ma-80	538	1	y	y	NOUN
ma-80	538	2			PROPN
ma-80	538	3	y	y	NOUN
ma-80	539	1	ln	ln	DET
ma-80	539	2	y	y	NOUN
ma-80	539	3	ln	ln	PRON
ma-80	539	4	w1	w1	NOUN
ma-80	539	5	y	y	NOUN
ma-80	539	6			X
ma-80	539	7	ln	ln	NOUN
ma-80	539	8	–	–	PUNCT
ma-80	539	9	ln–=	ln–=	NOUN
ma-80	539	10	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	NOUN
ma-80	539	11	(	(	PUNCT
ma-80	539	12	85	85	NUM
ma-80	539	13	)	)	PUNCT
ma-80	539	14	(	(	PUNCT
ma-80	539	15	86	86	NUM
ma-80	539	16	)	)	PUNCT
ma-80	539	17	etc	etc	X
ma-80	539	18	.	.	X
ma-80	540	1	the	the	DET
ma-80	540	2	number	number	NOUN
ma-80	540	3	of	of	ADP
ma-80	540	4	possible	possible	ADJ
ma-80	540	5	permutations	permutation	NOUN
ma-80	540	6	for	for	ADP
ma-80	540	7	approximations	approximation	NOUN
ma-80	540	8	to	to	ADP
ma-80	540	9	the	the	DET
ma-80	540	10	lambert	lambert	PROPN
ma-80	540	11	w	w	PROPN
ma-80	540	12	function	function	NOUN
ma-80	540	13	is	be	AUX
ma-80	540	14	clearly	clearly	ADV
ma-80	540	15	large	large	ADJ
ma-80	540	16	as	as	ADP
ma-80	540	17	the	the	DET
ma-80	540	18	iteration	iteration	NOUN
ma-80	540	19	order	order	NOUN
ma-80	540	20	increases	increase	NOUN
ma-80	540	21	.	.	PUNCT
ma-80	541	1	representative	representative	ADJ
ma-80	541	2	relative	relative	ADJ
ma-80	541	3	error	error	NOUN
ma-80	541	4	bounds	bound	NOUN
ma-80	541	5	,	,	PUNCT
ma-80	541	6	for	for	ADP
ma-80	541	7	the	the	DET
ma-80	541	8	interval	interval	NOUN
ma-80	541	9	,	,	PUNCT
ma-80	541	10	are	be	AUX
ma-80	541	11	tabulated	tabulate	VERB
ma-80	541	12	in	in	ADP
ma-80	541	13	table	table	NOUN
ma-80	541	14	5	5	NUM
ma-80	541	15	for	for	ADP
ma-80	541	16	the	the	DET
ma-80	541	17	base	base	ADJ
ma-80	541	18	approximations	approximation	NOUN
ma-80	541	19	of	of	ADP
ma-80	541	20	,	,	PUNCT
ma-80	541	21	and	and	CCONJ
ma-80	541	22	as	as	SCONJ
ma-80	541	23	specified	specify	VERB
ma-80	541	24	in	in	ADP
ma-80	541	25	theorem	theorem	ADJ
ma-80	541	26	3.1	3.1	NUM
ma-80	541	27	.	.	PUNCT
ma-80	542	1	graphs	graph	NOUN
ma-80	542	2	of	of	ADP
ma-80	542	3	the	the	DET
ma-80	542	4	relative	relative	ADJ
ma-80	542	5	errors	error	NOUN
ma-80	542	6	,	,	PUNCT
ma-80	542	7	based	base	VERB
ma-80	542	8	on	on	ADP
ma-80	542	9	the	the	DET
ma-80	542	10	approximations	approximation	NOUN
ma-80	542	11	and	and	CCONJ
ma-80	542	12	,	,	PUNCT
ma-80	542	13	are	be	AUX
ma-80	542	14	shown	show	VERB
ma-80	542	15	,	,	PUNCT
ma-80	542	16	respectively	respectively	ADV
ma-80	542	17	,	,	PUNCT
ma-80	542	18	in	in	ADP
ma-80	542	19	figure	figure	NOUN
ma-80	542	20	21	21	NUM
ma-80	542	21	and	and	CCONJ
ma-80	542	22	figure	figure	VERB
ma-80	542	23	22	22	NUM
ma-80	542	24	.	.	PUNCT
ma-80	543	1	w3	w3	PROPN
ma-80	543	2	y	y	PROPN
ma-80	543	3			PROPN
ma-80	543	4	y	y	NOUN
ma-80	543	5	ln	ln	PRON
ma-80	543	6	y	y	NOUN
ma-80	544	1	ln	ln	DET
ma-80	544	2	y	y	NOUN
ma-80	545	1	ln	ln	PRON
ma-80	545	2	w0	w0	PROPN
ma-80	545	3	y	y	NOUN
ma-80	545	4			NOUN
ma-80	545	5	ln	ln	NOUN
ma-80	545	6	–	–	PUNCT
ma-80	545	7	ln	ln	ADJ
ma-80	545	8	–	–	PUNCT
ma-80	545	9	ln–=	ln–=	NOUN
ma-80	545	10	w31	w31	ADJ
ma-80	545	11	y	y	NOUN
ma-80	545	12			PROPN
ma-80	545	13	y	y	NOUN
ma-80	546	1	ln	ln	DET
ma-80	546	2	y	y	NOUN
ma-80	547	1	ln	ln	DET
ma-80	547	2	y	y	NOUN
ma-80	547	3	ln	ln	PRON
ma-80	547	4	w1	w1	NOUN
ma-80	547	5	y	y	NOUN
ma-80	547	6			X
ma-80	547	7	ln	ln	NOUN
ma-80	547	8	–	–	PUNCT
ma-80	547	9	ln	ln	ADJ
ma-80	547	10	–	–	PUNCT
ma-80	548	1	ln–=	ln–=	NOUN
ma-80	548	2	w32	w32	NOUN
ma-80	548	3	y	y	NOUN
ma-80	548	4			PROPN
ma-80	548	5	y	y	NOUN
ma-80	548	6	ln	ln	PRON
ma-80	548	7	y	y	NOUN
ma-80	549	1	ln	ln	DET
ma-80	549	2	y	y	NOUN
ma-80	549	3	ln	ln	PRON
ma-80	549	4	w2	w2	NOUN
ma-80	549	5	y	y	NOUN
ma-80	549	6			ADJ
ma-80	549	7	ln	ln	NOUN
ma-80	549	8	–	–	PUNCT
ma-80	549	9	ln	ln	ADJ
ma-80	549	10	–	–	PUNCT
ma-80	549	11	ln–=	ln–=	NOUN
ma-80	549	12	w3	w3	PROPN
ma-80	549	13	21	21	NUM
ma-80	549	14	y	y	NOUN
ma-80	549	15			PROPN
ma-80	549	16	y	y	NOUN
ma-80	550	1	ln	ln	DET
ma-80	550	2	y	y	NOUN
ma-80	551	1	ln	ln	DET
ma-80	551	2	y	y	NOUN
ma-80	552	1	ln	ln	PRON
ma-80	552	2	w21	w21	PROPN
ma-80	552	3	y	y	NOUN
ma-80	552	4			NOUN
ma-80	552	5	ln	ln	NOUN
ma-80	552	6	–	–	PUNCT
ma-80	552	7	ln	ln	ADJ
ma-80	552	8	–	–	PUNCT
ma-80	552	9	ln–=	ln–=	NOUN
ma-80	552	10	w4	w4	NOUN
ma-80	552	11	y	y	PROPN
ma-80	552	12			PROPN
ma-80	552	13	y	y	NOUN
ma-80	552	14	ln	ln	PRON
ma-80	552	15	y	y	NOUN
ma-80	553	1	ln	ln	DET
ma-80	553	2	y	y	NOUN
ma-80	553	3	ln	ln	DET
ma-80	553	4	y	y	NOUN
ma-80	554	1	ln	ln	PRON
ma-80	554	2	w0	w0	PROPN
ma-80	554	3	y	y	NOUN
ma-80	554	4			NOUN
ma-80	554	5	ln	ln	NOUN
ma-80	554	6	–	–	PUNCT
ma-80	554	7	ln	ln	ADJ
ma-80	554	8	–	–	PUNCT
ma-80	554	9	ln	ln	ADJ
ma-80	554	10	–	–	PUNCT
ma-80	554	11	ln–=	ln–=	NOUN
ma-80	554	12	0	0	NUM
ma-80	554	13			NOUN
ma-80	554	14	w0	w0	VERB
ma-80	554	15	y	y	NOUN
ma-80	554	16			PROPN
ma-80	554	17	wu3	wu3	NOUN
ma-80	554	18	y	y	NOUN
ma-80	554	19	=	=	NOUN
ma-80	554	20	w0	w0	PROPN
ma-80	554	21	y	y	NOUN
ma-80	554	22			PROPN
ma-80	554	23	wu4	wu4	NOUN
ma-80	554	24	y	y	NOUN
ma-80	554	25	=	=	NOUN
ma-80	554	26	w0	w0	PROPN
ma-80	554	27	y	y	NOUN
ma-80	554	28			PROPN
ma-80	554	29	wu5	wu5	ADP
ma-80	554	30	y	y	NOUN
ma-80	554	31	=	=	NOUN
ma-80	554	32	w0	w0	PROPN
ma-80	554	33	y	y	NOUN
ma-80	554	34			PROPN
ma-80	554	35	wu4	wu4	NOUN
ma-80	554	36	y	y	NOUN
ma-80	554	37	=	=	NOUN
ma-80	554	38	w0	w0	PROPN
ma-80	554	39	y	y	NOUN
ma-80	554	40			PROPN
ma-80	554	41	wu5	wu5	ADP
ma-80	554	42	y	y	NOUN
ma-80	554	43	=	=	NOUN
ma-80	554	44	figure	figure	NOUN
ma-80	554	45	21	21	NUM
ma-80	554	46	.	.	PUNCT
ma-80	555	1	graph	graph	NOUN
ma-80	555	2	of	of	ADP
ma-80	555	3	the	the	DET
ma-80	555	4	relative	relative	ADJ
ma-80	555	5	errors	error	NOUN
ma-80	555	6	in	in	ADP
ma-80	555	7	approximations	approximation	NOUN
ma-80	555	8	to	to	ADP
ma-80	555	9	,	,	PUNCT
ma-80	555	10	based	base	VERB
ma-80	555	11	on	on	ADP
ma-80	555	12	(	(	PUNCT
ma-80	555	13	equation	equation	NOUN
ma-80	555	14	35	35	NUM
ma-80	555	15	)	)	PUNCT
ma-80	555	16	.	.	PUNCT
ma-80	556	1	w	w	NOUN
ma-80	556	2	y	y	NOUN
ma-80	556	3			PROPN
ma-80	556	4	w0	w0	VERB
ma-80	556	5	y	y	NOUN
ma-80	556	6			PROPN
ma-80	556	7	wu4	wu4	NOUN
ma-80	556	8	y	y	PROPN
ma-80	556	9	=	=	PROPN
ma-80	556	10	y	y	PROPN
ma-80	556	11	w0	w0	PROPN
ma-80	556	12	w1	w1	PROPN
ma-80	556	13	w3	w3	PROPN
ma-80	556	14	21	21	PROPN
ma-80	556	15	w32	w32	NOUN
ma-80	556	16	w4	w4	PROPN
ma-80	556	17	w2	w2	PROPN
ma-80	556	18	w3	w3	PROPN
ma-80	556	19	w31	w31	PROPN
ma-80	556	20	w21	w21	PROPN
ma-80	556	21	re	re	VERB
ma-80	556	22	y	y	NOUN
ma-80	556	23			PROPN
ma-80	556	24	figure	figure	NOUN
ma-80	556	25	22	22	NUM
ma-80	556	26	.	.	PUNCT
ma-80	557	1	graph	graph	NOUN
ma-80	557	2	of	of	ADP
ma-80	557	3	the	the	DET
ma-80	557	4	relative	relative	ADJ
ma-80	557	5	errors	error	NOUN
ma-80	557	6	in	in	ADP
ma-80	557	7	approximations	approximation	NOUN
ma-80	557	8	to	to	ADP
ma-80	557	9	,	,	PUNCT
ma-80	557	10	based	base	VERB
ma-80	557	11	on	on	ADP
ma-80	557	12	(	(	PUNCT
ma-80	557	13	equation	equation	NOUN
ma-80	557	14	36	36	NUM
ma-80	557	15	)	)	PUNCT
ma-80	557	16	.	.	PUNCT
ma-80	558	1	w	w	NOUN
ma-80	558	2	y	y	NOUN
ma-80	558	3			PROPN
ma-80	558	4	w0	w0	VERB
ma-80	558	5	y	y	NOUN
ma-80	558	6			PROPN
ma-80	558	7	wu5	wu5	ADP
ma-80	558	8	y	y	NOUN
ma-80	558	9	=	=	PROPN
ma-80	558	10	y	y	PROPN
ma-80	558	11	w0	w0	PROPN
ma-80	558	12	w1	w1	PROPN
ma-80	558	13	w3	w3	PROPN
ma-80	558	14	21	21	PROPN
ma-80	558	15	w32	w32	NOUN
ma-80	558	16	w2	w2	PROPN
ma-80	558	17	w3	w3	PROPN
ma-80	558	18	w31	w31	PROPN
ma-80	558	19	w21	w21	PROPN
ma-80	558	20	re	re	ADP
ma-80	558	21	y	y	PROPN
ma-80	558	22			PROPN
ma-80	558	23	w4	w4	NOUN
ma-80	558	24	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	PROPN
ma-80	558	25	6.1.1	6.1.1	NUM
ma-80	558	26	.	.	PUNCT
ma-80	559	1	explicit	explicit	ADJ
ma-80	559	2	approximations	approximation	NOUN
ma-80	559	3	.	.	PUNCT
ma-80	560	1	the	the	DET
ma-80	560	2	approximation	approximation	NOUN
ma-80	560	3	,	,	PUNCT
ma-80	560	4	based	base	VERB
ma-80	560	5	on	on	ADP
ma-80	560	6	,	,	PUNCT
ma-80	560	7	is	be	AUX
ma-80	560	8	(	(	PUNCT
ma-80	560	9	87	87	NUM
ma-80	560	10	)	)	PUNCT
ma-80	560	11	and	and	CCONJ
ma-80	560	12	has	have	VERB
ma-80	560	13	a	a	DET
ma-80	560	14	maximum	maximum	ADJ
ma-80	560	15	relative	relative	ADJ
ma-80	560	16	error	error	NOUN
ma-80	560	17	bound	bind	VERB
ma-80	560	18	,	,	PUNCT
ma-80	560	19	over	over	ADP
ma-80	560	20	the	the	DET
ma-80	560	21	interval	interval	NOUN
ma-80	560	22	,	,	PUNCT
ma-80	560	23	of	of	ADP
ma-80	560	24	which	which	PRON
ma-80	560	25	is	be	AUX
ma-80	560	26	a	a	DET
ma-80	560	27	factor	factor	NOUN
ma-80	560	28	of	of	ADP
ma-80	560	29	lower	low	ADJ
ma-80	560	30	that	that	SCONJ
ma-80	560	31	the	the	DET
ma-80	560	32	original	original	ADJ
ma-80	560	33	approximation	approximation	NOUN
ma-80	560	34	whose	whose	DET
ma-80	560	35	relative	relative	ADJ
ma-80	560	36	error	error	NOUN
ma-80	560	37	bound	bind	VERB
ma-80	560	38	is	be	AUX
ma-80	560	39	.	.	PUNCT
ma-80	561	1	the	the	DET
ma-80	561	2	approximation	approximation	NOUN
ma-80	561	3	,	,	PUNCT
ma-80	561	4	based	base	VERB
ma-80	561	5	on	on	ADP
ma-80	561	6	,	,	PUNCT
ma-80	561	7	is	be	AUX
ma-80	561	8	(	(	PUNCT
ma-80	561	9	88	88	NUM
ma-80	561	10	)	)	PUNCT
ma-80	561	11	where	where	SCONJ
ma-80	561	12	is	be	AUX
ma-80	561	13	specified	specify	VERB
ma-80	561	14	by	by	ADP
ma-80	561	15	equation	equation	NOUN
ma-80	561	16	35	35	NUM
ma-80	561	17	.	.	PUNCT
ma-80	562	1	the	the	DET
ma-80	562	2	maximum	maximum	ADJ
ma-80	562	3	relative	relative	ADJ
ma-80	562	4	error	error	NOUN
ma-80	562	5	bound	bind	VERB
ma-80	562	6	,	,	PUNCT
ma-80	562	7	over	over	ADP
ma-80	562	8	the	the	DET
ma-80	562	9	interval	interval	NOUN
ma-80	562	10	,	,	PUNCT
ma-80	562	11	is	be	AUX
ma-80	562	12	which	which	PRON
ma-80	562	13	is	be	AUX
ma-80	562	14	a	a	DET
ma-80	562	15	factor	factor	NOUN
ma-80	562	16	of	of	ADP
ma-80	562	17	lower	low	ADJ
ma-80	562	18	that	that	SCONJ
ma-80	562	19	the	the	DET
ma-80	562	20	original	original	ADJ
ma-80	562	21	approximation	approximation	NOUN
ma-80	562	22	whose	whose	DET
ma-80	562	23	relative	relative	ADJ
ma-80	562	24	error	error	NOUN
ma-80	562	25	bound	bind	VERB
ma-80	562	26	is	be	AUX
ma-80	562	27	.	.	PUNCT
ma-80	563	1	the	the	DET
ma-80	563	2	approximation	approximation	NOUN
ma-80	563	3	,	,	PUNCT
ma-80	563	4	based	base	VERB
ma-80	563	5	on	on	ADP
ma-80	563	6	,	,	PUNCT
ma-80	563	7	is	be	AUX
ma-80	563	8	table	table	NOUN
ma-80	563	9	5	5	NUM
ma-80	563	10	.	.	PUNCT
ma-80	563	11	relative	relative	ADJ
ma-80	563	12	error	error	NOUN
ma-80	563	13	bounds	bound	NOUN
ma-80	563	14	,	,	PUNCT
ma-80	563	15	for	for	ADP
ma-80	563	16	the	the	DET
ma-80	563	17	interval	interval	NOUN
ma-80	563	18	,	,	PUNCT
ma-80	563	19	based	base	VERB
ma-80	563	20	on	on	ADP
ma-80	563	21	iteration	iteration	NOUN
ma-80	563	22	and	and	CCONJ
ma-80	563	23	for	for	ADP
ma-80	563	24	the	the	DET
ma-80	563	25	specified	specified	ADJ
ma-80	563	26	base	base	NOUN
ma-80	563	27	approximations	approximation	NOUN
ma-80	563	28	of	of	ADP
ma-80	563	29	(	(	PUNCT
ma-80	563	30	equation	equation	NOUN
ma-80	563	31	33	33	NUM
ma-80	563	32	)	)	PUNCT
ma-80	563	33	,	,	PUNCT
ma-80	563	34	(	(	PUNCT
ma-80	563	35	equation	equation	NOUN
ma-80	563	36	35	35	NUM
ma-80	563	37	)	)	PUNCT
ma-80	563	38	and	and	CCONJ
ma-80	563	39	(	(	PUNCT
ma-80	563	40	equation	equation	NOUN
ma-80	563	41	36	36	NUM
ma-80	563	42	)	)	PUNCT
ma-80	563	43	.	.	PUNCT
ma-80	564	1	iteration	iteration	NOUN
ma-80	564	2	form	form	NOUN
ma-80	564	3	0	0	NUM
ma-80	564	4			NOUN
ma-80	564	5	wu3	wu3	VERB
ma-80	564	6	y	y	NOUN
ma-80	564	7			PROPN
ma-80	564	8	wu4	wu4	NOUN
ma-80	564	9	y	y	NOUN
ma-80	564	10			PROPN
ma-80	564	11	wu5	wu5	ADP
ma-80	564	12	y	y	NOUN
ma-80	564	13			PROPN
ma-80	564	14	w0	w0	VERB
ma-80	564	15	y	y	NOUN
ma-80	564	16			PROPN
ma-80	564	17	wu3	wu3	NOUN
ma-80	564	18	y	y	NOUN
ma-80	564	19	=	=	NOUN
ma-80	564	20	w0	w0	PROPN
ma-80	564	21	y	y	NOUN
ma-80	564	22			PROPN
ma-80	564	23	wu4	wu4	NOUN
ma-80	564	24	y	y	NOUN
ma-80	564	25	=	=	NOUN
ma-80	564	26	w0	w0	PROPN
ma-80	564	27	y	y	NOUN
ma-80	564	28			PROPN
ma-80	564	29	wu5	wu5	ADP
ma-80	564	30	y	y	NOUN
ma-80	564	31	=	=	NOUN
ma-80	564	32	w0	w0	PROPN
ma-80	564	33	1.33	1.33	NUM
ma-80	564	34	10	10	NUM
ma-80	564	35	3–	3–	NUM
ma-80	564	36	7.23	7.23	NUM
ma-80	564	37	10	10	NUM
ma-80	565	1	7–	7–	NOUN
ma-80	565	2	2.15	2.15	NUM
ma-80	565	3	10	10	NUM
ma-80	565	4	13–	13–	NUM
ma-80	565	5	w1	w1	NOUN
ma-80	565	6	4.08	4.08	NUM
ma-80	565	7	10	10	NUM
ma-80	566	1	4–	4–	PROPN
ma-80	566	2	1.84	1.84	NUM
ma-80	566	3	10	10	NUM
ma-80	566	4	7–	7–	NOUN
ma-80	566	5	4.95	4.95	NUM
ma-80	566	6	10	10	NUM
ma-80	566	7	14–	14–	NUM
ma-80	566	8	w2	w2	NOUN
ma-80	566	9	1.97	1.97	NUM
ma-80	566	10	10	10	NUM
ma-80	566	11	4–	4–	PROPN
ma-80	566	12	6.03	6.03	NUM
ma-80	566	13	10	10	NUM
ma-80	566	14	8–	8–	PROPN
ma-80	566	15	1.31	1.31	NUM
ma-80	566	16	10	10	NUM
ma-80	566	17	14–	14–	NUM
ma-80	566	18	w21	w21	PROPN
ma-80	566	19	1.40	1.40	NUM
ma-80	566	20	10	10	NUM
ma-80	567	1	4–	4–	PROPN
ma-80	567	2	2.47	2.47	NUM
ma-80	567	3	10	10	NUM
ma-80	567	4	8–	8–	PROPN
ma-80	567	5	3.95	3.95	NUM
ma-80	567	6	10	10	NUM
ma-80	567	7	15–	15–	NUM
ma-80	567	8	w3	w3	NOUN
ma-80	567	9	1.40	1.40	NUM
ma-80	567	10	10	10	NUM
ma-80	568	1	4–	4–	PROPN
ma-80	568	2	2.47	2.47	NUM
ma-80	568	3	10	10	NUM
ma-80	568	4	8–	8–	PROPN
ma-80	568	5	3.95	3.95	NUM
ma-80	568	6	10	10	NUM
ma-80	568	7	15–	15–	NUM
ma-80	568	8	w31	w31	NOUN
ma-80	568	9	1.46	1.46	NUM
ma-80	568	10	10	10	NUM
ma-80	568	11	4–	4–	PROPN
ma-80	568	12	1.23	1.23	NUM
ma-80	568	13	10	10	NUM
ma-80	569	1	8–	8–	PROPN
ma-80	569	2	1.34	1.34	NUM
ma-80	569	3	10	10	NUM
ma-80	569	4	15–	15–	NUM
ma-80	569	5	w32	w32	NOUN
ma-80	569	6	2.33	2.33	NUM
ma-80	569	7	10	10	NUM
ma-80	570	1	4–	4–	PROPN
ma-80	570	2	7.43	7.43	NUM
ma-80	570	3	10	10	NUM
ma-80	570	4	9–	9–	PROPN
ma-80	570	5	5.04	5.04	NUM
ma-80	570	6	10	10	NUM
ma-80	570	7	16–	16–	NUM
ma-80	570	8	w3	w3	PROPN
ma-80	570	9	21	21	NUM
ma-80	570	10	6.65	6.65	NUM
ma-80	570	11	10	10	NUM
ma-80	570	12	4–	4–	PROPN
ma-80	570	13	5.36	5.36	NUM
ma-80	570	14	10	10	NUM
ma-80	570	15	9–	9–	PROPN
ma-80	570	16	2.11	2.11	NUM
ma-80	570	17	10	10	NUM
ma-80	570	18	16–	16–	NUM
ma-80	570	19	w4	w4	NOUN
ma-80	570	20	1.46	1.46	NUM
ma-80	570	21	10	10	NUM
ma-80	571	1	4–	4–	PROPN
ma-80	571	2	1.23	1.23	NUM
ma-80	571	3	10	10	NUM
ma-80	571	4	8–	8–	PROPN
ma-80	571	5	1.34	1.34	NUM
ma-80	571	6	10	10	NUM
ma-80	571	7	15–	15–	NUM
ma-80	571	8	w3	w3	NOUN
ma-80	571	9	w0	w0	PROPN
ma-80	571	10	y	y	NOUN
ma-80	571	11			PROPN
ma-80	571	12	wu3	wu3	VERB
ma-80	571	13	y	y	NOUN
ma-80	571	14	=	=	NOUN
ma-80	571	15	w3	w3	PROPN
ma-80	571	16	3	3	NOUN
ma-80	571	17	y	y	PROPN
ma-80	571	18			PROPN
ma-80	571	19	y	y	NOUN
ma-80	572	1	ln	ln	DET
ma-80	572	2	y	y	NOUN
ma-80	572	3	ln	ln	DET
ma-80	572	4	y	y	NOUN
ma-80	573	1	ln	ln	PRON
ma-80	573	2	wu3	wu3	NOUN
ma-80	573	3	y	y	NOUN
ma-80	573	4			X
ma-80	574	1	ln	ln	NOUN
ma-80	574	2	–	–	PUNCT
ma-80	574	3	ln	ln	ADJ
ma-80	574	4	–	–	PUNCT
ma-80	574	5	ln–=	ln–=	NOUN
ma-80	574	6	y	y	NOUN
ma-80	575	1	ln	ln	DET
ma-80	575	2	y	y	NOUN
ma-80	575	3	ln	ln	DET
ma-80	575	4	y	y	NOUN
ma-80	575	5	ln	ln	NOUN
ma-80	576	1	1	1	NUM
ma-80	576	2	3y	3y	NUM
ma-80	576	3	y	y	PROPN
ma-80	576	4	1	1	NUM
ma-80	576	5	y+	y+	NOUN
ma-80	576	6	ln+	ln+	PROPN
ma-80	577	1	+	+	CCONJ
ma-80	577	2	1	1	NUM
ma-80	577	3	1	1	NUM
ma-80	577	4	y+	y+	NOUN
ma-80	577	5	ln+	ln+	PUNCT
ma-80	577	6			NOUN
ma-80	577	7	1	1	NUM
ma-80	577	8	1	1	NUM
ma-80	577	9	2y+	2y+	NUM
ma-80	577	10	1	1	NUM
ma-80	577	11	1	1	NUM
ma-80	577	12	y+	y+	NOUN
ma-80	577	13	ln+	ln+	PROPN
ma-80	577	14	-------------------------------ln+	-------------------------------ln+	PUNCT
ma-80	577	15	-----------------------------------------------------------------------------------------------lnln	-----------------------------------------------------------------------------------------------lnln	PROPN
ma-80	577	16	–	–	PUNCT
ma-80	577	17	ln	ln	ADJ
ma-80	577	18	–	–	PUNCT
ma-80	577	19	ln–=	ln–=	X
ma-80	577	20	0	0	NUM
ma-80	577	21			NUM
ma-80	577	22	1.40	1.40	NUM
ma-80	577	23	10	10	NUM
ma-80	577	24	4–	4–	PROPN
ma-80	577	25	9.5	9.5	NUM
ma-80	577	26	wu3	wu3	VERB
ma-80	577	27	y	y	NOUN
ma-80	577	28			PROPN
ma-80	577	29	1.33	1.33	NUM
ma-80	577	30	10	10	NUM
ma-80	577	31	3–	3–	PROPN
ma-80	577	32	w2	w2	NOUN
ma-80	577	33	w0	w0	VERB
ma-80	577	34	y	y	NOUN
ma-80	577	35			PROPN
ma-80	577	36	wu4	wu4	NOUN
ma-80	577	37	y	y	PROPN
ma-80	577	38	=	=	NOUN
ma-80	577	39	w2	w2	NOUN
ma-80	577	40	4	4	PROPN
ma-80	577	41	y	y	NOUN
ma-80	577	42			PROPN
ma-80	577	43	y	y	NOUN
ma-80	578	1	ln	ln	DET
ma-80	578	2	y	y	NOUN
ma-80	578	3	ln	ln	PRON
ma-80	578	4	wu4	wu4	NOUN
ma-80	578	5	y	y	NOUN
ma-80	578	6			X
ma-80	578	7	ln	ln	NOUN
ma-80	578	8	–	–	PUNCT
ma-80	578	9	ln	ln	ADJ
ma-80	578	10	–	–	PUNCT
ma-80	578	11	=	=	NUM
ma-80	578	12	wu4	wu4	NOUN
ma-80	578	13	y	y	NOUN
ma-80	578	14			PROPN
ma-80	578	15	0	0	NUM
ma-80	578	16			NUM
ma-80	579	1	6.03	6.03	NUM
ma-80	579	2	10	10	NUM
ma-80	579	3	8–	8–	PROPN
ma-80	579	4	12	12	NUM
ma-80	579	5	wu4	wu4	NOUN
ma-80	579	6	y	y	PROPN
ma-80	579	7			PROPN
ma-80	579	8	7.23	7.23	NUM
ma-80	579	9	10	10	NUM
ma-80	579	10	7–	7–	PROPN
ma-80	579	11	w3	w3	PROPN
ma-80	579	12	w0	w0	PROPN
ma-80	579	13	y	y	NOUN
ma-80	579	14			PROPN
ma-80	579	15	wu4	wu4	NOUN
ma-80	579	16	y	y	PROPN
ma-80	579	17	=	=	PROPN
ma-80	579	18	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	PROPN
ma-80	579	19	(	(	PUNCT
ma-80	579	20	89	89	NUM
ma-80	579	21	)	)	PUNCT
ma-80	579	22	and	and	CCONJ
ma-80	579	23	has	have	VERB
ma-80	579	24	a	a	DET
ma-80	579	25	maximum	maximum	ADJ
ma-80	579	26	relative	relative	ADJ
ma-80	579	27	error	error	NOUN
ma-80	579	28	bound	bind	VERB
ma-80	579	29	,	,	PUNCT
ma-80	579	30	over	over	ADP
ma-80	579	31	the	the	DET
ma-80	579	32	interval	interval	NOUN
ma-80	579	33	,	,	PUNCT
ma-80	579	34	of	of	ADP
ma-80	579	35	which	which	PRON
ma-80	579	36	is	be	AUX
ma-80	579	37	a	a	DET
ma-80	579	38	factor	factor	NOUN
ma-80	579	39	of	of	ADP
ma-80	579	40	lower	low	ADJ
ma-80	579	41	that	that	SCONJ
ma-80	579	42	the	the	DET
ma-80	579	43	original	original	ADJ
ma-80	579	44	approximation	approximation	NOUN
ma-80	579	45	whose	whose	DET
ma-80	579	46	relative	relative	ADJ
ma-80	579	47	error	error	NOUN
ma-80	579	48	bound	bind	VERB
ma-80	579	49	is	be	AUX
ma-80	579	50	.	.	PUNCT
ma-80	580	1	6.2	6.2	NUM
ma-80	580	2	.	.	PUNCT
ma-80	581	1	newton	newton	PROPN
ma-80	581	2	-	-	PUNCT
ma-80	581	3	raphson	raphson	PROPN
ma-80	581	4	iteration	iteration	NOUN
ma-80	581	5	.	.	PUNCT
ma-80	582	1	consistent	consistent	ADJ
ma-80	582	2	with	with	ADP
ma-80	582	3	equation	equation	NOUN
ma-80	582	4	22	22	NUM
ma-80	582	5	,	,	PUNCT
ma-80	582	6	the	the	DET
ma-80	582	7	approximations	approximation	NOUN
ma-80	582	8	stated	state	VERB
ma-80	582	9	in	in	ADP
ma-80	582	10	theorem	theorem	ADJ
ma-80	582	11	3.1	3.1	NUM
ma-80	582	12	,	,	PUNCT
ma-80	582	13	theorem	theorem	VERB
ma-80	582	14	3.2	3.2	NUM
ma-80	582	15	and	and	CCONJ
ma-80	582	16	theorem	theorem	VERB
ma-80	582	17	3.5	3.5	NUM
ma-80	582	18	can	can	AUX
ma-80	582	19	be	be	AUX
ma-80	582	20	utilized	utilize	VERB
ma-80	582	21	as	as	ADP
ma-80	582	22	the	the	DET
ma-80	582	23	basis	basis	NOUN
ma-80	582	24	for	for	ADP
ma-80	582	25	iterative	iterative	ADJ
ma-80	582	26	approximations	approximation	NOUN
ma-80	582	27	based	base	VERB
ma-80	582	28	on	on	ADP
ma-80	582	29	the	the	DET
ma-80	582	30	newton	newton	PROPN
ma-80	582	31	-	-	PUNCT
ma-80	582	32	raphson	raphson	PROPN
ma-80	582	33	method	method	NOUN
ma-80	582	34	.	.	PUNCT
ma-80	583	1	results	result	NOUN
ma-80	583	2	are	be	AUX
ma-80	583	3	detailed	detail	VERB
ma-80	583	4	in	in	ADP
ma-80	583	5	table	table	NOUN
ma-80	583	6	6	6	NUM
ma-80	583	7	.	.	PUNCT
ma-80	584	1	as	as	ADP
ma-80	584	2	an	an	DET
ma-80	584	3	example	example	NOUN
ma-80	584	4	,	,	PUNCT
ma-80	584	5	the	the	DET
ma-80	584	6	approximation	approximation	NOUN
ma-80	584	7	arising	arise	VERB
ma-80	584	8	from	from	ADP
ma-80	584	9	a	a	DET
ma-80	584	10	first	first	ADJ
ma-80	584	11	order	order	NOUN
ma-80	584	12	iteration	iteration	NOUN
ma-80	584	13	of	of	ADP
ma-80	584	14	(	(	PUNCT
ma-80	584	15	equation	equation	NOUN
ma-80	584	16	33	33	NUM
ma-80	584	17	)	)	PUNCT
ma-80	584	18	,	,	PUNCT
ma-80	584	19	has	have	VERB
ma-80	584	20	a	a	DET
ma-80	584	21	maximum	maximum	ADJ
ma-80	584	22	relative	relative	ADJ
ma-80	584	23	error	error	NOUN
ma-80	584	24	bound	bind	VERB
ma-80	584	25	,	,	PUNCT
ma-80	584	26	over	over	ADP
ma-80	584	27	the	the	DET
ma-80	584	28	interval	interval	NOUN
ma-80	584	29	,	,	PUNCT
ma-80	584	30	of	of	ADP
ma-80	584	31	which	which	PRON
ma-80	584	32	is	be	AUX
ma-80	584	33	a	a	DET
ma-80	584	34	factor	factor	NOUN
ma-80	584	35	of	of	ADP
ma-80	584	36	lower	low	ADJ
ma-80	584	37	that	that	SCONJ
ma-80	584	38	the	the	DET
ma-80	584	39	original	original	ADJ
ma-80	584	40	approximation	approximation	NOUN
ma-80	584	41	whose	whose	DET
ma-80	584	42	relative	relative	ADJ
ma-80	584	43	error	error	NOUN
ma-80	584	44	bound	bind	VERB
ma-80	584	45	is	be	AUX
ma-80	584	46	.	.	PUNCT
ma-80	585	1	the	the	DET
ma-80	585	2	approximation	approximation	NOUN
ma-80	585	3	is	be	AUX
ma-80	585	4	:	:	PUNCT
ma-80	585	5	(	(	PUNCT
ma-80	585	6	90	90	NUM
ma-80	585	7	)	)	PUNCT
ma-80	585	8	table	table	NOUN
ma-80	585	9	6	6	NUM
ma-80	585	10	.	.	PUNCT
ma-80	585	11	relative	relative	ADJ
ma-80	585	12	error	error	NOUN
ma-80	585	13	bounds	bound	NOUN
ma-80	585	14	,	,	PUNCT
ma-80	585	15	for	for	ADP
ma-80	585	16	the	the	DET
ma-80	585	17	interval	interval	NOUN
ma-80	585	18	,	,	PUNCT
ma-80	585	19	based	base	VERB
ma-80	585	20	on	on	ADP
ma-80	585	21	newton	newton	PROPN
ma-80	585	22	-	-	PUNCT
ma-80	585	23	raphson	raphson	NOUN
ma-80	585	24	iteration	iteration	NOUN
ma-80	585	25	and	and	CCONJ
ma-80	585	26	for	for	ADP
ma-80	585	27	the	the	DET
ma-80	585	28	specified	specified	ADJ
ma-80	585	29	base	base	NOUN
ma-80	585	30	approximations	approximation	NOUN
ma-80	585	31	,	,	PUNCT
ma-80	585	32	,	,	PUNCT
ma-80	585	33	of	of	ADP
ma-80	585	34	,	,	PUNCT
ma-80	585	35	,	,	PUNCT
ma-80	585	36	and	and	CCONJ
ma-80	585	37	.	.	PUNCT
ma-80	586	1	iteration	iteration	NOUN
ma-80	586	2	order	order	NOUN
ma-80	586	3	(	(	PUNCT
ma-80	586	4	equation	equation	NOUN
ma-80	586	5	31	31	NUM
ma-80	586	6	)	)	PUNCT
ma-80	586	7	(	(	PUNCT
ma-80	586	8	equation	equation	NOUN
ma-80	586	9	33	33	NUM
ma-80	586	10	)	)	PUNCT
ma-80	586	11	(	(	PUNCT
ma-80	586	12	equation	equation	NOUN
ma-80	586	13	35	35	NUM
ma-80	586	14	)	)	PUNCT
ma-80	586	15	(	(	PUNCT
ma-80	586	16	equation	equation	NOUN
ma-80	586	17	36	36	NUM
ma-80	586	18	)	)	PUNCT
ma-80	586	19	w3	w3	PROPN
ma-80	586	20	4	4	NOUN
ma-80	586	21	y	y	NOUN
ma-80	587	1			PROPN
ma-80	587	2	y	y	NOUN
ma-80	587	3	ln	ln	PRON
ma-80	587	4	y	y	NOUN
ma-80	588	1	ln	ln	DET
ma-80	588	2	y	y	NOUN
ma-80	588	3	ln	ln	PRON
ma-80	588	4	wu4	wu4	NOUN
ma-80	588	5	y	y	NOUN
ma-80	589	1			X
ma-80	589	2	ln	ln	NOUN
ma-80	589	3	–	–	PUNCT
ma-80	589	4	ln	ln	ADJ
ma-80	589	5	–	–	PUNCT
ma-80	589	6	ln	ln	ADJ
ma-80	589	7	–	–	PUNCT
ma-80	589	8	=	=	NOUN
ma-80	589	9	0	0	NUM
ma-80	589	10			NOUN
ma-80	589	11	2.47	2.47	NUM
ma-80	589	12	10	10	NUM
ma-80	589	13	8–	8–	PROPN
ma-80	589	14	29.3	29.3	NUM
ma-80	589	15	wu4	wu4	NOUN
ma-80	589	16	y	y	PROPN
ma-80	589	17			PROPN
ma-80	589	18	7.23	7.23	NUM
ma-80	589	19	10	10	NUM
ma-80	590	1	7–	7–	NOUN
ma-80	590	2	0	0	NUM
ma-80	590	3			VERB
ma-80	590	4	w0	w0	VERB
ma-80	590	5	y	y	NOUN
ma-80	590	6			NOUN
ma-80	590	7	wu2	wu2	VERB
ma-80	590	8	y	y	NOUN
ma-80	590	9			PROPN
ma-80	590	10	wu3	wu3	VERB
ma-80	590	11	y	y	NOUN
ma-80	590	12			PROPN
ma-80	590	13	wu4	wu4	NOUN
ma-80	590	14	y	y	NOUN
ma-80	590	15			PROPN
ma-80	590	16	wu5	wu5	ADP
ma-80	590	17	y	y	NOUN
ma-80	590	18			PROPN
ma-80	590	19	w0	w0	VERB
ma-80	590	20	y	y	NOUN
ma-80	590	21			NOUN
ma-80	590	22	wu2	wu2	VERB
ma-80	590	23	y	y	NOUN
ma-80	590	24	=	=	NOUN
ma-80	590	25	w0	w0	PROPN
ma-80	590	26	y	y	NOUN
ma-80	590	27			PROPN
ma-80	590	28	wu3	wu3	NOUN
ma-80	590	29	y	y	NOUN
ma-80	590	30	=	=	NOUN
ma-80	590	31	w0	w0	PROPN
ma-80	590	32	y	y	NOUN
ma-80	590	33			PROPN
ma-80	590	34	wu4	wu4	NOUN
ma-80	590	35	y	y	NOUN
ma-80	590	36	=	=	NOUN
ma-80	590	37	w0	w0	PROPN
ma-80	590	38	y	y	NOUN
ma-80	590	39			PROPN
ma-80	590	40	wu5	wu5	ADP
ma-80	590	41	y	y	NOUN
ma-80	590	42	=	=	NOUN
ma-80	590	43	0	0	NUM
ma-80	590	44	5.69	5.69	NUM
ma-80	590	45	10	10	NUM
ma-80	590	46	2–	2–	NUM
ma-80	590	47	1.33	1.33	NUM
ma-80	590	48	10	10	NUM
ma-80	590	49	3–	3–	NUM
ma-80	590	50	7.23	7.23	NUM
ma-80	590	51	10	10	NUM
ma-80	590	52	7–	7–	NOUN
ma-80	590	53	2.15	2.15	NUM
ma-80	590	54	10	10	NUM
ma-80	590	55	13–	13–	NUM
ma-80	590	56	1	1	NUM
ma-80	590	57	8.28	8.28	NUM
ma-80	590	58	10	10	NUM
ma-80	591	1	3–	3–	NUM
ma-80	591	2	5.12	5.12	NUM
ma-80	591	3	10	10	NUM
ma-80	591	4	6–	6–	PROPN
ma-80	591	5	1.49	1.49	NUM
ma-80	591	6	10	10	NUM
ma-80	591	7	12–	12–	NUM
ma-80	591	8	1.30	1.30	NUM
ma-80	591	9	10	10	NUM
ma-80	591	10	25–	25–	NUM
ma-80	591	11	2	2	NUM
ma-80	591	12	3.48	3.48	NUM
ma-80	591	13	10	10	NUM
ma-80	592	1	4–	4–	PROPN
ma-80	592	2	9.61	9.61	NUM
ma-80	592	3	10	10	NUM
ma-80	592	4	11–	11–	NUM
ma-80	592	5	6.98	6.98	NUM
ma-80	592	6	10	10	NUM
ma-80	592	7	24–	24–	NUM
ma-80	592	8	5.02	5.02	NUM
ma-80	592	9	10	10	NUM
ma-80	592	10	50–	50–	NUM
ma-80	592	11	3	3	NUM
ma-80	592	12	9.95	9.95	NUM
ma-80	592	13	10	10	NUM
ma-80	592	14	7–	7–	NOUN
ma-80	592	15	3.91	3.91	NUM
ma-80	592	16	10	10	NUM
ma-80	592	17	20–	20–	NUM
ma-80	592	18	1.62	1.62	NUM
ma-80	592	19	10	10	NUM
ma-80	592	20	46–	46–	NUM
ma-80	592	21	7.67	7.67	NUM
ma-80	592	22	10	10	NUM
ma-80	592	23	99–	99–	NUM
ma-80	592	24	4	4	NUM
ma-80	592	25	8.21	8.21	NUM
ma-80	592	26	10	10	NUM
ma-80	592	27	12–	12–	NUM
ma-80	592	28	7.08	7.08	NUM
ma-80	592	29	10	10	NUM
ma-80	592	30	39–	39–	NUM
ma-80	592	31	9.04	9.04	NUM
ma-80	592	32	10	10	NUM
ma-80	592	33	92–	92–	NUM
ma-80	592	34	1.81	1.81	NUM
ma-80	592	35	10	10	NUM
ma-80	592	36	196–	196–	NUM
ma-80	592	37	5	5	NUM
ma-80	592	38	5.60	5.60	NUM
ma-80	592	39	10	10	NUM
ma-80	592	40	22–	22–	NUM
ma-80	592	41	2.43	2.43	NUM
ma-80	592	42	10	10	NUM
ma-80	592	43	76–	76–	NUM
ma-80	592	44	2.85	2.85	NUM
ma-80	592	45	10	10	NUM
ma-80	592	46	182–	182–	NUM
ma-80	592	47	1.02	1.02	NUM
ma-80	592	48	10	10	NUM
ma-80	592	49	391–	391–	NUM
ma-80	592	50	wu3	wu3	VERB
ma-80	592	51	y	y	NOUN
ma-80	592	52			PROPN
ma-80	592	53	0	0	NUM
ma-80	592	54			NUM
ma-80	592	55	5.12	5.12	NUM
ma-80	592	56	10	10	NUM
ma-80	592	57	6–	6–	NUM
ma-80	592	58	260	260	NUM
ma-80	592	59	1.33	1.33	NUM
ma-80	592	60	10	10	NUM
ma-80	592	61	3–	3–	NUM
ma-80	592	62	w1	w1	NOUN
ma-80	592	63	3	3	NOUN
ma-80	592	64	y	y	NOUN
ma-80	592	65			PROPN
ma-80	592	66	1	1	NUM
ma-80	592	67	3y	3y	NUM
ma-80	592	68	y	y	PROPN
ma-80	592	69	1	1	NUM
ma-80	592	70	y+	y+	NOUN
ma-80	592	71	ln+	ln+	PROPN
ma-80	593	1	+	+	CCONJ
ma-80	593	2	1	1	NUM
ma-80	593	3	1	1	NUM
ma-80	593	4	y+	y+	NOUN
ma-80	593	5	ln+	ln+	PUNCT
ma-80	593	6			NOUN
ma-80	593	7	1	1	NUM
ma-80	593	8	1	1	NUM
ma-80	593	9	2y+	2y+	NUM
ma-80	593	10	1	1	NUM
ma-80	593	11	1	1	NUM
ma-80	593	12	y+	y+	NOUN
ma-80	593	13	ln+	ln+	PROPN
ma-80	593	14	-------------------------------ln+	-------------------------------ln+	PUNCT
ma-80	593	15	-----------------------------------------------------------------------------------------------ln	-----------------------------------------------------------------------------------------------ln	ADV
ma-80	593	16	–	–	PUNCT
ma-80	593	17	=	=	SYM
ma-80	593	18	1	1	NUM
ma-80	593	19	3y	3y	NUM
ma-80	593	20	y	y	PROPN
ma-80	593	21	1	1	NUM
ma-80	593	22	y+	y+	NOUN
ma-80	593	23	ln+	ln+	PROPN
ma-80	594	1	+	+	CCONJ
ma-80	594	2	1	1	NUM
ma-80	594	3	1	1	NUM
ma-80	594	4	y+	y+	NOUN
ma-80	594	5	ln+	ln+	PUNCT
ma-80	594	6			NOUN
ma-80	594	7	1	1	NUM
ma-80	594	8	1	1	NUM
ma-80	594	9	2y+	2y+	NUM
ma-80	594	10	1	1	NUM
ma-80	594	11	1	1	NUM
ma-80	594	12	y+	y+	NOUN
ma-80	594	13	ln+	ln+	PROPN
ma-80	594	14	-------------------------------ln+	-------------------------------ln+	PUNCT
ma-80	594	15	-----------------------------------------------------------------------------------------------ln	-----------------------------------------------------------------------------------------------ln	PROPN
ma-80	594	16	y	y	PROPN
ma-80	594	17	1	1	NUM
ma-80	594	18	1	1	NUM
ma-80	594	19	y+	y+	NOUN
ma-80	594	20	ln+	ln+	PUNCT
ma-80	594	21			NOUN
ma-80	594	22	1	1	NUM
ma-80	594	23	1	1	NUM
ma-80	594	24	2y+	2y+	NUM
ma-80	594	25	1	1	NUM
ma-80	594	26	1	1	NUM
ma-80	594	27	y+	y+	NOUN
ma-80	594	28	ln+	ln+	NOUN
ma-80	594	29	-------------------------------ln+	-------------------------------ln+	PROPN
ma-80	594	30	1	1	NUM
ma-80	594	31	3y	3y	NUM
ma-80	594	32	y	y	PROPN
ma-80	594	33	1	1	NUM
ma-80	594	34	y+	y+	NOUN
ma-80	594	35	ln+	ln+	PROPN
ma-80	595	1	+	+	PROPN
ma-80	595	2			ADJ
ma-80	595	3			PROPN
ma-80	595	4	--------------------------------------------------------------------------------------------------	--------------------------------------------------------------------------------------------------	CCONJ
ma-80	595	5	–	–	PUNCT
ma-80	595	6	1	1	NUM
ma-80	595	7	1	1	NUM
ma-80	595	8	3y	3y	NUM
ma-80	595	9	y	y	PROPN
ma-80	595	10	1	1	NUM
ma-80	595	11	y+	y+	NOUN
ma-80	595	12	ln+	ln+	PROPN
ma-80	596	1	+	+	CCONJ
ma-80	596	2	1	1	NUM
ma-80	596	3	1	1	NUM
ma-80	596	4	y+	y+	NOUN
ma-80	596	5	ln+	ln+	PUNCT
ma-80	596	6			NOUN
ma-80	596	7	1	1	NUM
ma-80	596	8	1	1	NUM
ma-80	596	9	2y+	2y+	NUM
ma-80	596	10	1	1	NUM
ma-80	596	11	1	1	NUM
ma-80	596	12	y+	y+	NOUN
ma-80	596	13	ln+	ln+	NOUN
ma-80	596	14	-------------------------------ln+	-------------------------------ln+	PROPN
ma-80	596	15	-----------------------------------------------------------------------------------------------ln+	-----------------------------------------------------------------------------------------------ln+	PUNCT
ma-80	596	16	------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------https://doi.org/10.28924/ada/ma.2.14	------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------https://doi.org/10.28924/ada/ma.2.14	PROPN
ma-80	596	17	7	7	NUM
ma-80	596	18	.	.	PUNCT
ma-80	596	19	applications	application	NOUN
ma-80	596	20	7.1	7.1	NUM
ma-80	596	21	.	.	PUNCT
ma-80	597	1	approximation	approximation	NOUN
ma-80	597	2	with	with	ADP
ma-80	597	3	fixed	fix	VERB
ma-80	597	4	relative	relative	ADJ
ma-80	597	5	error	error	NOUN
ma-80	597	6	bound	bind	VERB
ma-80	597	7	.	.	PUNCT
ma-80	598	1	there	there	PRON
ma-80	598	2	are	be	VERB
ma-80	598	3	many	many	ADJ
ma-80	598	4	applications	application	NOUN
ma-80	598	5	where	where	SCONJ
ma-80	598	6	the	the	DET
ma-80	598	7	lambert	lambert	PROPN
ma-80	598	8	w	w	PROPN
ma-80	598	9	function	function	PROPN
ma-80	598	10	is	be	AUX
ma-80	598	11	used	use	VERB
ma-80	598	12	to	to	PART
ma-80	598	13	model	model	VERB
ma-80	598	14	the	the	DET
ma-80	598	15	physical	physical	ADJ
ma-80	598	16	nature	nature	NOUN
ma-80	598	17	/	/	SYM
ma-80	598	18	characteristics	characteristic	NOUN
ma-80	598	19	of	of	ADP
ma-80	598	20	an	an	DET
ma-80	598	21	entity	entity	NOUN
ma-80	598	22	which	which	PRON
ma-80	598	23	are	be	AUX
ma-80	598	24	positive	positive	ADJ
ma-80	598	25	in	in	ADP
ma-80	598	26	nature	nature	NOUN
ma-80	598	27	.	.	PUNCT
ma-80	599	1	in	in	ADP
ma-80	599	2	many	many	ADJ
ma-80	599	3	of	of	ADP
ma-80	599	4	these	these	DET
ma-80	599	5	cases	case	NOUN
ma-80	599	6	the	the	DET
ma-80	599	7	parameter	parameter	NOUN
ma-80	599	8	values	value	NOUN
ma-80	599	9	are	be	AUX
ma-80	599	10	not	not	PART
ma-80	599	11	known	know	VERB
ma-80	599	12	with	with	ADP
ma-80	599	13	high	high	ADJ
ma-80	599	14	accuracy	accuracy	NOUN
ma-80	599	15	.	.	PUNCT
ma-80	600	1	for	for	ADP
ma-80	600	2	such	such	ADJ
ma-80	600	3	cases	case	NOUN
ma-80	600	4	,	,	PUNCT
ma-80	600	5	highly	highly	ADV
ma-80	600	6	accurate	accurate	ADJ
ma-80	600	7	computation	computation	NOUN
ma-80	600	8	of	of	ADP
ma-80	600	9	the	the	DET
ma-80	600	10	lambert	lambert	PROPN
ma-80	600	11	w	w	PROPN
ma-80	600	12	function	function	NOUN
ma-80	600	13	is	be	AUX
ma-80	600	14	not	not	PART
ma-80	600	15	required	require	VERB
ma-80	600	16	and	and	CCONJ
ma-80	600	17	a	a	DET
ma-80	600	18	fixed	fix	VERB
ma-80	600	19	approximation	approximation	NOUN
ma-80	600	20	,	,	PUNCT
ma-80	600	21	with	with	ADP
ma-80	600	22	a	a	DET
ma-80	600	23	set	set	VERB
ma-80	600	24	relative	relative	ADJ
ma-80	600	25	error	error	NOUN
ma-80	600	26	bound	bind	VERB
ma-80	600	27	,	,	PUNCT
ma-80	600	28	is	be	AUX
ma-80	600	29	useful	useful	ADJ
ma-80	600	30	rather	rather	ADV
ma-80	600	31	than	than	ADP
ma-80	600	32	relying	rely	VERB
ma-80	600	33	on	on	ADP
ma-80	600	34	,	,	PUNCT
ma-80	600	35	for	for	ADP
ma-80	600	36	example	example	NOUN
ma-80	600	37	,	,	PUNCT
ma-80	600	38	iterative	iterative	ADJ
ma-80	600	39	approximations	approximation	NOUN
ma-80	600	40	where	where	SCONJ
ma-80	600	41	the	the	DET
ma-80	600	42	relative	relative	ADJ
ma-80	600	43	error	error	NOUN
ma-80	600	44	achieved	achieve	VERB
ma-80	600	45	depends	depend	VERB
ma-80	600	46	on	on	ADP
ma-80	600	47	the	the	DET
ma-80	600	48	initial	initial	ADJ
ma-80	600	49	approximate	approximate	NOUN
ma-80	600	50	used	use	VERB
ma-80	600	51	.	.	PUNCT
ma-80	601	1	the	the	DET
ma-80	601	2	relatively	relatively	ADV
ma-80	601	3	simple	simple	ADJ
ma-80	601	4	approximation	approximation	NOUN
ma-80	601	5	for	for	ADP
ma-80	601	6	the	the	DET
ma-80	601	7	lambert	lambert	PROPN
ma-80	601	8	w	w	PROPN
ma-80	601	9	function	function	PROPN
ma-80	601	10	,	,	PUNCT
ma-80	601	11	as	as	SCONJ
ma-80	601	12	specified	specify	VERB
ma-80	601	13	by	by	ADP
ma-80	601	14	equation	equation	NOUN
ma-80	601	15	33	33	NUM
ma-80	601	16	,	,	PUNCT
ma-80	601	17	i.e.	i.e.	X
ma-80	601	18	(	(	PUNCT
ma-80	601	19	91	91	NUM
ma-80	601	20	)	)	PUNCT
ma-80	601	21	with	with	ADP
ma-80	601	22	a	a	DET
ma-80	601	23	relative	relative	ADJ
ma-80	601	24	error	error	NOUN
ma-80	601	25	bound	bind	VERB
ma-80	601	26	of	of	ADP
ma-80	601	27	over	over	ADP
ma-80	601	28	the	the	DET
ma-80	601	29	interval	interval	NOUN
ma-80	601	30	,	,	PUNCT
ma-80	601	31	is	be	AUX
ma-80	601	32	likely	likely	ADJ
ma-80	601	33	to	to	PART
ma-80	601	34	be	be	AUX
ma-80	601	35	useful	useful	ADJ
ma-80	601	36	.	.	PUNCT
ma-80	602	1	one	one	NUM
ma-80	602	2	application	application	NOUN
ma-80	602	3	,	,	PUNCT
ma-80	602	4	for	for	ADP
ma-80	602	5	example	example	NOUN
ma-80	602	6	,	,	PUNCT
ma-80	602	7	is	be	AUX
ma-80	602	8	in	in	ADP
ma-80	602	9	the	the	DET
ma-80	602	10	evaluation	evaluation	NOUN
ma-80	602	11	of	of	ADP
ma-80	602	12	the	the	DET
ma-80	602	13	collector	collector	NOUN
ma-80	602	14	current	current	NOUN
ma-80	602	15	in	in	ADP
ma-80	602	16	a	a	DET
ma-80	602	17	common	common	ADJ
ma-80	602	18	emitter	emitter	NOUN
ma-80	602	19	circuit	circuit	NOUN
ma-80	602	20	,	,	PUNCT
ma-80	602	21	e.g.	e.g.	ADV
ma-80	602	22	[	[	X
ma-80	602	23	2	2	NUM
ma-80	602	24	]	]	PUNCT
ma-80	602	25	,	,	PUNCT
ma-80	602	26	eqn	eqn	PROPN
ma-80	602	27	.	.	PUNCT
ma-80	603	1	21	21	NUM
ma-80	603	2	.	.	PUNCT
ma-80	604	1	for	for	ADP
ma-80	604	2	the	the	DET
ma-80	604	3	interval	interval	NOUN
ma-80	604	4	,	,	PUNCT
ma-80	604	5	the	the	DET
ma-80	604	6	approximation	approximation	NOUN
ma-80	604	7	detailed	detail	VERB
ma-80	604	8	in	in	ADP
ma-80	604	9	equation	equation	NOUN
ma-80	604	10	79	79	NUM
ma-80	604	11	,	,	PUNCT
ma-80	604	12	is	be	AUX
ma-80	604	13	of	of	ADP
ma-80	604	14	modest	modest	ADJ
ma-80	604	15	complexity	complexity	NOUN
ma-80	604	16	,	,	PUNCT
ma-80	604	17	is	be	AUX
ma-80	604	18	sharp	sharp	ADJ
ma-80	604	19	at	at	ADP
ma-80	604	20	the	the	DET
ma-80	604	21	points	point	NOUN
ma-80	604	22	and	and	CCONJ
ma-80	604	23	and	and	CCONJ
ma-80	604	24	has	have	VERB
ma-80	604	25	a	a	DET
ma-80	604	26	relative	relative	ADJ
ma-80	604	27	error	error	NOUN
ma-80	604	28	bound	bind	VERB
ma-80	604	29	of	of	ADP
ma-80	604	30	.	.	PUNCT
ma-80	605	1	for	for	ADP
ma-80	605	2	highly	highly	ADV
ma-80	605	3	accurate	accurate	ADJ
ma-80	605	4	approximations	approximation	NOUN
ma-80	605	5	over	over	ADP
ma-80	605	6	the	the	DET
ma-80	605	7	interval	interval	NOUN
ma-80	605	8	,	,	PUNCT
ma-80	605	9	an	an	DET
ma-80	605	10	explicit	explicit	ADJ
ma-80	605	11	analytical	analytical	ADJ
ma-80	605	12	approximation	approximation	NOUN
ma-80	605	13	,	,	PUNCT
ma-80	605	14	with	with	SCONJ
ma-80	605	15	a	a	DET
ma-80	605	16	relative	relative	ADJ
ma-80	605	17	error	error	NOUN
ma-80	605	18	bound	bind	VERB
ma-80	605	19	of	of	ADP
ma-80	605	20	,	,	PUNCT
ma-80	605	21	can	can	AUX
ma-80	605	22	be	be	AUX
ma-80	605	23	specified	specify	VERB
ma-80	605	24	by	by	ADP
ma-80	605	25	utilizing	utilize	VERB
ma-80	605	26	the	the	DET
ma-80	605	27	fifth	fifth	ADJ
ma-80	605	28	order	order	NOUN
ma-80	605	29	iterative	iterative	NOUN
ma-80	605	30	approximation	approximation	NOUN
ma-80	605	31	,	,	PUNCT
ma-80	605	32	denoted	denote	VERB
ma-80	605	33	,	,	PUNCT
ma-80	605	34	arising	arise	VERB
ma-80	605	35	from	from	ADP
ma-80	605	36	the	the	DET
ma-80	605	37	iteration	iteration	NOUN
ma-80	605	38	specified	specify	VERB
ma-80	605	39	by	by	ADP
ma-80	605	40	equation	equation	NOUN
ma-80	605	41	47	47	NUM
ma-80	605	42	and	and	CCONJ
ma-80	605	43	with	with	ADP
ma-80	605	44	,	,	PUNCT
ma-80	605	45	(	(	PUNCT
ma-80	605	46	see	see	VERB
ma-80	605	47	table	table	NOUN
ma-80	605	48	2	2	NUM
ma-80	605	49	)	)	PUNCT
ma-80	605	50	.	.	PUNCT
ma-80	606	1	an	an	DET
ma-80	606	2	alternative	alternative	ADJ
ma-80	606	3	analytical	analytical	ADJ
ma-80	606	4	expression	expression	NOUN
ma-80	606	5	,	,	PUNCT
ma-80	606	6	with	with	ADP
ma-80	606	7	a	a	DET
ma-80	606	8	relative	relative	ADJ
ma-80	606	9	error	error	NOUN
ma-80	606	10	bound	bind	VERB
ma-80	606	11	of	of	ADP
ma-80	606	12	over	over	ADP
ma-80	606	13	the	the	DET
ma-80	606	14	interval	interval	NOUN
ma-80	606	15	,	,	PUNCT
ma-80	606	16	is	be	AUX
ma-80	606	17	(	(	PUNCT
ma-80	606	18	92	92	NUM
ma-80	606	19	)	)	PUNCT
ma-80	606	20	where	where	SCONJ
ma-80	606	21	and	and	CCONJ
ma-80	606	22	are	be	AUX
ma-80	606	23	defined	define	VERB
ma-80	606	24	,	,	PUNCT
ma-80	606	25	respectively	respectively	ADV
ma-80	606	26	,	,	PUNCT
ma-80	606	27	in	in	ADP
ma-80	606	28	equation	equation	NOUN
ma-80	606	29	37	37	NUM
ma-80	606	30	and	and	CCONJ
ma-80	606	31	equation	equation	NOUN
ma-80	606	32	38	38	NUM
ma-80	606	33	.	.	PUNCT
ma-80	607	1	this	this	DET
ma-80	607	2	expression	expression	NOUN
ma-80	607	3	arises	arise	VERB
ma-80	607	4	from	from	ADP
ma-80	607	5	a	a	DET
ma-80	607	6	first	first	ADJ
ma-80	607	7	iteration	iteration	NOUN
ma-80	607	8	of	of	ADP
ma-80	607	9	the	the	DET
ma-80	607	10	newton	newton	PROPN
ma-80	607	11	-	-	PUNCT
ma-80	607	12	raphson	raphson	PROPN
ma-80	607	13	method	method	NOUN
ma-80	607	14	(	(	PUNCT
ma-80	607	15	equation	equation	NOUN
ma-80	607	16	22	22	NUM
ma-80	607	17	)	)	PUNCT
ma-80	607	18	utilizing	utilize	VERB
ma-80	607	19	the	the	DET
ma-80	607	20	fifth	fifth	ADJ
ma-80	607	21	order	order	NOUN
ma-80	607	22	approximation	approximation	NOUN
ma-80	607	23	specified	specify	VERB
ma-80	607	24	in	in	ADP
ma-80	607	25	equation	equation	NOUN
ma-80	607	26	36	36	NUM
ma-80	607	27	.	.	PUNCT
ma-80	608	1	the	the	DET
ma-80	608	2	relative	relative	ADJ
ma-80	608	3	error	error	NOUN
ma-80	608	4	bound	bind	VERB
ma-80	608	5	is	be	AUX
ma-80	608	6	specified	specify	VERB
ma-80	608	7	in	in	ADP
ma-80	608	8	table	table	NOUN
ma-80	608	9	6	6	NUM
ma-80	608	10	.	.	NOUN
ma-80	608	11	7.2	7.2	NUM
ma-80	608	12	.	.	PUNCT
ma-80	609	1	upper	upper	ADJ
ma-80	609	2	/	/	SYM
ma-80	609	3	lower	low	ADJ
ma-80	609	4	bounds	bound	NOUN
ma-80	609	5	for	for	ADP
ma-80	609	6	lambert	lambert	PROPN
ma-80	609	7	w.	w.	PROPN
ma-80	609	8	there	there	PRON
ma-80	609	9	is	be	VERB
ma-80	609	10	interest	interest	NOUN
ma-80	609	11	in	in	ADP
ma-80	609	12	upper	upper	ADJ
ma-80	609	13	/	/	SYM
ma-80	609	14	lower	low	ADJ
ma-80	609	15	bounds	bound	NOUN
ma-80	609	16	for	for	ADP
ma-80	609	17	the	the	DET
ma-80	609	18	lambert	lambert	PROPN
ma-80	609	19	w	w	PROPN
ma-80	609	20	function	function	PROPN
ma-80	609	21	,	,	PUNCT
ma-80	610	1	e.g.	e.g.	ADV
ma-80	610	2	[	[	X
ma-80	610	3	15	15	NUM
ma-80	610	4	]	]	PUNCT
ma-80	610	5	and	and	CCONJ
ma-80	610	6	[	[	X
ma-80	610	7	24	24	NUM
ma-80	610	8	]	]	PUNCT
ma-80	610	9	.	.	PUNCT
ma-80	611	1	alzahrani	alzahrani	PROPN
ma-80	611	2	and	and	CCONJ
ma-80	611	3	salem	salem	PROPN
ma-80	611	4	,	,	PUNCT
ma-80	611	5	[	[	X
ma-80	611	6	1	1	NUM
ma-80	611	7	]	]	PUNCT
ma-80	611	8	,	,	PUNCT
ma-80	611	9	detail	detail	NOUN
ma-80	611	10	bounds	bound	VERB
ma-80	611	11	for	for	ADP
ma-80	611	12	.	.	PUNCT
ma-80	612	1	the	the	DET
ma-80	612	2	following	follow	VERB
ma-80	612	3	bounds	bound	NOUN
ma-80	612	4	were	be	AUX
ma-80	612	5	proposed	propose	VERB
ma-80	612	6	by	by	ADP
ma-80	612	7	hoorfar	hoorfar	ADV
ma-80	612	8	(	(	PUNCT
ma-80	612	9	see	see	VERB
ma-80	612	10	,	,	PUNCT
ma-80	612	11	[	[	X
ma-80	612	12	17	17	NUM
ma-80	612	13	]	]	PUNCT
ma-80	612	14	,	,	PUNCT
ma-80	612	15	eqn	eqn	PROPN
ma-80	612	16	.	.	PROPN
ma-80	612	17	21	21	NUM
ma-80	612	18	)	)	PUNCT
ma-80	612	19	(	(	PUNCT
ma-80	612	20	93	93	NUM
ma-80	612	21	)	)	PUNCT
ma-80	612	22	for	for	ADP
ma-80	612	23	the	the	DET
ma-80	612	24	interval	interval	NOUN
ma-80	612	25	,	,	PUNCT
ma-80	612	26	the	the	DET
ma-80	612	27	relative	relative	ADJ
ma-80	612	28	error	error	NOUN
ma-80	612	29	bound	bind	VERB
ma-80	612	30	associated	associate	VERB
ma-80	612	31	with	with	ADP
ma-80	612	32	the	the	DET
ma-80	612	33	lower	low	ADJ
ma-80	612	34	bounded	bounded	ADJ
ma-80	612	35	function	function	NOUN
ma-80	612	36	is	be	AUX
ma-80	612	37	;	;	PUNCT
ma-80	612	38	the	the	DET
ma-80	612	39	relative	relative	ADJ
ma-80	612	40	error	error	NOUN
ma-80	612	41	bound	bind	VERB
ma-80	612	42	for	for	ADP
ma-80	612	43	the	the	DET
ma-80	612	44	upper	upper	ADJ
ma-80	612	45	bounded	bounded	ADJ
ma-80	612	46	function	function	NOUN
ma-80	612	47	is	be	AUX
ma-80	612	48	.	.	PUNCT
ma-80	613	1	wu3	wu3	VERB
ma-80	613	2	y	y	NOUN
ma-80	613	3			PROPN
ma-80	613	4	1	1	NUM
ma-80	613	5	3y	3y	NUM
ma-80	613	6	y	y	PROPN
ma-80	613	7	1	1	NUM
ma-80	613	8	y+	y+	NOUN
ma-80	613	9	ln+	ln+	PROPN
ma-80	614	1	+	+	CCONJ
ma-80	614	2	1	1	NUM
ma-80	614	3	1	1	NUM
ma-80	614	4	y+	y+	NOUN
ma-80	614	5	ln+	ln+	PUNCT
ma-80	614	6			NOUN
ma-80	614	7	1	1	NUM
ma-80	614	8	1	1	NUM
ma-80	614	9	2y+	2y+	NUM
ma-80	614	10	1	1	NUM
ma-80	614	11	1	1	NUM
ma-80	614	12	y+	y+	NOUN
ma-80	614	13	ln+	ln+	PROPN
ma-80	614	14	-------------------------------ln+	-------------------------------ln+	PUNCT
ma-80	614	15	-----------------------------------------------------------------------------------------------ln	-----------------------------------------------------------------------------------------------ln	PROPN
ma-80	614	16	=	=	NUM
ma-80	614	17	1.33	1.33	NUM
ma-80	614	18	10	10	NUM
ma-80	614	19	3	3	NUM
ma-80	614	20	–	–	PUNCT
ma-80	614	21	0	0	NUM
ma-80	614	22			NUM
ma-80	614	23	1	1	NUM
ma-80	614	24	e	e	NOUN
ma-80	614	25	–	–	PUNCT
ma-80	614	26	0	0	NUM
ma-80	614	27			NOUN
ma-80	614	28	w	w	PROPN
ma-80	614	29	2	2	NUM
ma-80	614	30	y	y	NOUN
ma-80	614	31			PROPN
ma-80	614	32	1	1	NUM
ma-80	614	33	e	e	NOUN
ma-80	614	34	–	–	PUNCT
ma-80	614	35	0	0	NUM
ma-80	614	36	9.68	9.68	NUM
ma-80	614	37	10	10	NUM
ma-80	614	38	4–	4–	NOUN
ma-80	614	39	0	0	NUM
ma-80	614	40			NUM
ma-80	614	41	7.98	7.98	NUM
ma-80	614	42	10	10	NUM
ma-80	614	43	18–	18–	NUM
ma-80	614	44	wk5	wk5	X
ma-80	614	45	z1	z1	NUM
ma-80	614	46	1	1	NUM
ma-80	614	47	ky+=	ky+=	PROPN
ma-80	614	48	k	k	PROPN
ma-80	614	49	0.4=	0.4=	PROPN
ma-80	614	50	1.30	1.30	NUM
ma-80	614	51	10	10	NUM
ma-80	614	52	25–	25–	NUM
ma-80	614	53	0	0	NUM
ma-80	614	54			VERB
ma-80	614	55	w1	w1	NOUN
ma-80	614	56	5	5	NOUN
ma-80	614	57	y	y	NOUN
ma-80	614	58			PROPN
ma-80	614	59	d5	d5	NOUN
ma-80	614	60	y	y	NOUN
ma-80	614	61			PROPN
ma-80	614	62	n5	n5	PROPN
ma-80	614	63	y	y	NOUN
ma-80	614	64			PROPN
ma-80	614	65	-------------ln	-------------ln	NOUN
ma-80	614	66	d5	d5	NOUN
ma-80	614	67	y	y	PROPN
ma-80	615	1			PROPN
ma-80	615	2	n5	n5	PROPN
ma-80	615	3	y	y	NOUN
ma-80	616	1			PROPN
ma-80	616	2	-------------ln	-------------ln	NOUN
ma-80	616	3	yn5	yn5	NOUN
ma-80	616	4	y	y	NOUN
ma-80	616	5			PROPN
ma-80	616	6	d5	d5	NOUN
ma-80	616	7	y	y	NOUN
ma-80	616	8			PUNCT
ma-80	616	9	----------------	----------------	PUNCT
ma-80	616	10	–	–	PUNCT
ma-80	616	11	1	1	NUM
ma-80	616	12	d5	d5	NOUN
ma-80	616	13	y	y	NOUN
ma-80	616	14			PROPN
ma-80	616	15	n5	n5	PROPN
ma-80	616	16	y	y	NOUN
ma-80	616	17			PUNCT
ma-80	616	18	-------------ln+	-------------ln+	PUNCT
ma-80	616	19	-----------------------------------------------	-----------------------------------------------	PUNCT
ma-80	616	20	–	–	PUNCT
ma-80	616	21	=	=	NOUN
ma-80	616	22	n5	n5	PROPN
ma-80	616	23	d5	d5	NOUN
ma-80	616	24	wu5	wu5	ADP
ma-80	616	25	y	y	PROPN
ma-80	616	26			PROPN
ma-80	616	27	w	w	PROPN
ma-80	616	28	1	1	NUM
ma-80	616	29	–	–	PUNCT
ma-80	616	30	y	y	PROPN
ma-80	616	31	y	y	NOUN
ma-80	617	1	ln	ln	PROPN
ma-80	617	2	-------------ln	-------------ln	VERB
ma-80	618	1	y	y	NOUN
ma-80	618	2	ln	ln	NOUN
ma-80	618	3	ln	ln	NOUN
ma-80	618	4	2	2	NUM
ma-80	618	5	y	y	NOUN
ma-80	619	1	ln	ln	DET
ma-80	619	2	-----------------------+	-----------------------+	PROPN
ma-80	619	3	w	w	NOUN
ma-80	619	4	y	y	NOUN
ma-80	620	1			PUNCT
ma-80	620	2	y	y	PROPN
ma-80	620	3	y	y	NOUN
ma-80	621	1	ln	ln	PROPN
ma-80	621	2	-------------ln	-------------ln	NOUN
ma-80	621	3	e	e	X
ma-80	621	4	e	e	X
ma-80	621	5	1	1	NUM
ma-80	621	6	–	–	PUNCT
ma-80	621	7	----------y	----------y	PUNCT
ma-80	621	8	ln	ln	NOUN
ma-80	621	9	ln	ln	VERB
ma-80	621	10	y	y	NOUN
ma-80	621	11	ln	ln	PROPN
ma-80	622	1	-----------------------.+	-----------------------.+	PUNCT
ma-80	622	2			PUNCT
ma-80	623	1	e	e	X
ma-80	623	2			NUM
ma-80	623	3			PUNCT
ma-80	623	4	0.0568	0.0568	NUM
ma-80	623	5	0.207	0.207	NUM
ma-80	623	6	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	NOUN
ma-80	623	7	the	the	DET
ma-80	623	8	bounds	bound	NOUN
ma-80	623	9	proposed	propose	VERB
ma-80	623	10	in	in	ADP
ma-80	623	11	[	[	X
ma-80	623	12	17	17	NUM
ma-80	623	13	]	]	PUNCT
ma-80	623	14	,	,	PUNCT
ma-80	623	15	eqn	eqn	PROPN
ma-80	623	16	.	.	PROPN
ma-80	624	1	25	25	NUM
ma-80	624	2	,	,	PUNCT
ma-80	624	3	27	27	NUM
ma-80	624	4	,	,	PUNCT
ma-80	624	5	have	have	VERB
ma-80	624	6	modest	modest	ADJ
ma-80	624	7	relative	relative	ADJ
ma-80	624	8	errors	error	NOUN
ma-80	624	9	for	for	ADP
ma-80	624	10	and	and	CCONJ
ma-80	624	11	are	be	AUX
ma-80	624	12	:	:	PUNCT
ma-80	624	13	(	(	PUNCT
ma-80	624	14	94	94	NUM
ma-80	624	15	)	)	PUNCT
ma-80	624	16	the	the	DET
ma-80	624	17	relative	relative	ADJ
ma-80	624	18	error	error	NOUN
ma-80	624	19	bounds	bound	NOUN
ma-80	624	20	in	in	ADP
ma-80	624	21	the	the	DET
ma-80	624	22	lower	low	ADJ
ma-80	624	23	and	and	CCONJ
ma-80	624	24	upper	upper	ADJ
ma-80	624	25	bounded	bounded	ADJ
ma-80	624	26	functions	function	NOUN
ma-80	624	27	,	,	PUNCT
ma-80	624	28	over	over	ADP
ma-80	624	29	the	the	DET
ma-80	624	30	interval	interval	NOUN
ma-80	624	31	,	,	PUNCT
ma-80	624	32	respectively	respectively	ADV
ma-80	624	33	,	,	PUNCT
ma-80	624	34	are	be	AUX
ma-80	624	35	and	and	CCONJ
ma-80	624	36	.	.	PUNCT
ma-80	625	1	the	the	DET
ma-80	625	2	relative	relative	ADJ
ma-80	625	3	errors	error	NOUN
ma-80	625	4	decrease	decrease	VERB
ma-80	625	5	for	for	ADP
ma-80	625	6	.	.	PUNCT
ma-80	626	1	by	by	ADP
ma-80	626	2	construction	construction	NOUN
ma-80	626	3	,	,	PUNCT
ma-80	626	4	,	,	PUNCT
ma-80	626	5	,	,	PUNCT
ma-80	626	6	as	as	SCONJ
ma-80	626	7	defined	define	VERB
ma-80	626	8	in	in	ADP
ma-80	626	9	theorem	theorem	ADJ
ma-80	626	10	3.1	3.1	NUM
ma-80	626	11	,	,	PUNCT
ma-80	626	12	are	be	AUX
ma-80	626	13	a	a	DET
ma-80	626	14	sequence	sequence	NOUN
ma-80	626	15	of	of	ADP
ma-80	626	16	increasingly	increasingly	ADV
ma-80	626	17	accurate	accurate	ADJ
ma-80	626	18	lower	low	ADJ
ma-80	626	19	bounds	bound	NOUN
ma-80	626	20	for	for	ADP
ma-80	626	21	.	.	PUNCT
ma-80	627	1	similarly	similarly	ADV
ma-80	627	2	,	,	PUNCT
ma-80	627	3	,	,	PUNCT
ma-80	627	4	,	,	PUNCT
ma-80	627	5	is	be	AUX
ma-80	627	6	a	a	DET
ma-80	627	7	sequence	sequence	NOUN
ma-80	627	8	of	of	ADP
ma-80	627	9	increasingly	increasingly	ADV
ma-80	627	10	accurate	accurate	ADJ
ma-80	627	11	upper	upper	ADJ
ma-80	627	12	bounds	bound	NOUN
ma-80	627	13	for	for	ADP
ma-80	627	14	.	.	PUNCT
ma-80	628	1	for	for	ADP
ma-80	628	2	example	example	NOUN
ma-80	628	3	:	:	PUNCT
ma-80	628	4	(	(	PUNCT
ma-80	628	5	95	95	NUM
ma-80	628	6	)	)	PUNCT
ma-80	628	7	with	with	ADP
ma-80	628	8	relative	relative	ADJ
ma-80	628	9	error	error	NOUN
ma-80	628	10	bounds	bound	NOUN
ma-80	628	11	for	for	ADP
ma-80	628	12	the	the	DET
ma-80	628	13	interval	interval	NOUN
ma-80	628	14	of	of	ADP
ma-80	628	15	,	,	PUNCT
ma-80	628	16	respectively	respectively	ADV
ma-80	628	17	and	and	CCONJ
ma-80	628	18	(	(	PUNCT
ma-80	628	19	see	see	VERB
ma-80	628	20	table	table	NOUN
ma-80	628	21	1	1	NUM
ma-80	628	22	)	)	PUNCT
ma-80	628	23	.	.	PUNCT
ma-80	629	1	higher	high	ADJ
ma-80	629	2	order	order	NOUN
ma-80	629	3	approximations	approximation	NOUN
ma-80	629	4	lead	lead	VERB
ma-80	629	5	to	to	ADP
ma-80	629	6	lower	low	ADJ
ma-80	629	7	relative	relative	ADJ
ma-80	629	8	bounds	bound	NOUN
ma-80	629	9	and	and	CCONJ
ma-80	629	10	these	these	PRON
ma-80	629	11	can	can	AUX
ma-80	629	12	be	be	AUX
ma-80	629	13	made	make	VERB
ma-80	629	14	arbitrarily	arbitrarily	ADV
ma-80	629	15	small	small	ADJ
ma-80	629	16	.	.	PUNCT
ma-80	630	1	the	the	DET
ma-80	630	2	relative	relative	ADJ
ma-80	630	3	error	error	NOUN
ma-80	630	4	bounds	bound	NOUN
ma-80	630	5	associated	associate	VERB
ma-80	630	6	with	with	ADP
ma-80	630	7	over	over	ADP
ma-80	630	8	the	the	DET
ma-80	630	9	interval	interval	NOUN
ma-80	630	10	are	be	AUX
ma-80	630	11	,	,	PUNCT
ma-80	630	12	respectively	respectively	ADV
ma-80	630	13	,	,	PUNCT
ma-80	630	14	and	and	CCONJ
ma-80	630	15	.	.	PUNCT
ma-80	631	1	the	the	DET
ma-80	631	2	relative	relative	ADJ
ma-80	631	3	error	error	NOUN
ma-80	631	4	bounds	bound	NOUN
ma-80	631	5	associated	associate	VERB
ma-80	631	6	with	with	ADP
ma-80	631	7	over	over	ADP
ma-80	631	8	the	the	DET
ma-80	631	9	interval	interval	NOUN
ma-80	631	10	are	be	AUX
ma-80	631	11	,	,	PUNCT
ma-80	631	12	respectively	respectively	ADV
ma-80	631	13	,	,	PUNCT
ma-80	631	14	and	and	CCONJ
ma-80	631	15	.	.	PUNCT
ma-80	632	1	one	one	NUM
ma-80	632	2	potential	potential	ADJ
ma-80	632	3	application	application	NOUN
ma-80	632	4	for	for	ADP
ma-80	632	5	the	the	DET
ma-80	632	6	upper	upper	ADJ
ma-80	632	7	bound	bind	VERB
ma-80	632	8	is	be	AUX
ma-80	632	9	a	a	DET
ma-80	632	10	bound	bind	VERB
ma-80	632	11	for	for	ADP
ma-80	632	12	the	the	DET
ma-80	632	13	prime	prime	ADJ
ma-80	632	14	counting	counting	NOUN
ma-80	632	15	function	function	NOUN
ma-80	632	16	,	,	PUNCT
ma-80	633	1	e.g.	e.g.	ADV
ma-80	633	2	[	[	X
ma-80	633	3	27	27	NUM
ma-80	633	4	]	]	PUNCT
ma-80	633	5	.	.	PUNCT
ma-80	634	1	7.3	7.3	NUM
ma-80	634	2	.	.	PUNCT
ma-80	635	1	spline	spline	NOUN
ma-80	635	2	approximations	approximation	NOUN
ma-80	635	3	based	base	VERB
ma-80	635	4	on	on	ADP
ma-80	635	5	upper	upper	ADJ
ma-80	635	6	/	/	SYM
ma-80	635	7	lower	low	ADJ
ma-80	635	8	bounds	bound	NOUN
ma-80	635	9	.	.	PUNCT
ma-80	636	1	consider	consider	VERB
ma-80	636	2	the	the	DET
ma-80	636	3	upper	upper	ADJ
ma-80	636	4	,	,	PUNCT
ma-80	636	5	,	,	PUNCT
ma-80	636	6	and	and	CCONJ
ma-80	636	7	lower	low	ADJ
ma-80	636	8	,	,	PUNCT
ma-80	636	9	,	,	PUNCT
ma-80	636	10	bounded	bound	VERB
ma-80	636	11	functions	function	NOUN
ma-80	636	12	for	for	ADP
ma-80	636	13	the	the	DET
ma-80	636	14	lambert	lambert	PROPN
ma-80	636	15	w	w	PROPN
ma-80	636	16	function	function	PROPN
ma-80	636	17	as	as	SCONJ
ma-80	636	18	illustrated	illustrate	VERB
ma-80	636	19	in	in	ADP
ma-80	636	20	figure	figure	NOUN
ma-80	636	21	23	23	NUM
ma-80	636	22	and	and	CCONJ
ma-80	636	23	as	as	SCONJ
ma-80	636	24	defined	define	VERB
ma-80	636	25	in	in	ADP
ma-80	636	26	theorem	theorem	NOUN
ma-80	636	27	3.1	3.1	NUM
ma-80	636	28	.	.	PUNCT
ma-80	637	1	for	for	ADP
ma-80	637	2	fixed	fix	VERB
ma-80	637	3	at	at	ADP
ma-80	637	4	,	,	PUNCT
ma-80	637	5	a	a	DET
ma-80	637	6	spline	spline	NOUN
ma-80	637	7	approximation	approximation	NOUN
ma-80	637	8	,	,	PUNCT
ma-80	637	9	as	as	SCONJ
ma-80	637	10	specified	specify	VERB
ma-80	637	11	by	by	ADP
ma-80	637	12	equation	equation	NOUN
ma-80	637	13	70	70	NUM
ma-80	637	14	and	and	CCONJ
ma-80	637	15	based	base	VERB
ma-80	637	16	on	on	ADP
ma-80	637	17	the	the	DET
ma-80	637	18	points	point	NOUN
ma-80	637	19	,	,	PUNCT
ma-80	637	20	and	and	CCONJ
ma-80	637	21	,	,	PUNCT
ma-80	637	22	,	,	PUNCT
ma-80	637	23	can	can	AUX
ma-80	637	24	readily	readily	ADV
ma-80	637	25	be	be	AUX
ma-80	637	26	determined	determine	VERB
ma-80	637	27	.	.	PUNCT
ma-80	638	1	from	from	ADP
ma-80	638	2	such	such	DET
ma-80	638	3	an	an	DET
ma-80	638	4	approximation	approximation	NOUN
ma-80	638	5	,	,	PUNCT
ma-80	638	6	an	an	DET
ma-80	638	7	approximation	approximation	NOUN
ma-80	638	8	to	to	PART
ma-80	638	9	can	can	AUX
ma-80	638	10	then	then	ADV
ma-80	638	11	be	be	AUX
ma-80	638	12	specified	specify	VERB
ma-80	638	13	.	.	PUNCT
ma-80	639	1	theorem	theorem	VERB
ma-80	639	2	7.1	7.1	NUM
ma-80	639	3	.	.	PUNCT
ma-80	640	1	spline	spline	NOUN
ma-80	640	2	approximations	approximation	NOUN
ma-80	640	3	based	base	VERB
ma-80	640	4	on	on	ADP
ma-80	640	5	upper	upper	ADJ
ma-80	640	6	/	/	SYM
ma-80	640	7	lower	low	ADJ
ma-80	640	8	bounds	bound	NOUN
ma-80	640	9	.	.	PUNCT
ma-80	641	1	consider	consider	VERB
ma-80	641	2	the	the	DET
ma-80	641	3	lower	low	ADJ
ma-80	641	4	and	and	CCONJ
ma-80	641	5	upper	upper	ADJ
ma-80	641	6	bounded	bounded	ADJ
ma-80	641	7	approximations	approximation	NOUN
ma-80	641	8	,	,	PUNCT
ma-80	641	9	and	and	CCONJ
ma-80	641	10	,	,	PUNCT
ma-80	641	11	defined	define	VERB
ma-80	641	12	in	in	ADP
ma-80	641	13	theorem	theorem	NOUN
ma-80	641	14	3.1	3.1	NUM
ma-80	641	15	.	.	PUNCT
ma-80	642	1	the	the	DET
ma-80	642	2	zero	zero	NUM
ma-80	642	3	y	y	PROPN
ma-80	642	4	e	e	PROPN
ma-80	642	5	y	y	PROPN
ma-80	642	6	y	y	PROPN
ma-80	642	7	ln	ln	PROPN
ma-80	642	8	-------------ln	-------------ln	INTJ
ma-80	643	1	y	y	PROPN
ma-80	643	2	y	y	PROPN
ma-80	643	3	ln	ln	PROPN
ma-80	643	4	-------------ln	-------------ln	NOUN
ma-80	644	1	1	1	NUM
ma-80	644	2	y	y	NOUN
ma-80	644	3	y	y	NOUN
ma-80	644	4	ln	ln	PROPN
ma-80	644	5	-------------ln+	-------------ln+	PUNCT
ma-80	644	6	---------------------------------	---------------------------------	PUNCT
ma-80	644	7	–	–	PUNCT
ma-80	644	8	1	1	NUM
ma-80	644	9	y	y	NOUN
ma-80	644	10	ln	ln	NOUN
ma-80	644	11	ln	ln	VERB
ma-80	644	12	y	y	NOUN
ma-80	644	13	ln	ln	PROPN
ma-80	645	1	-----------------------–ln	-----------------------–ln	PROPN
ma-80	645	2	w	w	ADP
ma-80	645	3	y	y	PROPN
ma-80	645	4			NOUN
ma-80	645	5			PROPN
ma-80	646	1	y	y	PROPN
ma-80	646	2	y	y	PROPN
ma-80	646	3	ln	ln	PROPN
ma-80	646	4	-------------ln	-------------ln	NOUN
ma-80	646	5	1	1	NUM
ma-80	646	6	y	y	NOUN
ma-80	646	7	ln	ln	NOUN
ma-80	646	8	ln	ln	NOUN
ma-80	646	9	y	y	PROPN
ma-80	646	10	ln	ln	PROPN
ma-80	646	11	-----------------------	-----------------------	PROPN
ma-80	646	12	–	–	PUNCT
ma-80	646	13	1	1	NUM
ma-80	646	14	1	1	NUM
ma-80	646	15	y	y	NOUN
ma-80	646	16	ln	ln	NOUN
ma-80	646	17	ln	ln	VERB
ma-80	646	18	y	y	NOUN
ma-80	646	19	ln	ln	PROPN
ma-80	647	1	-----------------------–ln	-----------------------–ln	ADP
ma-80	647	2	1	1	NUM
ma-80	647	3	y	y	NOUN
ma-80	647	4	y	y	NOUN
ma-80	648	1	ln	ln	PROPN
ma-80	648	2	-------------ln+	-------------ln+	X
ma-80	648	3	-------------------------------------------–	-------------------------------------------–	PROPN
ma-80	648	4	.ln	.ln	PROPN
ma-80	648	5	–	–	PUNCT
ma-80	648	6	e	e	NOUN
ma-80	648	7			VERB
ma-80	649	1	5.96	5.96	NUM
ma-80	649	2	10	10	NUM
ma-80	649	3	3–	3–	NUM
ma-80	649	4	4.10	4.10	NUM
ma-80	649	5	10	10	NUM
ma-80	649	6	3–	3–	NUM
ma-80	649	7	y	y	NOUN
ma-80	649	8	10	10	NUM
ma-80	649	9	»	»	NOUN
ma-80	649	10	wli	wli	NOUN
ma-80	649	11	y	y	NOUN
ma-80	649	12			PUNCT
ma-80	650	1	i	i	NOUN
ma-80	650	2	1	1	NUM
ma-80	650	3	2	2	NUM
ma-80	650	4			NOUN
ma-80	650	5			X
ma-80	650	6			NUM
ma-80	650	7	w	w	NOUN
ma-80	650	8	y	y	NOUN
ma-80	650	9			PROPN
ma-80	650	10	wui	wui	NOUN
ma-80	650	11	y	y	NOUN
ma-80	651	1			PUNCT
ma-80	651	2	i	i	NOUN
ma-80	651	3	1	1	NUM
ma-80	651	4	2	2	NUM
ma-80	651	5			NOUN
ma-80	651	6			X
ma-80	652	1			VERB
ma-80	652	2	w	w	NOUN
ma-80	652	3	y	y	NOUN
ma-80	652	4			NOUN
ma-80	652	5	wl3	wl3	NOUN
ma-80	652	6	y	y	NOUN
ma-80	652	7			PUNCT
ma-80	652	8	y	y	NOUN
ma-80	652	9	1	1	NUM
ma-80	652	10	1	1	NUM
ma-80	652	11	y+	y+	NOUN
ma-80	652	12	ln+	ln+	PUNCT
ma-80	652	13			NOUN
ma-80	652	14	1	1	NUM
ma-80	652	15	1	1	NUM
ma-80	652	16	2y+	2y+	NUM
ma-80	652	17	1	1	NUM
ma-80	652	18	1	1	NUM
ma-80	652	19	y+	y+	NOUN
ma-80	652	20	ln+	ln+	NOUN
ma-80	652	21	-------------------------------ln+	-------------------------------ln+	PROPN
ma-80	652	22	1	1	NUM
ma-80	652	23	3y	3y	NUM
ma-80	652	24	y	y	PROPN
ma-80	652	25	1	1	NUM
ma-80	652	26	y+	y+	NOUN
ma-80	652	27	ln+	ln+	PROPN
ma-80	653	1	+	+	CCONJ
ma-80	653	2	--------------------------------------------------------------------------------------------------=	--------------------------------------------------------------------------------------------------=	PUNCT
ma-80	653	3	w	w	PRON
ma-80	653	4	y	y	NOUN
ma-80	653	5			NOUN
ma-80	653	6			PROPN
ma-80	653	7	wu3	wu3	VERB
ma-80	653	8	y	y	NOUN
ma-80	653	9			PROPN
ma-80	653	10	1	1	NUM
ma-80	653	11	3y	3y	NUM
ma-80	653	12	y	y	PROPN
ma-80	653	13	1	1	NUM
ma-80	653	14	y+	y+	NOUN
ma-80	653	15	ln+	ln+	PROPN
ma-80	654	1	+	+	CCONJ
ma-80	654	2	1	1	NUM
ma-80	654	3	1	1	NUM
ma-80	654	4	y+	y+	NOUN
ma-80	654	5	ln+	ln+	PUNCT
ma-80	654	6			NOUN
ma-80	654	7	1	1	NUM
ma-80	654	8	1	1	NUM
ma-80	654	9	2y+	2y+	NUM
ma-80	654	10	1	1	NUM
ma-80	654	11	1	1	NUM
ma-80	654	12	y+	y+	NOUN
ma-80	654	13	ln+	ln+	NOUN
ma-80	654	14	-------------------------------ln+	-------------------------------ln+	PUNCT
ma-80	654	15	----------------------------------------------------------------------------------------------ln=	----------------------------------------------------------------------------------------------ln=	NOUN
ma-80	654	16	y	y	PROPN
ma-80	654	17	0	0	NUM
ma-80	654	18			NUM
ma-80	654	19	0	0	NUM
ma-80	654	20			VERB
ma-80	655	1	8.32	8.32	NUM
ma-80	655	2	10	10	NUM
ma-80	655	3	3–	3–	NUM
ma-80	655	4	1.33	1.33	NUM
ma-80	655	5	10	10	NUM
ma-80	655	6	3–	3–	NUM
ma-80	655	7	wl4	wl4	ADJ
ma-80	655	8	y	y	NOUN
ma-80	655	9			PROPN
ma-80	655	10	w	w	NOUN
ma-80	655	11	y	y	NOUN
ma-80	655	12			PROPN
ma-80	655	13	wu4	wu4	NOUN
ma-80	655	14	y	y	NOUN
ma-80	655	15			VERB
ma-80	655	16			PROPN
ma-80	655	17	0	0	NUM
ma-80	655	18			PUNCT
ma-80	656	1	3.88	3.88	NUM
ma-80	656	2	10	10	NUM
ma-80	656	3	6–	6–	PROPN
ma-80	656	4	7.23	7.23	NUM
ma-80	656	5	10	10	NUM
ma-80	657	1	7–	7–	NOUN
ma-80	657	2	wl5	wl5	NOUN
ma-80	657	3	y	y	NOUN
ma-80	657	4			PROPN
ma-80	657	5	w	w	NOUN
ma-80	657	6	y	y	NOUN
ma-80	657	7			PROPN
ma-80	657	8	wu5	wu5	ADP
ma-80	657	9	y	y	PROPN
ma-80	657	10			NOUN
ma-80	657	11			PROPN
ma-80	657	12	0	0	NUM
ma-80	657	13			PUNCT
ma-80	657	14	1.08	1.08	NUM
ma-80	657	15	10	10	NUM
ma-80	657	16	12–	12–	NUM
ma-80	657	17	2.15	2.15	NUM
ma-80	657	18	10	10	NUM
ma-80	657	19	13–	13–	NUM
ma-80	657	20	ith	ith	PROPN
ma-80	657	21	wui	wui	PROPN
ma-80	658	1	wli	wli	PROPN
ma-80	658	2	y	y	PROPN
ma-80	658	3	yo	yo	PROPN
ma-80	658	4	uo	uo	INTJ
ma-80	658	5	uo	uo	VERB
ma-80	659	1	exp	exp	PROPN
ma-80	660	1	uo	uo	PROPN
ma-80	660	2			PROPN
ma-80	660	3	uo	uo	NOUN
ma-80	660	4	wli	wli	PROPN
ma-80	660	5	yo	yo	PROPN
ma-80	660	6	=	=	PROPN
ma-80	660	7	vo	vo	PROPN
ma-80	660	8	vo	vo	PROPN
ma-80	660	9	exp	exp	PROPN
ma-80	660	10	vo	vo	PROPN
ma-80	660	11			PROPN
ma-80	660	12	vo	vo	X
ma-80	660	13	wui	wui	PROPN
ma-80	660	14	yo	yo	PROPN
ma-80	660	15	=	=	PROPN
ma-80	660	16	xo	xo	PROPN
ma-80	660	17	w	w	PROPN
ma-80	660	18	yo	yo	PROPN
ma-80	660	19	=	=	PROPN
ma-80	660	20	ith	ith	PROPN
ma-80	660	21	wli	wli	PROPN
ma-80	660	22	wui	wui	PROPN
ma-80	660	23	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	PROPN
ma-80	660	24	order	order	NOUN
ma-80	660	25	spline	spline	NOUN
ma-80	660	26	approximation	approximation	NOUN
ma-80	660	27	for	for	ADP
ma-80	660	28	the	the	DET
ma-80	660	29	lambert	lambert	PROPN
ma-80	660	30	w	w	PROPN
ma-80	660	31	function	function	PROPN
ma-80	660	32	,	,	PUNCT
ma-80	660	33	based	base	VERB
ma-80	660	34	on	on	ADP
ma-80	660	35	the	the	DET
ma-80	660	36	approximations	approximation	NOUN
ma-80	660	37	and	and	CCONJ
ma-80	660	38	,	,	PUNCT
ma-80	660	39	is	be	AUX
ma-80	660	40	(	(	PUNCT
ma-80	660	41	96	96	NUM
ma-80	660	42	)	)	PUNCT
ma-80	660	43	the	the	DET
ma-80	660	44	order	order	NOUN
ma-80	660	45	spline	spline	NOUN
ma-80	660	46	approximation	approximation	NOUN
ma-80	660	47	for	for	ADP
ma-80	660	48	the	the	DET
ma-80	660	49	lambert	lambert	PROPN
ma-80	660	50	w	w	PROPN
ma-80	660	51	function	function	PROPN
ma-80	660	52	,	,	PUNCT
ma-80	660	53	based	base	VERB
ma-80	660	54	on	on	ADP
ma-80	660	55	the	the	DET
ma-80	660	56	approximations	approximation	NOUN
ma-80	660	57	and	and	CCONJ
ma-80	660	58	,	,	PUNCT
ma-80	660	59	is	be	AUX
ma-80	660	60	(	(	PUNCT
ma-80	660	61	97	97	NUM
ma-80	660	62	)	)	PUNCT
ma-80	660	63	where	where	SCONJ
ma-80	660	64	,	,	PUNCT
ma-80	660	65	and	and	CCONJ
ma-80	660	66	is	be	AUX
ma-80	660	67	defined	define	VERB
ma-80	660	68	by	by	ADP
ma-80	660	69	equation	equation	NOUN
ma-80	660	70	120	120	NUM
ma-80	660	71	.	.	PUNCT
ma-80	661	1	proof	proof	NOUN
ma-80	661	2	.	.	PUNCT
ma-80	662	1	the	the	DET
ma-80	662	2	proof	proof	NOUN
ma-80	662	3	is	be	AUX
ma-80	662	4	detailed	detail	VERB
ma-80	662	5	in	in	ADP
ma-80	662	6	appendix	appendix	ADJ
ma-80	662	7	h.	h.	PROPN
ma-80	663	1	7.3.1	7.3.1	PROPN
ma-80	663	2	.	.	PUNCT
ma-80	663	3	results	result	NOUN
ma-80	663	4	.	.	PUNCT
ma-80	664	1	results	result	NOUN
ma-80	664	2	are	be	AUX
ma-80	664	3	detailed	detail	VERB
ma-80	664	4	in	in	ADP
ma-80	664	5	table	table	NOUN
ma-80	664	6	7	7	NUM
ma-80	664	7	and	and	CCONJ
ma-80	664	8	clearly	clearly	ADV
ma-80	664	9	show	show	VERB
ma-80	664	10	the	the	DET
ma-80	664	11	high	high	ADJ
ma-80	664	12	accuracy	accuracy	NOUN
ma-80	664	13	of	of	ADP
ma-80	664	14	the	the	DET
ma-80	664	15	approximations	approximation	NOUN
ma-80	664	16	.	.	PUNCT
ma-80	665	1	for	for	ADP
ma-80	665	2	example	example	NOUN
ma-80	665	3	,	,	PUNCT
ma-80	665	4	the	the	DET
ma-80	665	5	zero	zero	NUM
ma-80	665	6	order	order	NOUN
ma-80	665	7	spline	spline	NOUN
ma-80	665	8	approximations	approximation	NOUN
ma-80	665	9	,	,	PUNCT
ma-80	665	10	as	as	SCONJ
ma-80	665	11	specified	specify	VERB
ma-80	665	12	by	by	ADP
ma-80	665	13	equation	equation	NOUN
ma-80	665	14	96	96	NUM
ma-80	665	15	,	,	PUNCT
ma-80	665	16	yields	yield	NOUN
ma-80	665	17	relative	relative	ADJ
ma-80	665	18	error	error	NOUN
ma-80	665	19	bounds	bound	NOUN
ma-80	665	20	,	,	PUNCT
ma-80	665	21	for	for	ADP
ma-80	665	22	the	the	DET
ma-80	665	23	interval	interval	NOUN
ma-80	665	24	,	,	PUNCT
ma-80	665	25	of	of	ADP
ma-80	665	26	,	,	PUNCT
ma-80	665	27	and	and	CCONJ
ma-80	665	28	,	,	PUNCT
ma-80	665	29	respectively	respectively	ADV
ma-80	665	30	,	,	PUNCT
ma-80	665	31	based	base	VERB
ma-80	665	32	on	on	ADP
ma-80	665	33	third	third	ADJ
ma-80	665	34	,	,	PUNCT
ma-80	665	35	fourth	fourth	ADJ
ma-80	665	36	and	and	CCONJ
ma-80	665	37	fifth	fifth	ADJ
ma-80	665	38	order	order	NOUN
ma-80	665	39	approximations	approximation	NOUN
ma-80	665	40	for	for	ADP
ma-80	665	41	the	the	DET
ma-80	665	42	figure	figure	NOUN
ma-80	665	43	23	23	NUM
ma-80	665	44	.	.	PUNCT
ma-80	666	1	illustration	illustration	NOUN
ma-80	666	2	of	of	ADP
ma-80	666	3	upper	upper	ADJ
ma-80	666	4	and	and	CCONJ
ma-80	666	5	lower	low	ADJ
ma-80	666	6	bounded	bounded	ADJ
ma-80	666	7	approximations	approximation	NOUN
ma-80	666	8	to	to	ADP
ma-80	666	9	the	the	DET
ma-80	666	10	lambert	lambert	PROPN
ma-80	666	11	w	w	PROPN
ma-80	666	12	function	function	PROPN
ma-80	666	13	and	and	CCONJ
ma-80	666	14	the	the	DET
ma-80	666	15	points	point	NOUN
ma-80	666	16	,	,	PUNCT
ma-80	666	17	,	,	PUNCT
ma-80	666	18	which	which	PRON
ma-80	666	19	are	be	AUX
ma-80	666	20	the	the	DET
ma-80	666	21	basis	basis	NOUN
ma-80	666	22	for	for	ADP
ma-80	666	23	spline	spline	NOUN
ma-80	666	24	based	base	VERB
ma-80	666	25	approximations	approximation	NOUN
ma-80	666	26	.	.	PUNCT
ma-80	667	1	uo	uo	PROPN
ma-80	667	2	uo	uo	NOUN
ma-80	668	1	exp	exp	PROPN
ma-80	668	2	uo	uo	PROPN
ma-80	668	3			PROPN
ma-80	668	4	vo	vo	NOUN
ma-80	668	5	vo	vo	PROPN
ma-80	668	6	exp	exp	PROPN
ma-80	669	1	vo	vo	PROPN
ma-80	669	2			PROPN
ma-80	669	3	uo	uo	NOUN
ma-80	669	4	uo	uo	NOUN
ma-80	670	1	exp	exp	PROPN
ma-80	671	1	uo	uo	PROPN
ma-80	671	2	wli	wli	PROPN
ma-80	671	3	yo	yo	PROPN
ma-80	671	4	=	=	PROPN
ma-80	671	5	y	y	PROPN
ma-80	671	6	xo	xo	PROPN
ma-80	671	7	w	w	PROPN
ma-80	671	8	yo	yo	PROPN
ma-80	671	9	=	=	PROPN
ma-80	671	10	wli	wli	PROPN
ma-80	671	11	y	y	PROPN
ma-80	671	12			PROPN
ma-80	672	1	w	w	NOUN
ma-80	672	2	y	y	NOUN
ma-80	672	3			PROPN
ma-80	672	4	x	x	SYM
ma-80	672	5	spline	spline	PROPN
ma-80	672	6	approx	approx	PROPN
ma-80	672	7	.	.	PUNCT
ma-80	673	1	based	base	VERB
ma-80	673	2	on	on	ADP
ma-80	673	3	wui	wui	PROPN
ma-80	673	4	y	y	PROPN
ma-80	673	5			PROPN
ma-80	673	6	vo	vo	X
ma-80	673	7	wui	wui	PROPN
ma-80	673	8	yo	yo	PROPN
ma-80	673	9	=	=	PROPN
ma-80	673	10	vo	vo	PROPN
ma-80	673	11	vo	vo	PROPN
ma-80	673	12	expyo	expyo	PROPN
ma-80	673	13	ith	ith	PROPN
ma-80	673	14	wli	wli	PROPN
ma-80	673	15	wui	wui	PROPN
ma-80	673	16	w0	w0	PROPN
ma-80	673	17	i	i	X
ma-80	673	18	y	y	PROPN
ma-80	673	19			PROPN
ma-80	673	20	wli	wli	NOUN
ma-80	673	21	y	y	NOUN
ma-80	673	22	wui	wui	NOUN
ma-80	673	23	y	y	NOUN
ma-80	673	24			PROPN
ma-80	673	25	wui	wui	X
ma-80	673	26	y	y	NOUN
ma-80	673	27			PROPN
ma-80	673	28	exp	exp	VERB
ma-80	673	29	wli	wli	PROPN
ma-80	673	30	y	y	NOUN
ma-80	673	31			NOUN
ma-80	673	32	exp–	exp–	VERB
ma-80	673	33	y	y	PROPN
ma-80	673	34	wui	wui	X
ma-80	673	35	y	y	PROPN
ma-80	674	1			PROPN
ma-80	674	2	wli	wli	NOUN
ma-80	674	3	y	y	PROPN
ma-80	674	4	–	–	PROPN
ma-80	674	5	+	+	NOUN
ma-80	674	6	wui	wui	ADJ
ma-80	674	7	y	y	NOUN
ma-80	674	8			PROPN
ma-80	674	9	wui	wui	X
ma-80	674	10	y	y	NOUN
ma-80	674	11			ADJ
ma-80	674	12	exp	exp	VERB
ma-80	674	13	wli	wli	PROPN
ma-80	674	14	y	y	PROPN
ma-80	674	15			PROPN
ma-80	674	16	wli	wli	NOUN
ma-80	674	17	y	y	NOUN
ma-80	674	18			X
ma-80	674	19	exp	exp	PROPN
ma-80	674	20	–	–	PUNCT
ma-80	674	21	-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------.=	-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------.=	PUNCT
ma-80	675	1	nth	nth	PROPN
ma-80	675	2	ith	ith	PROPN
ma-80	675	3	wli	wli	PROPN
ma-80	675	4	wui	wui	PROPN
ma-80	675	5	wn	wn	PROPN
ma-80	675	6	i	i	X
ma-80	675	7	y	y	PROPN
ma-80	675	8			PROPN
ma-80	675	9	vo	vo	NOUN
ma-80	675	10	vo	vo	PROPN
ma-80	675	11	exp	exp	PROPN
ma-80	675	12	y–	y–	PROPN
ma-80	675	13	n	n	PROPN
ma-80	675	14	1	1	NUM
ma-80	675	15	+	+	NUM
ma-80	675	16	vo	vo	NOUN
ma-80	675	17	vo	vo	NOUN
ma-80	675	18	exp	exp	PROPN
ma-80	675	19	uo	uo	PROPN
ma-80	675	20	uo	uo	PROPN
ma-80	675	21	exp–	exp–	PROPN
ma-80	675	22	n	n	PROPN
ma-80	675	23	1	1	NUM
ma-80	675	24	+	+	CCONJ
ma-80	675	25	-----------------------------------------------------------------------=	-----------------------------------------------------------------------=	PROPN
ma-80	675	26	y	y	PROPN
ma-80	675	27	uo	uo	PROPN
ma-80	675	28	uo	uo	PROPN
ma-80	675	29	exp–	exp–	PROPN
ma-80	675	30	r	r	PROPN
ma-80	675	31	n	n	CCONJ
ma-80	675	32	r+	r+	NOUN
ma-80	675	33	!uo	!uo	PROPN
ma-80	676	1	r!n	r!n	PROPN
ma-80	676	2	!	!	PROPN
ma-80	676	3	vo	vo	PROPN
ma-80	676	4	vo	vo	PROPN
ma-80	676	5	exp	exp	PROPN
ma-80	676	6	uo	uo	PROPN
ma-80	676	7	uo	uo	PROPN
ma-80	676	8	exp–	exp–	PROPN
ma-80	677	1	r	r	PROPN
ma-80	677	2	-------------------------------------------------------------------------+	-------------------------------------------------------------------------+	PROPN
ma-80	677	3	pr	pr	PROPN
ma-80	677	4	u	u	PROPN
ma-80	677	5	–	–	PUNCT
ma-80	677	6	uo	uo	NOUN
ma-80	677	7	e	e	X
ma-80	678	1	r	r	NOUN
ma-80	678	2	u–	u–	NOUN
ma-80	678	3	uo	uo	PROPN
ma-80	678	4	–	–	PUNCT
ma-80	678	5	r	r	NOUN
ma-80	678	6	u–	u–	NOUN
ma-80	678	7			PROPN
ma-80	678	8	!	!	NOUN
ma-80	678	9	1	1	NUM
ma-80	678	10	uo+	uo+	PROPN
ma-80	678	11	2	2	NOUN
ma-80	678	12	r	r	NOUN
ma-80	678	13	u–	u–	NOUN
ma-80	678	14			PROPN
ma-80	678	15	1	1	NUM
ma-80	678	16	–	–	PUNCT
ma-80	678	17	------------------------------------------------------------n	------------------------------------------------------------n	X
ma-80	679	1	u+	u+	ADJ
ma-80	679	2			PROPN
ma-80	679	3	!	!	PUNCT
ma-80	680	1	u!n	u!n	PROPN
ma-80	680	2	!	!	PUNCT
ma-80	680	3	-------------------	-------------------	PROPN
ma-80	680	4	u	u	NOUN
ma-80	681	1	0=	0=	NOUN
ma-80	681	2	r	r	NOUN
ma-80	681	3	1	1	NUM
ma-80	681	4	–	–	PUNCT
ma-80	681	5			X
ma-80	681	6	1	1	NUM
ma-80	681	7	vo	vo	NOUN
ma-80	681	8	vo	vo	PROPN
ma-80	681	9	exp	exp	PROPN
ma-80	681	10	uo	uo	PROPN
ma-80	681	11	uo	uo	PROPN
ma-80	681	12	exp–	exp–	PROPN
ma-80	682	1	u	u	PROPN
ma-80	682	2	-----------------------------------------------------------------	-----------------------------------------------------------------	PUNCT
ma-80	682	3			ADJ
ma-80	682	4	r	r	NOUN
ma-80	682	5	0=	0=	NOUN
ma-80	683	1	n	n	NOUN
ma-80	683	2			X
ma-80	684	1	+	+	CCONJ
ma-80	684	2	y	y	PROPN
ma-80	684	3	uo	uo	PROPN
ma-80	684	4	uo	uo	PROPN
ma-80	684	5	exp–	exp–	PROPN
ma-80	684	6	n	n	PROPN
ma-80	684	7	1	1	NUM
ma-80	684	8	+	+	NUM
ma-80	684	9	vo	vo	NOUN
ma-80	684	10	vo	vo	NOUN
ma-80	684	11	exp	exp	PROPN
ma-80	684	12	uo	uo	PROPN
ma-80	684	13	uo	uo	PROPN
ma-80	684	14	exp–	exp–	PROPN
ma-80	684	15	n	n	PROPN
ma-80	684	16	1	1	NUM
ma-80	684	17	+	+	NUM
ma-80	684	18	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PROPN
ma-80	684	19	vo	vo	NOUN
ma-80	684	20	vo	vo	PROPN
ma-80	684	21	exp	exp	PROPN
ma-80	684	22	y–	y–	PROPN
ma-80	684	23	r	r	PROPN
ma-80	684	24	n	n	PROPN
ma-80	684	25	r+	r+	VERB
ma-80	684	26	!vo	!vo	PROPN
ma-80	684	27	r!n	r!n	PROPN
ma-80	684	28	!	!	PROPN
ma-80	684	29	vo	vo	PROPN
ma-80	684	30	vo	vo	PROPN
ma-80	684	31	exp	exp	PROPN
ma-80	684	32	uo	uo	PROPN
ma-80	684	33	uo	uo	PROPN
ma-80	684	34	exp–	exp–	PROPN
ma-80	684	35	r	r	PROPN
ma-80	684	36	-------------------------------------------------------------------------+	-------------------------------------------------------------------------+	NUM
ma-80	684	37	1–	1–	NUM
ma-80	684	38	r	r	DET
ma-80	684	39	u	u	NOUN
ma-80	684	40	–	–	PUNCT
ma-80	684	41	pr	pr	NOUN
ma-80	684	42	u	u	NOUN
ma-80	684	43	–	–	PUNCT
ma-80	684	44	vo	vo	NOUN
ma-80	684	45	e	e	PROPN
ma-80	684	46	r	r	NOUN
ma-80	684	47	u–	u–	NOUN
ma-80	684	48	vo	vo	PUNCT
ma-80	684	49	–	–	PUNCT
ma-80	684	50	r	r	NOUN
ma-80	684	51	u–	u–	NOUN
ma-80	684	52			PROPN
ma-80	684	53	!	!	NOUN
ma-80	684	54	1	1	NUM
ma-80	684	55	vo+	vo+	PROPN
ma-80	684	56	2	2	VERB
ma-80	684	57	r	r	NOUN
ma-80	684	58	u–	u–	NOUN
ma-80	684	59			PROPN
ma-80	684	60	1	1	NUM
ma-80	684	61	–	–	PUNCT
ma-80	684	62	-----------------------------------------------------------------n	-----------------------------------------------------------------n	PUNCT
ma-80	684	63	u+	u+	PROPN
ma-80	684	64			PROPN
ma-80	684	65	!	!	PUNCT
ma-80	685	1	u!n	u!n	PROPN
ma-80	685	2	!	!	PUNCT
ma-80	685	3	-------------------	-------------------	PROPN
ma-80	685	4	u	u	NOUN
ma-80	686	1	0=	0=	NOUN
ma-80	686	2	r	r	NOUN
ma-80	686	3	1	1	NUM
ma-80	686	4	–	–	PUNCT
ma-80	686	5			X
ma-80	686	6	1	1	NUM
ma-80	686	7	vo	vo	NOUN
ma-80	686	8	vo	vo	PROPN
ma-80	686	9	exp	exp	PROPN
ma-80	686	10	uo	uo	PROPN
ma-80	686	11	uo	uo	PROPN
ma-80	686	12	exp–	exp–	PROPN
ma-80	687	1	u	u	PROPN
ma-80	687	2	-----------------------------------------------------------------	-----------------------------------------------------------------	PUNCT
ma-80	687	3			ADJ
ma-80	687	4	r	r	NOUN
ma-80	687	5	0=	0=	NOUN
ma-80	688	1	n	n	NOUN
ma-80	688	2			X
ma-80	688	3	uo	uo	NOUN
ma-80	688	4	wli	wli	PROPN
ma-80	688	5	y	y	PROPN
ma-80	688	6	=	=	PROPN
ma-80	688	7	vo	vo	X
ma-80	688	8	wui	wui	PROPN
ma-80	688	9	y	y	PROPN
ma-80	688	10	=	=	NOUN
ma-80	688	11	pk	pk	NOUN
ma-80	688	12	0	0	NUM
ma-80	688	13			NUM
ma-80	688	14			NOUN
ma-80	688	15	3.84	3.84	NUM
ma-80	688	16	10	10	NUM
ma-80	688	17	5–	5–	PROPN
ma-80	688	18	8.56	8.56	NUM
ma-80	688	19	10	10	NUM
ma-80	688	20	12–	12–	NUM
ma-80	688	21	6.80	6.80	NUM
ma-80	688	22	10	10	NUM
ma-80	688	23	25–	25–	NUM
ma-80	688	24	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	PROPN
ma-80	688	25	lambert	lambert	PROPN
ma-80	688	26	w	w	PROPN
ma-80	688	27	function	function	NOUN
ma-80	688	28	detailed	detail	VERB
ma-80	688	29	in	in	ADP
ma-80	688	30	equation	equation	NOUN
ma-80	688	31	3.1	3.1	NUM
ma-80	688	32	such	such	ADJ
ma-80	688	33	convergence	convergence	NOUN
ma-80	688	34	is	be	AUX
ma-80	688	35	approximately	approximately	ADV
ma-80	688	36	quadratic	quadratic	ADJ
ma-80	688	37	.	.	PUNCT
ma-80	689	1	7.3.2	7.3.2	NUM
ma-80	689	2	.	.	PUNCT
ma-80	689	3	application	application	NOUN
ma-80	689	4	.	.	PUNCT
ma-80	690	1	the	the	DET
ma-80	690	2	omega	omega	NOUN
ma-80	690	3	constant	constant	ADJ
ma-80	690	4	,	,	PUNCT
ma-80	690	5	defined	define	VERB
ma-80	690	6	as	as	ADP
ma-80	690	7	,	,	PUNCT
ma-80	690	8	can	can	AUX
ma-80	690	9	be	be	AUX
ma-80	690	10	evaluated	evaluate	VERB
ma-80	690	11	by	by	ADP
ma-80	690	12	using	use	VERB
ma-80	690	13	equation	equation	NOUN
ma-80	690	14	96	96	NUM
ma-80	690	15	with	with	ADP
ma-80	690	16	relative	relative	ADJ
ma-80	690	17	errors	error	NOUN
ma-80	690	18	,	,	PUNCT
ma-80	690	19	respectively	respectively	ADV
ma-80	690	20	,	,	PUNCT
ma-80	690	21	of	of	ADP
ma-80	690	22	,	,	PUNCT
ma-80	690	23	,	,	PUNCT
ma-80	690	24	and	and	CCONJ
ma-80	690	25	for	for	ADP
ma-80	690	26	the	the	DET
ma-80	690	27	case	case	NOUN
ma-80	690	28	of	of	ADP
ma-80	690	29	upper	upper	ADJ
ma-80	690	30	and	and	CCONJ
ma-80	690	31	lower	low	ADJ
ma-80	690	32	bounded	bounded	ADJ
ma-80	690	33	approximations	approximation	NOUN
ma-80	690	34	of	of	ADP
ma-80	690	35	orders	order	NOUN
ma-80	690	36	two	two	NUM
ma-80	690	37	to	to	PART
ma-80	690	38	five	five	NUM
ma-80	690	39	,	,	PUNCT
ma-80	690	40	i.e.	i.e.	X
ma-80	690	41	,	,	PUNCT
ma-80	690	42	,	,	PUNCT
ma-80	690	43	and	and	CCONJ
ma-80	690	44	.	.	PUNCT
ma-80	691	1	7.4	7.4	NUM
ma-80	691	2	.	.	PUNCT
ma-80	692	1	asymptotic	asymptotic	ADJ
ma-80	692	2	approximations	approximation	NOUN
ma-80	692	3	.	.	PUNCT
ma-80	693	1	as	as	SCONJ
ma-80	693	2	is	be	AUX
ma-80	693	3	evident	evident	ADJ
ma-80	693	4	in	in	ADP
ma-80	693	5	the	the	DET
ma-80	693	6	results	result	NOUN
ma-80	693	7	shown	show	VERB
ma-80	693	8	in	in	ADP
ma-80	693	9	figure	figure	NOUN
ma-80	693	10	11	11	NUM
ma-80	693	11	,	,	PUNCT
ma-80	693	12	apart	apart	ADV
ma-80	693	13	from	from	ADP
ma-80	693	14	the	the	DET
ma-80	693	15	results	result	NOUN
ma-80	693	16	for	for	ADP
ma-80	693	17	and	and	CCONJ
ma-80	693	18	,	,	PUNCT
ma-80	693	19	the	the	DET
ma-80	693	20	relative	relative	ADJ
ma-80	693	21	errors	error	NOUN
ma-80	693	22	in	in	ADP
ma-80	693	23	the	the	DET
ma-80	693	24	approximations	approximation	NOUN
ma-80	693	25	defined	define	VERB
ma-80	693	26	in	in	ADP
ma-80	693	27	theorem	theorem	NOUN
ma-80	693	28	3.1	3.1	NUM
ma-80	693	29	,	,	PUNCT
ma-80	693	30	for	for	ADP
ma-80	693	31	a	a	DET
ma-80	693	32	set	set	NOUN
ma-80	693	33	order	order	NOUN
ma-80	693	34	,	,	PUNCT
ma-80	693	35	decrease	decrease	NOUN
ma-80	693	36	as	as	ADP
ma-80	693	37	their	their	PRON
ma-80	693	38	argument	argument	NOUN
ma-80	693	39	increases	increase	VERB
ma-80	693	40	,	,	PUNCT
ma-80	693	41	i.e.	i.e.	X
ma-80	693	42	for	for	ADP
ma-80	693	43	a	a	DET
ma-80	693	44	set	set	NOUN
ma-80	693	45	order	order	NOUN
ma-80	693	46	,	,	PUNCT
ma-80	693	47	the	the	DET
ma-80	693	48	approximations	approximation	NOUN
ma-80	693	49	asymptotically	asymptotically	ADV
ma-80	693	50	approach	approach	VERB
ma-80	693	51	the	the	DET
ma-80	693	52	lambert	lambert	PROPN
ma-80	693	53	w	w	PROPN
ma-80	693	54	function	function	NOUN
ma-80	693	55	as	as	SCONJ
ma-80	693	56	their	their	PRON
ma-80	693	57	arguments	argument	NOUN
ma-80	693	58	become	become	VERB
ma-80	693	59	unbounded	unbounded	ADJ
ma-80	693	60	.	.	PUNCT
ma-80	694	1	thus	thus	ADV
ma-80	694	2	:	:	PUNCT
ma-80	694	3	(	(	PUNCT
ma-80	694	4	98	98	NUM
ma-80	694	5	)	)	PUNCT
ma-80	694	6	7.4.1	7.4.1	NUM
ma-80	694	7	.	.	PUNCT
ma-80	695	1	lambert	lambert	PROPN
ma-80	695	2	w	w	PROPN
ma-80	695	3	function	function	PROPN
ma-80	695	4	and	and	CCONJ
ma-80	695	5	prime	prime	ADJ
ma-80	695	6	counting	counting	NOUN
ma-80	695	7	function	function	NOUN
ma-80	695	8	.	.	PUNCT
ma-80	696	1	the	the	DET
ma-80	696	2	prime	prime	ADJ
ma-80	696	3	number	number	NOUN
ma-80	696	4	theorem	theorem	VERB
ma-80	696	5	states	state	NOUN
ma-80	696	6	that	that	SCONJ
ma-80	696	7	the	the	DET
ma-80	696	8	relative	relative	ADJ
ma-80	696	9	error	error	NOUN
ma-80	696	10	between	between	ADP
ma-80	696	11	the	the	DET
ma-80	696	12	prime	prime	ADJ
ma-80	696	13	counting	counting	NOUN
ma-80	696	14	function	function	NOUN
ma-80	696	15	and	and	CCONJ
ma-80	696	16	decreases	decrease	VERB
ma-80	696	17	to	to	ADP
ma-80	696	18	zero	zero	NUM
ma-80	696	19	as	as	ADP
ma-80	696	20	,	,	PUNCT
ma-80	696	21	i.e.	i.e.	X
ma-80	696	22	(	(	PUNCT
ma-80	696	23	99	99	NUM
ma-80	696	24	)	)	PUNCT
ma-80	696	25	table	table	NOUN
ma-80	696	26	7	7	NUM
ma-80	696	27	.	.	PUNCT
ma-80	696	28	relative	relative	ADJ
ma-80	696	29	error	error	NOUN
ma-80	696	30	bounds	bound	NOUN
ma-80	696	31	,	,	PUNCT
ma-80	696	32	over	over	ADP
ma-80	696	33	the	the	DET
ma-80	696	34	interval	interval	NOUN
ma-80	696	35	,	,	PUNCT
ma-80	696	36	for	for	ADP
ma-80	696	37	spline	spline	NOUN
ma-80	696	38	approximations	approximation	NOUN
ma-80	696	39	to	to	ADP
ma-80	696	40	the	the	DET
ma-80	696	41	lambert	lambert	PROPN
ma-80	696	42	w	w	PROPN
ma-80	696	43	function	function	PROPN
ma-80	696	44	based	base	VERB
ma-80	696	45	on	on	ADP
ma-80	696	46	upper	upper	ADJ
ma-80	696	47	and	and	CCONJ
ma-80	696	48	lower	low	ADJ
ma-80	696	49	bounded	bounded	ADJ
ma-80	696	50	functions	function	NOUN
ma-80	696	51	.	.	PUNCT
ma-80	697	1	upper	upper	ADJ
ma-80	697	2	/	/	SYM
ma-80	697	3	lower	low	ADJ
ma-80	697	4	bounded	bound	VERB
ma-80	697	5	functions	function	NOUN
ma-80	697	6	spline	spline	NOUN
ma-80	697	7	order	order	NOUN
ma-80	697	8	approximation	approximation	NOUN
ma-80	697	9	relative	relative	ADJ
ma-80	697	10	error	error	NOUN
ma-80	697	11	bound	bind	VERB
ma-80	697	12	,	,	PUNCT
ma-80	697	13	1	1	NUM
ma-80	697	14	increasing	increase	VERB
ma-80	697	15	re	re	VERB
ma-80	697	16	as	as	ADP
ma-80	697	17	(	(	PUNCT
ma-80	697	18	equation	equation	NOUN
ma-80	697	19	31	31	NUM
ma-80	697	20	)	)	PUNCT
ma-80	697	21	2	2	NUM
ma-80	697	22	increasing	increase	VERB
ma-80	697	23	re	re	VERB
ma-80	697	24	as	as	ADP
ma-80	697	25	,	,	PUNCT
ma-80	697	26	0	0	NUM
ma-80	697	27	(	(	PUNCT
ma-80	697	28	equation	equation	NOUN
ma-80	697	29	32	32	NUM
ma-80	697	30	,	,	PUNCT
ma-80	697	31	equation	equation	NOUN
ma-80	697	32	33	33	NUM
ma-80	697	33	)	)	PUNCT
ma-80	697	34	1	1	NUM
ma-80	697	35	2	2	NUM
ma-80	697	36	3	3	NUM
ma-80	697	37	4	4	NUM
ma-80	697	38	,	,	PUNCT
ma-80	697	39	0	0	NUM
ma-80	698	1	(	(	PUNCT
ma-80	698	2	equation	equation	NOUN
ma-80	698	3	34	34	NUM
ma-80	698	4	,	,	PUNCT
ma-80	698	5	equation	equation	NOUN
ma-80	698	6	35	35	NUM
ma-80	698	7	)	)	PUNCT
ma-80	698	8	1	1	NUM
ma-80	698	9	2	2	NUM
ma-80	698	10	3	3	NUM
ma-80	698	11	4	4	NUM
ma-80	698	12	,	,	PUNCT
ma-80	698	13	0	0	NUM
ma-80	698	14	(	(	PUNCT
ma-80	698	15	equation	equation	NOUN
ma-80	698	16	36	36	NUM
ma-80	698	17	)	)	PUNCT
ma-80	698	18	1	1	NUM
ma-80	698	19	w	w	NOUN
ma-80	698	20	1	1	NUM
ma-80	698	21			PROPN
ma-80	698	22	1.94	1.94	NUM
ma-80	698	23	10	10	NUM
ma-80	698	24	5–	5–	PROPN
ma-80	698	25	4.71	4.71	NUM
ma-80	698	26	10	10	NUM
ma-80	698	27	11–	11–	NUM
ma-80	698	28	2.76	2.76	NUM
ma-80	698	29	10	10	NUM
ma-80	698	30	22–	22–	NUM
ma-80	698	31	9.48	9.48	NUM
ma-80	698	32	10	10	NUM
ma-80	698	33	45–	45–	NUM
ma-80	698	34	w0	w0	PROPN
ma-80	698	35	2	2	NOUN
ma-80	698	36	1	1	NUM
ma-80	698	37			PROPN
ma-80	698	38	w0	w0	PROPN
ma-80	698	39	3	3	NOUN
ma-80	698	40	1	1	NUM
ma-80	698	41			PROPN
ma-80	698	42	w0	w0	NOUN
ma-80	698	43	4	4	NOUN
ma-80	698	44	1	1	NUM
ma-80	698	45			PROPN
ma-80	698	46	w0	w0	NOUN
ma-80	698	47	5	5	NOUN
ma-80	698	48	1	1	NUM
ma-80	698	49			PROPN
ma-80	698	50	0	0	NUM
ma-80	699	1			NUM
ma-80	699	2			X
ma-80	699	3	wl2	wl2	PROPN
ma-80	699	4	y	y	PROPN
ma-80	699	5			PROPN
ma-80	699	6	wu2	wu2	VERB
ma-80	699	7	y	y	NOUN
ma-80	699	8			PROPN
ma-80	699	9	w1	w1	NOUN
ma-80	699	10	2	2	NOUN
ma-80	699	11	y	y	PROPN
ma-80	699	12			PROPN
ma-80	699	13	w2	w2	PROPN
ma-80	699	14	2	2	PROPN
ma-80	699	15	y	y	PROPN
ma-80	699	16			PROPN
ma-80	699	17	wl3	wl3	PROPN
ma-80	699	18	y	y	PROPN
ma-80	699	19			PROPN
ma-80	699	20	wu3	wu3	VERB
ma-80	699	21	y	y	NOUN
ma-80	699	22			PROPN
ma-80	699	23	w0	w0	PROPN
ma-80	699	24	3	3	NOUN
ma-80	699	25	3.84	3.84	NUM
ma-80	699	26	10	10	NUM
ma-80	699	27	5–	5–	PROPN
ma-80	699	28	w1	w1	NOUN
ma-80	699	29	3	3	NOUN
ma-80	699	30	1.92	1.92	NUM
ma-80	699	31	10	10	NUM
ma-80	699	32	8–	8–	PROPN
ma-80	699	33	w2	w2	NOUN
ma-80	699	34	3	3	NOUN
ma-80	699	35	1.46	1.46	NUM
ma-80	699	36	10	10	NUM
ma-80	699	37	11–	11–	NUM
ma-80	699	38	w3	w3	PROPN
ma-80	699	39	3	3	NOUN
ma-80	699	40	1.31	1.31	NUM
ma-80	699	41	10	10	NUM
ma-80	699	42	14–	14–	NUM
ma-80	699	43	w4	w4	NOUN
ma-80	699	44	3	3	NOUN
ma-80	699	45	1.27	1.27	NUM
ma-80	699	46	10	10	NUM
ma-80	699	47	17–	17–	NUM
ma-80	699	48	wl4	wl4	ADJ
ma-80	699	49	y	y	NOUN
ma-80	699	50			PROPN
ma-80	699	51	wu4	wu4	NOUN
ma-80	699	52	y	y	NOUN
ma-80	699	53			PROPN
ma-80	699	54	w0	w0	PROPN
ma-80	699	55	4	4	NOUN
ma-80	699	56	8.56	8.56	NUM
ma-80	699	57	10	10	NUM
ma-80	699	58	12–	12–	NUM
ma-80	699	59	w1	w1	NOUN
ma-80	699	60	4	4	NOUN
ma-80	699	61	5.60	5.60	NUM
ma-80	699	62	10	10	NUM
ma-80	699	63	22–	22–	NUM
ma-80	699	64	w2	w2	NOUN
ma-80	699	65	4	4	NOUN
ma-80	699	66	5.05	5.05	NUM
ma-80	699	67	10	10	NUM
ma-80	699	68	32–	32–	NUM
ma-80	699	69	w3	w3	PROPN
ma-80	699	70	4	4	NOUN
ma-80	699	71	5.18	5.18	NUM
ma-80	699	72	10	10	NUM
ma-80	699	73	42–	42–	NUM
ma-80	699	74	w4	w4	NOUN
ma-80	699	75	4	4	NOUN
ma-80	699	76	5.68	5.68	NUM
ma-80	699	77	10	10	NUM
ma-80	699	78	52–	52–	NUM
ma-80	699	79	wl5	wl5	NOUN
ma-80	699	80	y	y	NOUN
ma-80	699	81			PROPN
ma-80	699	82	wu5	wu5	ADP
ma-80	699	83	y	y	NOUN
ma-80	699	84			PROPN
ma-80	699	85	w0	w0	NOUN
ma-80	699	86	5	5	NOUN
ma-80	699	87	6.80	6.80	NUM
ma-80	699	88	10	10	NUM
ma-80	699	89	25–	25–	NUM
ma-80	699	90	w1	w1	NOUN
ma-80	699	91	5	5	NUM
ma-80	699	92	3.01	3.01	NUM
ma-80	699	93	10	10	NUM
ma-80	699	94	48–	48–	NUM
ma-80	699	95	wl1	wl1	NOUN
ma-80	699	96	y	y	NOUN
ma-80	699	97			PROPN
ma-80	699	98	wl2	wl2	PROPN
ma-80	699	99	y	y	PROPN
ma-80	699	100			PROPN
ma-80	699	101	wli	wli	NOUN
ma-80	699	102	y	y	NOUN
ma-80	699	103			PROPN
ma-80	699	104	w	w	NOUN
ma-80	699	105	y	y	NOUN
ma-80	699	106			PUNCT
ma-80	700	1	i	i	PRON
ma-80	700	2	3	3	NUM
ma-80	700	3			PROPN
ma-80	700	4			PROPN
ma-80	700	5			NUM
ma-80	700	6	wui	wui	X
ma-80	700	7	y	y	PROPN
ma-80	700	8			PROPN
ma-80	700	9	w	w	NOUN
ma-80	700	10	y	y	NOUN
ma-80	700	11			PUNCT
ma-80	700	12	i	i	NOUN
ma-80	700	13	1	1	NUM
ma-80	700	14	2	2	NUM
ma-80	700	15	3	3	NUM
ma-80	700	16			NOUN
ma-80	700	17			NUM
ma-80	700	18			NOUN
ma-80	700	19	.	.	X
ma-80	700	20			ADJ
ma-80	700	21	y	y	NOUN
ma-80	700	22			PUNCT
ma-80	700	23	y	y	PROPN
ma-80	700	24	y	y	NOUN
ma-80	701	1	ln	ln	INTJ
ma-80	701	2	y	y	PROPN
ma-80	701	3			PROPN
ma-80	701	4			PROPN
ma-80	701	5	y	y	NOUN
ma-80	701	6			PROPN
ma-80	701	7	y	y	PROPN
ma-80	701	8	y	y	NOUN
ma-80	701	9	.ln	.ln	PUNCT
ma-80	701	10	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	PROPN
ma-80	701	11	as	as	ADP
ma-80	701	12	(	(	PUNCT
ma-80	701	13	equation	equation	NOUN
ma-80	701	14	115	115	NUM
ma-80	701	15	)	)	PUNCT
ma-80	701	16	,	,	PUNCT
ma-80	701	17	an	an	DET
ma-80	701	18	equivalent	equivalent	ADJ
ma-80	701	19	statement	statement	NOUN
ma-80	701	20	for	for	ADP
ma-80	701	21	the	the	DET
ma-80	701	22	prime	prime	ADJ
ma-80	701	23	number	number	NOUN
ma-80	701	24	theorem	theorem	VERB
ma-80	701	25	is	be	AUX
ma-80	701	26	(	(	PUNCT
ma-80	701	27	100	100	NUM
ma-80	701	28	)	)	PUNCT
ma-80	701	29	with	with	ADP
ma-80	701	30	the	the	DET
ma-80	701	31	manipulation	manipulation	NOUN
ma-80	701	32	of	of	ADP
ma-80	701	33	(	(	PUNCT
ma-80	701	34	101	101	NUM
ma-80	701	35	)	)	PUNCT
ma-80	701	36	and	and	CCONJ
ma-80	701	37	with	with	ADP
ma-80	701	38	for	for	ADP
ma-80	701	39	large	large	ADJ
ma-80	701	40	,	,	PUNCT
ma-80	701	41	it	it	PRON
ma-80	701	42	follows	follow	VERB
ma-80	701	43	that	that	SCONJ
ma-80	701	44	(	(	PUNCT
ma-80	701	45	102	102	NUM
ma-80	701	46	)	)	PUNCT
ma-80	701	47	which	which	PRON
ma-80	701	48	has	have	AUX
ma-80	701	49	been	be	AUX
ma-80	701	50	proposed	propose	VERB
ma-80	701	51	by	by	ADP
ma-80	701	52	visser	visser	PROPN
ma-80	702	1	[	[	X
ma-80	702	2	27	27	NUM
ma-80	702	3	]	]	PUNCT
ma-80	702	4	and	and	CCONJ
ma-80	702	5	briefly	briefly	ADV
ma-80	702	6	discussed	discuss	VERB
ma-80	702	7	by	by	ADP
ma-80	702	8	iacono	iacono	NOUN
ma-80	702	9	and	and	CCONJ
ma-80	702	10	boyd	boyd	PROPN
ma-80	702	11	,	,	PUNCT
ma-80	702	12	[	[	X
ma-80	702	13	17	17	NUM
ma-80	702	14	]	]	PUNCT
ma-80	702	15	,	,	PUNCT
ma-80	702	16	section	section	NOUN
ma-80	702	17	4.4	4.4	NUM
ma-80	702	18	.	.	PUNCT
ma-80	703	1	visser	visser	PROPN
ma-80	703	2	has	have	AUX
ma-80	703	3	proved	prove	VERB
ma-80	703	4	that	that	PRON
ma-80	703	5	is	be	AUX
ma-80	703	6	an	an	DET
ma-80	703	7	upper	upper	ADJ
ma-80	703	8	bound	bind	VERB
ma-80	703	9	for	for	ADP
ma-80	703	10	the	the	DET
ma-80	703	11	prime	prime	ADJ
ma-80	703	12	counting	counting	NOUN
ma-80	703	13	function	function	NOUN
ma-80	703	14	whilst	whilst	SCONJ
ma-80	703	15	is	be	AUX
ma-80	703	16	a	a	DET
ma-80	703	17	lower	lower	ADV
ma-80	703	18	bound	bind	VERB
ma-80	703	19	for	for	ADP
ma-80	703	20	large	large	ADJ
ma-80	703	21	.	.	PUNCT
ma-80	704	1	the	the	DET
ma-80	704	2	magnitude	magnitude	NOUN
ma-80	704	3	of	of	ADP
ma-80	704	4	the	the	DET
ma-80	704	5	relative	relative	ADJ
ma-80	704	6	error	error	NOUN
ma-80	704	7	in	in	ADP
ma-80	704	8	the	the	DET
ma-80	704	9	approximation	approximation	NOUN
ma-80	704	10	of	of	ADP
ma-80	704	11	is	be	AUX
ma-80	704	12	lower	low	ADJ
ma-80	704	13	than	than	ADP
ma-80	704	14	the	the	DET
ma-80	704	15	magnitude	magnitude	NOUN
ma-80	704	16	of	of	ADP
ma-80	704	17	the	the	DET
ma-80	704	18	relative	relative	ADJ
ma-80	704	19	error	error	NOUN
ma-80	704	20	in	in	ADP
ma-80	704	21	the	the	DET
ma-80	704	22	approximation	approximation	NOUN
ma-80	704	23	for	for	ADP
ma-80	704	24	greater	great	ADJ
ma-80	704	25	than	than	ADP
ma-80	704	26	around	around	ADV
ma-80	704	27	with	with	ADP
ma-80	704	28	the	the	DET
ma-80	704	29	relative	relative	ADJ
ma-80	704	30	error	error	NOUN
ma-80	704	31	decreasing	decrease	VERB
ma-80	704	32	as	as	ADP
ma-80	704	33	increases	increase	NOUN
ma-80	704	34	.	.	PUNCT
ma-80	705	1	however	however	ADV
ma-80	705	2	,	,	PUNCT
ma-80	705	3	the	the	DET
ma-80	705	4	magnitude	magnitude	NOUN
ma-80	705	5	of	of	ADP
ma-80	705	6	the	the	DET
ma-80	705	7	relative	relative	ADJ
ma-80	705	8	error	error	NOUN
ma-80	705	9	in	in	ADP
ma-80	705	10	the	the	DET
ma-80	705	11	approximation	approximation	NOUN
ma-80	705	12	is	be	AUX
ma-80	705	13	of	of	ADP
ma-80	705	14	the	the	DET
ma-80	705	15	order	order	NOUN
ma-80	705	16	of	of	ADP
ma-80	705	17	for	for	ADP
ma-80	705	18	.	.	PUNCT
ma-80	706	1	7.5	7.5	NUM
ma-80	706	2	.	.	PUNCT
ma-80	706	3	floor	floor	NOUN
ma-80	706	4	and	and	CCONJ
ma-80	706	5	integral	integral	ADJ
ma-80	706	6	of	of	ADP
ma-80	706	7	floor	floor	NOUN
ma-80	706	8	of	of	ADP
ma-80	706	9	lambert	lambert	PROPN
ma-80	706	10	w.	w.	PROPN
ma-80	707	1	it	it	PRON
ma-80	707	2	is	be	AUX
ma-80	707	3	possible	possible	ADJ
ma-80	707	4	to	to	PART
ma-80	707	5	specify	specify	VERB
ma-80	707	6	approximations	approximation	NOUN
ma-80	707	7	for	for	ADP
ma-80	707	8	the	the	DET
ma-80	707	9	lambert	lambert	PROPN
ma-80	707	10	w	w	PROPN
ma-80	707	11	function	function	PROPN
ma-80	707	12	,	,	PUNCT
ma-80	707	13	with	with	ADP
ma-80	707	14	a	a	DET
ma-80	707	15	set	set	ADJ
ma-80	707	16	accuracy	accuracy	NOUN
ma-80	707	17	bound	bind	VERB
ma-80	707	18	,	,	PUNCT
ma-80	707	19	if	if	SCONJ
ma-80	707	20	an	an	DET
ma-80	707	21	explicit	explicit	ADJ
ma-80	707	22	expression	expression	NOUN
ma-80	707	23	for	for	ADP
ma-80	707	24	the	the	DET
ma-80	707	25	floor	floor	NOUN
ma-80	707	26	of	of	ADP
ma-80	707	27	the	the	DET
ma-80	707	28	lambert	lambert	NOUN
ma-80	707	29	function	function	NOUN
ma-80	707	30	can	can	AUX
ma-80	707	31	be	be	AUX
ma-80	707	32	specified	specify	VERB
ma-80	707	33	.	.	PUNCT
ma-80	708	1	the	the	DET
ma-80	708	2	graph	graph	NOUN
ma-80	708	3	of	of	ADP
ma-80	708	4	is	be	AUX
ma-80	708	5	shown	show	VERB
ma-80	708	6	in	in	ADP
ma-80	708	7	figure	figure	NOUN
ma-80	708	8	24	24	NUM
ma-80	708	9	.	.	PUNCT
ma-80	709	1	theorem	theorem	VERB
ma-80	709	2	7.2	7.2	NUM
ma-80	709	3	.	.	PUNCT
ma-80	709	4	floor	floor	NOUN
ma-80	709	5	of	of	ADP
ma-80	709	6	lambert	lambert	PROPN
ma-80	709	7	w.	w.	PROPN
ma-80	709	8	the	the	DET
ma-80	709	9	floor	floor	NOUN
ma-80	709	10	of	of	ADP
ma-80	709	11	the	the	DET
ma-80	709	12	lambert	lambert	PROPN
ma-80	709	13	w	w	PROPN
ma-80	709	14	function	function	NOUN
ma-80	709	15	can	can	AUX
ma-80	709	16	be	be	AUX
ma-80	709	17	ascertained	ascertain	VERB
ma-80	709	18	,	,	PUNCT
ma-80	709	19	without	without	ADP
ma-80	709	20	knowledge	knowledge	NOUN
ma-80	709	21	of	of	ADP
ma-80	709	22	the	the	DET
ma-80	709	23	function	function	NOUN
ma-80	709	24	itself	itself	PRON
ma-80	709	25	,	,	PUNCT
ma-80	709	26	according	accord	VERB
ma-80	709	27	to	to	ADP
ma-80	709	28	(	(	PUNCT
ma-80	709	29	103	103	NUM
ma-80	709	30	)	)	PUNCT
ma-80	709	31	where	where	SCONJ
ma-80	709	32	,	,	PUNCT
ma-80	709	33	is	be	AUX
ma-80	709	34	fixed	fix	VERB
ma-80	709	35	,	,	PUNCT
ma-80	710	1	is	be	AUX
ma-80	710	2	the	the	DET
ma-80	710	3	unit	unit	NOUN
ma-80	710	4	step	step	NOUN
ma-80	710	5	function	function	NOUN
ma-80	710	6	and	and	CCONJ
ma-80	710	7	is	be	AUX
ma-80	710	8	an	an	DET
ma-80	710	9	upper	upper	ADJ
ma-80	710	10	bound	bind	VERB
ma-80	710	11	for	for	ADP
ma-80	710	12	the	the	DET
ma-80	710	13	lambert	lambert	PROPN
ma-80	710	14	w	w	PROPN
ma-80	710	15	function	function	PROPN
ma-80	710	16	as	as	SCONJ
ma-80	710	17	specified	specify	VERB
ma-80	710	18	in	in	ADP
ma-80	710	19	theorem	theorem	ADJ
ma-80	710	20	3.1	3.1	NUM
ma-80	710	21	.	.	PUNCT
ma-80	711	1	w	w	PROPN
ma-80	711	2	z	z	PROPN
ma-80	711	3	z	z	PROPN
ma-80	711	4	ln	ln	NOUN
ma-80	711	5			PROPN
ma-80	711	6	z	z	PROPN
ma-80	711	7	ln=	ln=	PUNCT
ma-80	712	1			ADJ
ma-80	712	2	y	y	NOUN
ma-80	712	3			PUNCT
ma-80	712	4	y	y	PROPN
ma-80	712	5	w	w	PROPN
ma-80	712	6	y	y	PROPN
ma-80	712	7	y	y	PROPN
ma-80	712	8	ln	ln	NOUN
ma-80	713	1	.	.	PROPN
ma-80	713	2	w	w	NOUN
ma-80	713	3	y	y	PROPN
ma-80	713	4	y	y	PROPN
ma-80	713	5	ln	ln	NOUN
ma-80	713	6			ADP
ma-80	713	7	y	y	PROPN
ma-80	713	8	ln	ln	PROPN
ma-80	714	1	xe	xe	INTJ
ma-80	714	2	x	x	X
ma-80	715	1	ln	ln	PROPN
ma-80	716	1	x	x	X
ma-80	716	2	x	x	PUNCT
ma-80	716	3	ln+	ln+	PROPN
ma-80	716	4	w	w	PROPN
ma-80	716	5	y	y	PROPN
ma-80	716	6			PROPN
ma-80	716	7	w	w	NOUN
ma-80	716	8	y	y	NOUN
ma-80	716	9			NOUN
ma-80	716	10	ln+	ln+	NOUN
ma-80	716	11	=	=	NOUN
ma-80	716	12	=	=	PUNCT
ma-80	717	1	=	=	PUNCT
ma-80	717	2	=	=	PUNCT
ma-80	717	3	w	w	NOUN
ma-80	717	4	y	y	NOUN
ma-80	717	5			PROPN
ma-80	717	6	w	w	NOUN
ma-80	717	7	y	y	NOUN
ma-80	717	8			NOUN
ma-80	717	9	ln	ln	NOUN
ma-80	717	10	»	»	PUNCT
ma-80	717	11	y	y	PROPN
ma-80	717	12			PROPN
ma-80	717	13	y	y	NOUN
ma-80	717	14			PUNCT
ma-80	717	15	y	y	PROPN
ma-80	717	16	w	w	PROPN
ma-80	717	17	y	y	PROPN
ma-80	717	18			PROPN
ma-80	718	1			NOUN
ma-80	718	2	y	y	PROPN
ma-80	718	3	w	w	PROPN
ma-80	718	4	y	y	PROPN
ma-80	719	1			PROPN
ma-80	720	1	y	y	PROPN
ma-80	720	2	y	y	NOUN
ma-80	721	1	ln	ln	NUM
ma-80	721	2	y	y	PROPN
ma-80	721	3			ADJ
ma-80	721	4	y	y	NOUN
ma-80	721	5			PUNCT
ma-80	721	6	y	y	PROPN
ma-80	721	7	w	w	NOUN
ma-80	721	8	y	y	NOUN
ma-80	721	9			X
ma-80	721	10			NOUN
ma-80	721	11	y	y	NOUN
ma-80	721	12			PUNCT
ma-80	722	1	y	y	PROPN
ma-80	722	2	w	w	PROPN
ma-80	722	3	y	y	PROPN
ma-80	722	4	y	y	PROPN
ma-80	722	5	ln	ln	PUNCT
ma-80	723	1			PRON
ma-80	723	2	y	y	PROPN
ma-80	723	3	5000	5000	NUM
ma-80	723	4	y	y	PROPN
ma-80	723	5			ADJ
ma-80	723	6	y	y	NOUN
ma-80	723	7			PUNCT
ma-80	724	1	y	y	PROPN
ma-80	724	2	w	w	NOUN
ma-80	724	3	y	y	NOUN
ma-80	724	4			NOUN
ma-80	724	5	0.05	0.05	NUM
ma-80	724	6	y	y	PROPN
ma-80	724	7	10	10	NUM
ma-80	724	8	9	9	NUM
ma-80	724	9	=	=	SYM
ma-80	724	10	w	w	NOUN
ma-80	724	11	y	y	NOUN
ma-80	724	12			PROPN
ma-80	724	13	figure	figure	NOUN
ma-80	724	14	24	24	NUM
ma-80	724	15	.	.	PUNCT
ma-80	724	16	graph	graph	NOUN
ma-80	724	17	of	of	ADP
ma-80	724	18	and	and	CCONJ
ma-80	724	19	.	.	PUNCT
ma-80	725	1	w	w	NOUN
ma-80	725	2	y	y	NOUN
ma-80	725	3			PROPN
ma-80	725	4	w	w	NOUN
ma-80	725	5	y	y	NOUN
ma-80	725	6			PUNCT
ma-80	726	1	y	y	PROPN
ma-80	726	2	w	w	NOUN
ma-80	726	3	y	y	PROPN
ma-80	726	4			PROPN
ma-80	726	5	w	w	NOUN
ma-80	726	6	y	y	NOUN
ma-80	726	7			PROPN
ma-80	726	8	2e	2e	NOUN
ma-80	726	9	2e	2e	NOUN
ma-80	726	10	4e	4e	NOUN
ma-80	726	11	4	4	NUM
ma-80	726	12	3e	3e	NOUN
ma-80	726	13	3	3	NUM
ma-80	726	14	w	w	NOUN
ma-80	726	15	y	y	NOUN
ma-80	726	16			PUNCT
ma-80	726	17	u	u	NOUN
ma-80	726	18	y	y	PROPN
ma-80	726	19	ke	ke	PROPN
ma-80	726	20	k	k	PROPN
ma-80	726	21	–	–	PUNCT
ma-80	726	22			NOUN
ma-80	726	23			PUNCT
ma-80	726	24	k	k	SYM
ma-80	726	25	1=	1=	X
ma-80	726	26			VERB
ma-80	726	27			X
ma-80	726	28	u	u	NOUN
ma-80	726	29	y	y	PROPN
ma-80	726	30	ke	ke	PROPN
ma-80	726	31	k	k	PROPN
ma-80	726	32	–	–	PUNCT
ma-80	726	33			NOUN
ma-80	726	34			PUNCT
ma-80	726	35	k	k	SYM
ma-80	726	36	1=	1=	NUM
ma-80	726	37	1	1	NUM
ma-80	726	38	wui	wui	PROPN
ma-80	726	39	y	y	PROPN
ma-80	726	40	+	+	PUNCT
ma-80	726	41			X
ma-80	726	42	=	=	PROPN
ma-80	726	43	=	=	SYM
ma-80	726	44	y	y	PROPN
ma-80	726	45	0	0	NUM
ma-80	726	46			NUM
ma-80	726	47	i	i	NOUN
ma-80	726	48	1	1	NUM
ma-80	726	49	2	2	NUM
ma-80	726	50			NOUN
ma-80	726	51			X
ma-80	726	52			PUNCT
ma-80	726	53	u	u	NOUN
ma-80	726	54	wui	wui	X
ma-80	726	55	y	y	NOUN
ma-80	727	1			PROPN
ma-80	727	2	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	NOUN
ma-80	727	3	proof	proof	NOUN
ma-80	727	4	.	.	PUNCT
ma-80	728	1	this	this	DET
ma-80	728	2	result	result	NOUN
ma-80	728	3	follows	follow	VERB
ma-80	728	4	from	from	ADP
ma-80	728	5	the	the	DET
ma-80	728	6	fact	fact	NOUN
ma-80	728	7	that	that	SCONJ
ma-80	728	8	and	and	CCONJ
ma-80	728	9	,	,	PUNCT
ma-80	728	10	,	,	PUNCT
ma-80	728	11	fixed	fix	VERB
ma-80	728	12	,	,	PUNCT
ma-80	728	13	is	be	AUX
ma-80	728	14	an	an	DET
ma-80	728	15	upper	upper	ADJ
ma-80	728	16	bound	bind	VERB
ma-80	728	17	for	for	ADP
ma-80	728	18	,	,	PUNCT
ma-80	728	19	i.e.	i.e.	X
ma-80	728	20	.	.	PUNCT
ma-80	729	1	it	it	PRON
ma-80	729	2	then	then	ADV
ma-80	729	3	follows	follow	VERB
ma-80	729	4	that	that	SCONJ
ma-80	729	5	the	the	DET
ma-80	729	6	upper	upper	ADJ
ma-80	729	7	limit	limit	NOUN
ma-80	729	8	of	of	ADP
ma-80	729	9	the	the	DET
ma-80	729	10	summation	summation	NOUN
ma-80	729	11	can	can	AUX
ma-80	729	12	be	be	AUX
ma-80	729	13	specified	specify	VERB
ma-80	729	14	as	as	ADP
ma-80	729	15	.	.	PUNCT
ma-80	730	1	7.5.1	7.5.1	X
ma-80	730	2	.	.	PUNCT
ma-80	730	3	notes	note	NOUN
ma-80	730	4	.	.	PUNCT
ma-80	731	1	the	the	DET
ma-80	731	2	simplest	simple	ADJ
ma-80	731	3	upper	upper	ADJ
ma-80	731	4	bound	bind	VERB
ma-80	731	5	,	,	PUNCT
ma-80	731	6	specified	specify	VERB
ma-80	731	7	in	in	ADP
ma-80	731	8	theorem	theorem	ADJ
ma-80	731	9	3.1	3.1	NUM
ma-80	731	10	,	,	PUNCT
ma-80	731	11	for	for	ADP
ma-80	731	12	the	the	DET
ma-80	731	13	lambert	lambert	PROPN
ma-80	731	14	w	w	PROPN
ma-80	731	15	function	function	PROPN
ma-80	731	16	is	be	AUX
ma-80	731	17	and	and	CCONJ
ma-80	731	18	,	,	PUNCT
ma-80	731	19	thus	thus	ADV
ma-80	731	20	:	:	PUNCT
ma-80	731	21	(	(	PUNCT
ma-80	731	22	104	104	X
ma-80	731	23	)	)	PUNCT
ma-80	731	24	the	the	DET
ma-80	731	25	graphs	graph	NOUN
ma-80	731	26	of	of	ADP
ma-80	731	27	,	,	PUNCT
ma-80	731	28	for	for	ADP
ma-80	731	29	,	,	PUNCT
ma-80	731	30	are	be	AUX
ma-80	731	31	shown	show	VERB
ma-80	731	32	in	in	ADP
ma-80	731	33	figure	figure	NOUN
ma-80	731	34	25	25	NUM
ma-80	731	35	and	and	CCONJ
ma-80	731	36	it	it	PRON
ma-80	731	37	follows	follow	VERB
ma-80	731	38	that	that	SCONJ
ma-80	731	39	the	the	DET
ma-80	731	40	use	use	NOUN
ma-80	731	41	of	of	ADP
ma-80	731	42	as	as	ADP
ma-80	731	43	the	the	DET
ma-80	731	44	upper	upper	ADJ
ma-80	731	45	limit	limit	NOUN
ma-80	731	46	for	for	ADP
ma-80	731	47	the	the	DET
ma-80	731	48	summation	summation	NOUN
ma-80	731	49	results	result	NOUN
ma-80	731	50	in	in	ADP
ma-80	731	51	an	an	DET
ma-80	731	52	increasing	increase	VERB
ma-80	731	53	small	small	ADJ
ma-80	731	54	number	number	NOUN
ma-80	731	55	of	of	ADP
ma-80	731	56	additional	additional	ADJ
ma-80	731	57	zero	zero	NUM
ma-80	731	58	terms	term	NOUN
ma-80	731	59	in	in	ADP
ma-80	731	60	the	the	DET
ma-80	731	61	summation	summation	NOUN
ma-80	731	62	defining	define	VERB
ma-80	731	63	as	as	ADP
ma-80	731	64	increases	increase	NOUN
ma-80	731	65	.	.	PUNCT
ma-80	732	1	the	the	DET
ma-80	732	2	use	use	NOUN
ma-80	732	3	of	of	ADP
ma-80	732	4	results	result	NOUN
ma-80	732	5	,	,	PUNCT
ma-80	732	6	depending	depend	VERB
ma-80	732	7	on	on	ADP
ma-80	732	8	the	the	DET
ma-80	732	9	value	value	NOUN
ma-80	732	10	of	of	ADP
ma-80	732	11	,	,	PUNCT
ma-80	732	12	in	in	ADP
ma-80	732	13	an	an	DET
ma-80	732	14	additional	additional	ADJ
ma-80	732	15	zero	zero	NUM
ma-80	732	16	term	term	NOUN
ma-80	732	17	in	in	ADP
ma-80	732	18	the	the	DET
ma-80	732	19	summation	summation	NOUN
ma-80	732	20	defining	define	VERB
ma-80	732	21	.	.	PUNCT
ma-80	733	1	7.5.2	7.5.2	X
ma-80	733	2	.	.	PUNCT
ma-80	733	3	integral	integral	ADJ
ma-80	733	4	of	of	ADP
ma-80	733	5	floor	floor	NOUN
ma-80	733	6	of	of	ADP
ma-80	733	7	lambert	lambert	PROPN
ma-80	733	8	w.	w.	PROPN
ma-80	733	9	using	use	VERB
ma-80	733	10	the	the	DET
ma-80	733	11	result	result	NOUN
ma-80	733	12	for	for	ADP
ma-80	733	13	the	the	DET
ma-80	733	14	floor	floor	NOUN
ma-80	733	15	of	of	ADP
ma-80	733	16	the	the	DET
ma-80	733	17	lambert	lambert	PROPN
ma-80	733	18	w	w	PROPN
ma-80	733	19	function	function	PROPN
ma-80	733	20	,	,	PUNCT
ma-80	733	21	as	as	SCONJ
ma-80	733	22	specified	specify	VERB
ma-80	733	23	in	in	ADP
ma-80	733	24	theorem	theorem	NOUN
ma-80	733	25	7.2	7.2	NUM
ma-80	733	26	,	,	PUNCT
ma-80	733	27	it	it	PRON
ma-80	733	28	is	be	AUX
ma-80	733	29	possible	possible	ADJ
ma-80	733	30	to	to	PART
ma-80	733	31	explicitly	explicitly	ADV
ma-80	733	32	specify	specify	VERB
ma-80	733	33	the	the	DET
ma-80	733	34	integral	integral	NOUN
ma-80	733	35	of	of	ADP
ma-80	733	36	the	the	DET
ma-80	733	37	floor	floor	NOUN
ma-80	733	38	of	of	ADP
ma-80	733	39	the	the	DET
ma-80	733	40	lambert	lambert	PROPN
ma-80	733	41	w	w	PROPN
ma-80	733	42	function	function	PROPN
ma-80	733	43	.	.	PUNCT
ma-80	734	1	theorem	theorem	VERB
ma-80	734	2	7.3	7.3	NUM
ma-80	734	3	.	.	PUNCT
ma-80	735	1	integral	integral	ADJ
ma-80	735	2	of	of	ADP
ma-80	735	3	floor	floor	NOUN
ma-80	735	4	of	of	ADP
ma-80	735	5	lambert	lambert	PROPN
ma-80	735	6	w.	w.	PROPN
ma-80	735	7	the	the	DET
ma-80	735	8	integral	integral	NOUN
ma-80	735	9	of	of	ADP
ma-80	735	10	the	the	DET
ma-80	735	11	floor	floor	NOUN
ma-80	735	12	of	of	ADP
ma-80	735	13	the	the	DET
ma-80	735	14	lambert	lambert	PROPN
ma-80	735	15	w	w	PROPN
ma-80	735	16	function	function	NOUN
ma-80	735	17	can	can	AUX
ma-80	735	18	be	be	AUX
ma-80	735	19	explicitly	explicitly	ADV
ma-80	735	20	specified	specify	VERB
ma-80	735	21	according	accord	VERB
ma-80	735	22	to	to	ADP
ma-80	735	23	(	(	PUNCT
ma-80	735	24	105	105	NUM
ma-80	735	25	)	)	PUNCT
ma-80	735	26	where	where	SCONJ
ma-80	735	27	is	be	AUX
ma-80	735	28	specified	specify	VERB
ma-80	735	29	in	in	ADP
ma-80	735	30	theorem	theorem	ADJ
ma-80	735	31	7.2	7.2	NUM
ma-80	735	32	.	.	PUNCT
ma-80	736	1	proof	proof	NOUN
ma-80	736	2	.	.	PUNCT
ma-80	737	1	the	the	DET
ma-80	737	2	required	require	VERB
ma-80	737	3	result	result	NOUN
ma-80	737	4	follows	follow	VERB
ma-80	737	5	,	,	PUNCT
ma-80	737	6	consistent	consistent	ADJ
ma-80	737	7	with	with	ADP
ma-80	737	8	the	the	DET
ma-80	737	9	graph	graph	NOUN
ma-80	737	10	of	of	ADP
ma-80	737	11	shown	show	VERB
ma-80	737	12	in	in	ADP
ma-80	737	13	figure	figure	NOUN
ma-80	737	14	24	24	NUM
ma-80	737	15	,	,	PUNCT
ma-80	737	16	according	accord	VERB
ma-80	737	17	to	to	ADP
ma-80	737	18	w	w	PROPN
ma-80	737	19	ke	ke	NOUN
ma-80	737	20	k	k	ADJ
ma-80	737	21			NOUN
ma-80	737	22	k=	k=	CCONJ
ma-80	737	23	wui	wui	X
ma-80	738	1	y	y	PROPN
ma-80	738	2			PUNCT
ma-80	738	3	i	i	NOUN
ma-80	738	4	1	1	NUM
ma-80	738	5	2	2	NUM
ma-80	738	6			NOUN
ma-80	739	1			X
ma-80	739	2			VERB
ma-80	739	3	i	i	NOUN
ma-80	739	4	w	w	VERB
ma-80	739	5	y	y	NOUN
ma-80	739	6			PUNCT
ma-80	739	7	w	w	NOUN
ma-80	739	8	y	y	NOUN
ma-80	739	9			PROPN
ma-80	739	10	wui	wui	X
ma-80	739	11	y	y	NOUN
ma-80	739	12			CCONJ
ma-80	739	13	1	1	NUM
ma-80	739	14	wui	wui	NOUN
ma-80	739	15	y	y	NOUN
ma-80	739	16	+	+	NOUN
ma-80	739	17	wu1	wu1	ADJ
ma-80	739	18	y	y	NOUN
ma-80	739	19			PROPN
ma-80	739	20	1	1	NUM
ma-80	739	21	y+	y+	NOUN
ma-80	739	22	ln=	ln=	NOUN
ma-80	740	1	w	w	NOUN
ma-80	740	2	y	y	NOUN
ma-80	740	3			PUNCT
ma-80	740	4	u	u	NOUN
ma-80	740	5	y	y	PROPN
ma-80	740	6	ke	ke	PROPN
ma-80	740	7	k	k	PROPN
ma-80	740	8	–	–	PUNCT
ma-80	740	9			NOUN
ma-80	740	10			PUNCT
ma-80	740	11	k	k	X
ma-80	740	12	1=	1=	NUM
ma-80	740	13	1	1	NUM
ma-80	740	14	1	1	NUM
ma-80	740	15	y+	y+	NOUN
ma-80	740	16	ln+	ln+	PROPN
ma-80	740	17			X
ma-80	740	18	=	=	NOUN
ma-80	740	19	y	y	NOUN
ma-80	740	20	0	0	NOUN
ma-80	740	21	.	.	PUNCT
ma-80	741	1	1	1	NUM
ma-80	741	2	wui	wui	NOUN
ma-80	741	3	y	y	NOUN
ma-80	741	4			PROPN
ma-80	741	5	w	w	NOUN
ma-80	741	6	y	y	NOUN
ma-80	741	7	–+	–+	NUM
ma-80	741	8	i	i	PRON
ma-80	741	9	1	1	NUM
ma-80	741	10	2	2	NUM
ma-80	741	11	3	3	NOUN
ma-80	741	12			NOUN
ma-80	741	13			VERB
ma-80	741	14	1	1	NUM
ma-80	741	15	wu1	wu1	NOUN
ma-80	741	16	y	y	NOUN
ma-80	741	17	+	+	NUM
ma-80	741	18	1	1	NUM
ma-80	741	19	1	1	NUM
ma-80	741	20	y+	y+	NOUN
ma-80	741	21	ln+=	ln+=	NOUN
ma-80	741	22	w	w	NOUN
ma-80	741	23	y	y	NOUN
ma-80	741	24			PUNCT
ma-80	741	25	y	y	NOUN
ma-80	741	26	1	1	NUM
ma-80	741	27	wu2	wu2	VERB
ma-80	741	28	y	y	NOUN
ma-80	741	29	+	+	PUNCT
ma-80	741	30	y	y	PROPN
ma-80	741	31	w	w	NOUN
ma-80	741	32	y	y	PROPN
ma-80	741	33			PROPN
ma-80	741	34	figure	figure	NOUN
ma-80	741	35	25	25	NUM
ma-80	741	36	.	.	PUNCT
ma-80	742	1	graph	graph	NOUN
ma-80	742	2	of	of	ADP
ma-80	742	3	for	for	ADP
ma-80	742	4	.	.	PUNCT
ma-80	742	5	1	1	NUM
ma-80	742	6	wui	wui	NOUN
ma-80	742	7	y	y	NOUN
ma-80	742	8			PROPN
ma-80	742	9	w	w	NOUN
ma-80	742	10	y	y	NOUN
ma-80	742	11	–+	–+	NUM
ma-80	743	1	i	i	PRON
ma-80	743	2	1	1	NUM
ma-80	743	3	2	2	NUM
ma-80	743	4	3	3	NOUN
ma-80	743	5			PROPN
ma-80	743	6	y	y	PROPN
ma-80	743	7	1	1	NUM
ma-80	743	8	wui	wui	NOUN
ma-80	743	9	y	y	NOUN
ma-80	743	10			PROPN
ma-80	743	11	w	w	NOUN
ma-80	743	12	y	y	NOUN
ma-80	743	13	–+	–+	NUM
ma-80	744	1	i	i	PRON
ma-80	744	2	1=	1=	VERB
ma-80	744	3	i	i	PRON
ma-80	744	4	2=	2=	NUM
ma-80	744	5	i	i	PRON
ma-80	744	6	3=	3=	NUM
ma-80	744	7	w	w	ADP
ma-80	744	8			ADJ
ma-80	744	9			PROPN
ma-80	744	10	d	d	NOUN
ma-80	744	11	0	0	NUM
ma-80	744	12	y	y	PROPN
ma-80	744	13			PUNCT
ma-80	744	14	e	e	X
ma-80	744	15	e	e	X
ma-80	744	16	1–	1–	NUM
ma-80	744	17	2	2	ADJ
ma-80	744	18	------------------1	------------------1	PROPN
ma-80	744	19	–	–	PUNCT
ma-80	744	20	e	e	X
ma-80	744	21	w	w	NOUN
ma-80	744	22	y	y	NOUN
ma-80	744	23			PROPN
ma-80	744	24	1	1	NUM
ma-80	744	25	w	w	NOUN
ma-80	744	26	y	y	NOUN
ma-80	744	27			PROPN
ma-80	744	28	2	2	NUM
ma-80	744	29	w	w	NOUN
ma-80	744	30	y	y	NOUN
ma-80	744	31			PROPN
ma-80	744	32	2	2	NUM
ma-80	744	33	–	–	PUNCT
ma-80	744	34	+	+	NUM
ma-80	744	35			ADJ
ma-80	744	36	+	+	NOUN
ma-80	744	37	+	+	NOUN
ma-80	744	38	w	w	NOUN
ma-80	744	39	y	y	NOUN
ma-80	744	40			PROPN
ma-80	744	41	1	1	NUM
ma-80	744	42	–	–	PUNCT
ma-80	744	43	w	w	NOUN
ma-80	744	44	y	y	NOUN
ma-80	744	45	+	+	PROPN
ma-80	744	46	e1	e1	PROPN
ma-80	744	47	w	w	ADP
ma-80	744	48	y	y	NOUN
ma-80	744	49	+	+	PUNCT
ma-80	745	1	w	w	DET
ma-80	745	2	y	y	NOUN
ma-80	745	3			PROPN
ma-80	745	4	2	2	NUM
ma-80	745	5	e	e	NOUN
ma-80	745	6	w	w	NOUN
ma-80	745	7	y	y	NOUN
ma-80	745	8			PROPN
ma-80	745	9	1	1	NUM
ma-80	745	10	–	–	PUNCT
ma-80	745	11	+	+	CCONJ
ma-80	746	1			ADJ
ma-80	746	2	+	+	SYM
ma-80	746	3	=	=	X
ma-80	746	4	w	w	NOUN
ma-80	746	5	y	y	NOUN
ma-80	746	6			PUNCT
ma-80	746	7	y	y	PROPN
ma-80	746	8	w	w	NOUN
ma-80	746	9	y	y	NOUN
ma-80	746	10			PUNCT
ma-80	746	11	e	e	NOUN
ma-80	746	12	w	w	NOUN
ma-80	746	13	y	y	NOUN
ma-80	746	14			PROPN
ma-80	746	15	–	–	PUNCT
ma-80	746	16			NOUN
ma-80	746	17			X
ma-80	746	18	w	w	NOUN
ma-80	746	19	y	y	NOUN
ma-80	746	20			PROPN
ma-80	746	21	w	w	NOUN
ma-80	746	22	y	y	NOUN
ma-80	746	23			PROPN
ma-80	746	24	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	NOUN
ma-80	746	25	(	(	PUNCT
ma-80	746	26	106	106	NUM
ma-80	746	27	)	)	PUNCT
ma-80	746	28	where	where	SCONJ
ma-80	746	29	the	the	DET
ma-80	746	30	following	follow	VERB
ma-80	746	31	result	result	NOUN
ma-80	746	32	has	have	AUX
ma-80	746	33	been	be	AUX
ma-80	746	34	used	use	VERB
ma-80	746	35	:	:	PUNCT
ma-80	746	36	(	(	PUNCT
ma-80	746	37	107	107	NUM
ma-80	746	38	)	)	PUNCT
ma-80	746	39	7.6	7.6	NUM
ma-80	746	40	.	.	PUNCT
ma-80	747	1	set	set	VERB
ma-80	747	2	accuracy	accuracy	NOUN
ma-80	747	3	approximation	approximation	NOUN
ma-80	747	4	for	for	ADP
ma-80	747	5	lambert	lambert	PROPN
ma-80	747	6	w.	w.	PROPN
ma-80	747	7	consider	consider	VERB
ma-80	747	8	a	a	DET
ma-80	747	9	set	set	ADJ
ma-80	747	10	accuracy	accuracy	NOUN
ma-80	747	11	limit	limit	NOUN
ma-80	747	12	of	of	ADP
ma-80	747	13	required	require	VERB
ma-80	747	14	for	for	ADP
ma-80	747	15	the	the	DET
ma-80	747	16	evaluation	evaluation	NOUN
ma-80	747	17	of	of	ADP
ma-80	747	18	.	.	PUNCT
ma-80	748	1	this	this	PRON
ma-80	748	2	can	can	AUX
ma-80	748	3	be	be	AUX
ma-80	748	4	achieved	achieve	VERB
ma-80	748	5	by	by	ADP
ma-80	748	6	a	a	DET
ma-80	748	7	step	step	NOUN
ma-80	748	8	approximation	approximation	NOUN
ma-80	748	9	,	,	PUNCT
ma-80	748	10	with	with	ADP
ma-80	748	11	a	a	DET
ma-80	748	12	resolution	resolution	NOUN
ma-80	748	13	of	of	ADP
ma-80	748	14	,	,	PUNCT
ma-80	748	15	and	and	CCONJ
ma-80	748	16	such	such	DET
ma-80	748	17	an	an	DET
ma-80	748	18	approximation	approximation	NOUN
ma-80	748	19	is	be	AUX
ma-80	748	20	:	:	PUNCT
ma-80	748	21	(	(	PUNCT
ma-80	748	22	108	108	NUM
ma-80	748	23	)	)	PUNCT
ma-80	748	24	where	where	SCONJ
ma-80	748	25	,	,	PUNCT
ma-80	748	26	,	,	PUNCT
ma-80	748	27	fixed	fix	VERB
ma-80	748	28	,	,	PUNCT
ma-80	748	29	is	be	AUX
ma-80	748	30	a	a	DET
ma-80	748	31	set	set	VERB
ma-80	748	32	function	function	NOUN
ma-80	748	33	defined	define	VERB
ma-80	748	34	in	in	ADP
ma-80	748	35	theorem	theorem	NOUN
ma-80	748	36	3.1	3.1	NUM
ma-80	748	37	.	.	PUNCT
ma-80	749	1	as	as	ADP
ma-80	749	2	an	an	DET
ma-80	749	3	example	example	NOUN
ma-80	749	4	,	,	PUNCT
ma-80	749	5	the	the	DET
ma-80	749	6	error	error	NOUN
ma-80	749	7	in	in	ADP
ma-80	749	8	the	the	DET
ma-80	749	9	approximation	approximation	NOUN
ma-80	749	10	to	to	ADP
ma-80	749	11	,	,	PUNCT
ma-80	749	12	with	with	ADP
ma-80	749	13	a	a	DET
ma-80	749	14	resolution	resolution	NOUN
ma-80	749	15	of	of	ADP
ma-80	749	16	,	,	PUNCT
ma-80	749	17	is	be	AUX
ma-80	749	18	shown	show	VERB
ma-80	749	19	in	in	ADP
ma-80	749	20	figure	figure	NOUN
ma-80	749	21	26	26	NUM
ma-80	749	22	.	.	PUNCT
ma-80	750	1	7.6.1	7.6.1	NUM
ma-80	750	2	.	.	PUNCT
ma-80	750	3	computationally	computationally	ADV
ma-80	750	4	efficient	efficient	ADJ
ma-80	750	5	implementation	implementation	NOUN
ma-80	750	6	.	.	PUNCT
ma-80	751	1	the	the	DET
ma-80	751	2	direct	direct	ADJ
ma-80	751	3	approximation	approximation	NOUN
ma-80	751	4	detailed	detail	VERB
ma-80	751	5	in	in	ADP
ma-80	751	6	equation	equation	NOUN
ma-80	751	7	108	108	NUM
ma-80	751	8	,	,	PUNCT
ma-80	751	9	for	for	ADP
ma-80	751	10	a	a	DET
ma-80	751	11	set	set	NOUN
ma-80	751	12	error	error	NOUN
ma-80	751	13	level	level	NOUN
ma-80	751	14	of	of	ADP
ma-80	751	15	,	,	PUNCT
ma-80	751	16	requires	require	VERB
ma-80	751	17	,	,	PUNCT
ma-80	751	18	approximately	approximately	ADV
ma-80	751	19	,	,	PUNCT
ma-80	751	20	a	a	DET
ma-80	751	21	summation	summation	NOUN
ma-80	751	22	of	of	ADP
ma-80	751	23	terms	term	NOUN
ma-80	751	24	.	.	PUNCT
ma-80	752	1	the	the	DET
ma-80	752	2	approach	approach	NOUN
ma-80	752	3	detailed	detail	VERB
ma-80	752	4	below	below	ADP
ma-80	752	5	requires	require	NOUN
ma-80	752	6	,	,	PUNCT
ma-80	752	7	approximately	approximately	ADV
ma-80	752	8	,	,	PUNCT
ma-80	752	9	the	the	DET
ma-80	752	10	summation	summation	NOUN
ma-80	752	11	of	of	ADP
ma-80	752	12	terms	term	NOUN
ma-80	752	13	which	which	PRON
ma-80	752	14	represents	represent	VERB
ma-80	752	15	a	a	DET
ma-80	752	16	significant	significant	ADJ
ma-80	752	17	reduction	reduction	NOUN
ma-80	752	18	for	for	ADP
ma-80	752	19	modest	modest	ADJ
ma-80	752	20	to	to	PART
ma-80	752	21	large	large	ADJ
ma-80	752	22	.	.	PUNCT
ma-80	753	1	for	for	ADP
ma-80	753	2	example	example	NOUN
ma-80	753	3	,	,	PUNCT
ma-80	753	4	for	for	ADP
ma-80	753	5	and	and	CCONJ
ma-80	753	6	,	,	PUNCT
ma-80	753	7	the	the	DET
ma-80	753	8	direct	direct	ADJ
ma-80	753	9	approach	approach	NOUN
ma-80	753	10	requires	require	VERB
ma-80	753	11	a	a	DET
ma-80	753	12	summation	summation	NOUN
ma-80	753	13	of	of	ADP
ma-80	753	14	approximately	approximately	ADV
ma-80	753	15	terms	term	NOUN
ma-80	753	16	whilst	whilst	SCONJ
ma-80	753	17	the	the	DET
ma-80	753	18	approach	approach	NOUN
ma-80	753	19	detailed	detail	VERB
ma-80	753	20	below	below	ADV
ma-80	753	21	requires	require	VERB
ma-80	753	22	close	close	ADV
ma-80	753	23	to	to	ADP
ma-80	753	24	terms	term	NOUN
ma-80	753	25	.	.	PUNCT
ma-80	754	1	w	w	ADP
ma-80	754	2			ADJ
ma-80	754	3			PROPN
ma-80	754	4	d	d	PROPN
ma-80	754	5	0	0	NUM
ma-80	755	1	y	y	PROPN
ma-80	755	2			PUNCT
ma-80	756	1	k	k	PROPN
ma-80	757	1	k	k	PROPN
ma-80	757	2	1+	1+	PROPN
ma-80	757	3	ek	ek	NUM
ma-80	757	4	1	1	NUM
ma-80	757	5	+	+	NUM
ma-80	757	6	ke	ke	PROPN
ma-80	757	7	k	k	PROPN
ma-80	757	8	–	–	PUNCT
ma-80	757	9			PROPN
ma-80	757	10			PROPN
ma-80	758	1	k	k	PROPN
ma-80	758	2	0=	0=	PROPN
ma-80	759	1	max	max	PROPN
ma-80	759	2	0	0	NUM
ma-80	760	1	w	w	NOUN
ma-80	760	2	y	y	NOUN
ma-80	760	3			PROPN
ma-80	760	4	1–	1–	NUM
ma-80	760	5			X
ma-80	760	6			X
ma-80	761	1	w	w	ADP
ma-80	761	2	y	y	NOUN
ma-80	761	3			PUNCT
ma-80	761	4	y	y	PROPN
ma-80	761	5	w	w	NOUN
ma-80	761	6	y	y	NOUN
ma-80	761	7			PUNCT
ma-80	761	8	e	e	NOUN
ma-80	761	9	w	w	NOUN
ma-80	761	10	y	y	NOUN
ma-80	761	11			PROPN
ma-80	761	12	–	–	PUNCT
ma-80	761	13			NOUN
ma-80	761	14	+=	+=	PROPN
ma-80	761	15	e	e	PROPN
ma-80	761	16	e	e	X
ma-80	761	17	1–	1–	NUM
ma-80	761	18	2	2	PROPN
ma-80	761	19	------------------1	------------------1	PROPN
ma-80	761	20	–	–	PUNCT
ma-80	761	21	e	e	X
ma-80	761	22	w	w	NOUN
ma-80	761	23	y	y	NOUN
ma-80	761	24			PROPN
ma-80	761	25	1	1	NUM
ma-80	761	26	w	w	NOUN
ma-80	761	27	y	y	NOUN
ma-80	761	28			PROPN
ma-80	761	29	2	2	NUM
ma-80	761	30	w	w	NOUN
ma-80	761	31	y	y	NOUN
ma-80	761	32			PROPN
ma-80	761	33	2	2	NUM
ma-80	761	34	–	–	PUNCT
ma-80	761	35	+	+	NUM
ma-80	761	36			ADJ
ma-80	761	37	+	+	NOUN
ma-80	761	38	+	+	NOUN
ma-80	761	39	w	w	NOUN
ma-80	761	40	y	y	NOUN
ma-80	761	41			PROPN
ma-80	761	42	1	1	NUM
ma-80	761	43	–	–	PUNCT
ma-80	761	44	w	w	NOUN
ma-80	761	45	y	y	NOUN
ma-80	761	46	+	+	PROPN
ma-80	761	47	e1	e1	PROPN
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ma-80	761	49	y	y	NOUN
ma-80	761	50	+	+	PUNCT
ma-80	762	1	w	w	DET
ma-80	762	2	y	y	NOUN
ma-80	762	3			PROPN
ma-80	762	4	2	2	NUM
ma-80	762	5	e	e	NOUN
ma-80	762	6	w	w	NOUN
ma-80	762	7	y	y	NOUN
ma-80	762	8			PROPN
ma-80	762	9	1	1	NUM
ma-80	762	10	–	–	PUNCT
ma-80	762	11	+	+	CCONJ
ma-80	763	1			ADJ
ma-80	763	2	+	+	SYM
ma-80	763	3	=	=	X
ma-80	763	4	w	w	NOUN
ma-80	763	5	y	y	NOUN
ma-80	763	6			PUNCT
ma-80	763	7	y	y	PROPN
ma-80	763	8	w	w	NOUN
ma-80	763	9	y	y	NOUN
ma-80	764	1			PUNCT
ma-80	764	2	e	e	NOUN
ma-80	764	3	w	w	NOUN
ma-80	764	4	y	y	NOUN
ma-80	764	5			PROPN
ma-80	764	6	–	–	PUNCT
ma-80	764	7			NOUN
ma-80	764	8			X
ma-80	765	1	k	k	PROPN
ma-80	765	2	k	k	PROPN
ma-80	765	3	1+	1+	PROPN
ma-80	765	4	ek	ek	PROPN
ma-80	765	5	1	1	NUM
ma-80	765	6	+	+	NUM
ma-80	765	7	ke	ke	PROPN
ma-80	765	8	k	k	PROPN
ma-80	765	9	–	–	PUNCT
ma-80	765	10			PROPN
ma-80	765	11			X
ma-80	765	12	k	k	PROPN
ma-80	765	13	1=	1=	X
ma-80	765	14	n	n	PRON
ma-80	765	15	1	1	NUM
ma-80	765	16	–	–	PUNCT
ma-80	765	17			X
ma-80	765	18	e	e	X
ma-80	765	19	e	e	X
ma-80	765	20	1–	1–	NUM
ma-80	765	21	2	2	ADJ
ma-80	765	22	------------------1	------------------1	PROPN
ma-80	765	23	–	–	PUNCT
ma-80	765	24	e	e	NOUN
ma-80	765	25	n	n	CCONJ
ma-80	765	26	1	1	NUM
ma-80	765	27	n	n	NUM
ma-80	765	28	2n	2n	NUM
ma-80	765	29	2	2	NUM
ma-80	765	30	–	–	PUNCT
ma-80	765	31	+	+	NOUN
ma-80	765	32			ADJ
ma-80	765	33			NOUN
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ma-80	765	35	1	1	NUM
ma-80	765	36	n+	n+	ADP
ma-80	765	37	1	1	NUM
ma-80	765	38	–	–	PUNCT
ma-80	765	39	n+	n+	NOUN
ma-80	765	40			NOUN
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ma-80	765	42	2	2	NUM
ma-80	765	43	e	e	NOUN
ma-80	765	44	1	1	NUM
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ma-80	765	46	n+	n+	PUNCT
ma-80	766	1	+	+	PUNCT
ma-80	766	2	+	+	PUNCT
ma-80	766	3	+	+	ADJ
ma-80	766	4			ADJ
ma-80	766	5	.=	.=	NOUN
ma-80	766	6			X
ma-80	766	7	w	w	X
ma-80	766	8	y	y	NOUN
ma-80	766	9			PUNCT
ma-80	766	10			PUNCT
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ma-80	766	12	y	y	NOUN
ma-80	766	13			PUNCT
ma-80	766	14			PUNCT
ma-80	766	15	u	u	PROPN
ma-80	766	16	y	y	PROPN
ma-80	766	17	kek–	kek–	NOUN
ma-80	766	18			PROPN
ma-80	767	1	k	k	X
ma-80	767	2	1=	1=	NUM
ma-80	767	3	1	1	NUM
ma-80	767	4	1	1	NUM
ma-80	767	5			NOUN
ma-80	767	6	--wui	--wui	PUNCT
ma-80	767	7	y	y	PROPN
ma-80	767	8	+	+	X
ma-80	767	9			X
ma-80	767	10	=	=	NOUN
ma-80	767	11	y	y	NOUN
ma-80	767	12	0	0	NOUN
ma-80	767	13	.	.	PUNCT
ma-80	768	1	wui	wui	PROPN
ma-80	769	1	i	i	PRON
ma-80	769	2	1	1	NUM
ma-80	769	3	2	2	NUM
ma-80	769	4			NOUN
ma-80	769	5			X
ma-80	769	6			VERB
ma-80	769	7	i	i	NOUN
ma-80	769	8	w	w	VERB
ma-80	769	9	y	y	NOUN
ma-80	769	10			PUNCT
ma-80	769	11			NOUN
ma-80	769	12	1	1	NUM
ma-80	769	13	10=	10=	NUM
ma-80	769	14	figure	figure	NOUN
ma-80	769	15	26	26	NUM
ma-80	769	16	.	.	PUNCT
ma-80	770	1	graph	graph	NOUN
ma-80	770	2	in	in	ADP
ma-80	770	3	the	the	DET
ma-80	770	4	error	error	NOUN
ma-80	770	5	in	in	ADP
ma-80	770	6	for	for	ADP
ma-80	770	7	the	the	DET
ma-80	770	8	case	case	NOUN
ma-80	770	9	of	of	ADP
ma-80	770	10	.w	.w	PUNCT
ma-80	770	11	y	y	PROPN
ma-80	770	12			PROPN
ma-80	770	13			PUNCT
ma-80	771	1	0.1=	0.1=	PROPN
ma-80	771	2	y	y	PROPN
ma-80	771	3	w	w	VERB
ma-80	771	4	y	y	NOUN
ma-80	771	5			PROPN
ma-80	771	6	w	w	NOUN
ma-80	771	7	y	y	NOUN
ma-80	771	8			PROPN
ma-80	771	9	–	–	PUNCT
ma-80	771	10			NOUN
ma-80	771	11	10	10	NUM
ma-80	771	12	q	q	NOUN
ma-80	771	13	–	–	PUNCT
ma-80	771	14	=	=	SYM
ma-80	771	15	10	10	NUM
ma-80	771	16	q	q	NOUN
ma-80	771	17	w	w	NOUN
ma-80	771	18	y	y	NOUN
ma-80	771	19			PROPN
ma-80	771	20	w	w	NOUN
ma-80	771	21	y	y	NOUN
ma-80	771	22			PROPN
ma-80	771	23	11q	11q	NOUN
ma-80	771	24	1–+	1–+	NUM
ma-80	771	25	q	q	NOUN
ma-80	771	26	w	w	NOUN
ma-80	771	27	y	y	NOUN
ma-80	771	28			PROPN
ma-80	771	29	10=	10=	NUM
ma-80	771	30	q	q	NOUN
ma-80	771	31	6=	6=	NUM
ma-80	771	32	10	10	NUM
ma-80	771	33	7	7	NUM
ma-80	771	34	75	75	NUM
ma-80	771	35	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	NOUN
ma-80	771	36	theorem	theorem	NOUN
ma-80	771	37	7.4	7.4	NUM
ma-80	771	38	.	.	PUNCT
ma-80	772	1	direct	direct	ADJ
ma-80	772	2	evaluation	evaluation	NOUN
ma-80	772	3	of	of	ADP
ma-80	772	4	lambert	lambert	PROPN
ma-80	772	5	w	w	PROPN
ma-80	772	6	with	with	ADP
ma-80	772	7	specified	specified	ADJ
ma-80	772	8	resolution	resolution	NOUN
ma-80	772	9	.	.	PUNCT
ma-80	773	1	the	the	DET
ma-80	773	2	lambert	lambert	PROPN
ma-80	773	3	w	w	PROPN
ma-80	773	4	function	function	NOUN
ma-80	773	5	can	can	AUX
ma-80	773	6	be	be	AUX
ma-80	773	7	evaluated	evaluate	VERB
ma-80	773	8	,	,	PUNCT
ma-80	773	9	with	with	ADP
ma-80	773	10	a	a	DET
ma-80	773	11	maximum	maximum	ADJ
ma-80	773	12	error	error	NOUN
ma-80	773	13	of	of	ADP
ma-80	773	14	,	,	PUNCT
ma-80	773	15	according	accord	VERB
ma-80	773	16	to	to	ADP
ma-80	773	17	(	(	PUNCT
ma-80	773	18	109	109	NUM
ma-80	773	19	)	)	PUNCT
ma-80	773	20	where	where	SCONJ
ma-80	773	21	is	be	AUX
ma-80	773	22	defined	define	VERB
ma-80	773	23	in	in	ADP
ma-80	773	24	theorem	theorem	ADJ
ma-80	773	25	7.2	7.2	NUM
ma-80	773	26	and	and	CCONJ
ma-80	773	27	is	be	AUX
ma-80	773	28	the	the	DET
ma-80	773	29	digit	digit	NOUN
ma-80	773	30	in	in	ADP
ma-80	773	31	the	the	DET
ma-80	773	32	decimal	decimal	ADJ
ma-80	773	33	expansion	expansion	NOUN
ma-80	773	34	of	of	ADP
ma-80	773	35	:	:	PUNCT
ma-80	773	36	(	(	PUNCT
ma-80	773	37	110	110	NUM
ma-80	773	38	)	)	PUNCT
ma-80	773	39	proof	proof	NOUN
ma-80	773	40	.	.	PUNCT
ma-80	774	1	the	the	DET
ma-80	774	2	floor	floor	NOUN
ma-80	774	3	of	of	ADP
ma-80	774	4	the	the	DET
ma-80	774	5	lambert	lambert	PROPN
ma-80	774	6	w	w	PROPN
ma-80	774	7	function	function	PROPN
ma-80	774	8	has	have	AUX
ma-80	774	9	been	be	AUX
ma-80	774	10	defined	define	VERB
ma-80	774	11	in	in	ADP
ma-80	774	12	theorem	theorem	NOUN
ma-80	774	13	7.2	7.2	NUM
ma-80	774	14	.	.	PUNCT
ma-80	775	1	consider	consider	VERB
ma-80	775	2	the	the	DET
ma-80	775	3	illustration	illustration	NOUN
ma-80	775	4	shown	show	VERB
ma-80	775	5	in	in	ADP
ma-80	775	6	figure	figure	NOUN
ma-80	775	7	27	27	NUM
ma-80	775	8	.	.	PUNCT
ma-80	776	1	with	with	ADP
ma-80	776	2	(	(	PUNCT
ma-80	776	3	111	111	NUM
ma-80	776	4	)	)	PUNCT
ma-80	776	5	and	and	CCONJ
ma-80	776	6	with	with	ADP
ma-80	776	7	being	be	AUX
ma-80	776	8	the	the	DET
ma-80	776	9	digit	digit	NOUN
ma-80	776	10	to	to	ADP
ma-80	776	11	the	the	DET
ma-80	776	12	right	right	NOUN
ma-80	776	13	of	of	ADP
ma-80	776	14	the	the	DET
ma-80	776	15	decimal	decimal	ADJ
ma-80	776	16	point	point	NOUN
ma-80	776	17	,	,	PUNCT
ma-80	776	18	it	it	PRON
ma-80	776	19	follows	follow	VERB
ma-80	776	20	that	that	SCONJ
ma-80	776	21	(	(	PUNCT
ma-80	776	22	112	112	NUM
ma-80	776	23	)	)	PUNCT
ma-80	776	24	iteration	iteration	NOUN
ma-80	776	25	with	with	ADP
ma-80	776	26	finer	fine	ADJ
ma-80	776	27	resolution	resolution	NOUN
ma-80	776	28	,	,	PUNCT
ma-80	776	29	and	and	CCONJ
ma-80	776	30	from	from	ADP
ma-80	776	31	the	the	DET
ma-80	776	32	point	point	NOUN
ma-80	776	33	defined	define	VERB
ma-80	776	34	by	by	ADP
ma-80	776	35	,	,	PUNCT
ma-80	776	36	yields	yield	NOUN
ma-80	776	37	etc	etc	X
ma-80	776	38	.	.	PROPN
ma-80	776	39			PROPN
ma-80	777	1	10	10	NUM
ma-80	777	2	q	q	NOUN
ma-80	777	3	–	–	PUNCT
ma-80	777	4	=	=	NOUN
ma-80	777	5	w	w	NOUN
ma-80	777	6	y	y	NOUN
ma-80	777	7			PROPN
ma-80	777	8	w	w	NOUN
ma-80	777	9	y	y	NOUN
ma-80	777	10			PROPN
ma-80	777	11	d1	d1	VERB
ma-80	777	12	y	y	NOUN
ma-80	777	13			PROPN
ma-80	777	14			NOUN
ma-80	777	15	dq	dq	NOUN
ma-80	777	16	y	y	NOUN
ma-80	777	17	+	+	PUNCT
ma-80	778	1	+	+	PUNCT
ma-80	779	1	+	+	NUM
ma-80	779	2	=	=	PROPN
ma-80	779	3	w	w	ADP
ma-80	779	4	y	y	NOUN
ma-80	779	5			PROPN
ma-80	779	6	10	10	NUM
ma-80	779	7	q	q	NOUN
ma-80	779	8	dq	dq	NUM
ma-80	779	9	y	y	NOUN
ma-80	779	10			PROPN
ma-80	779	11	qth	qth	NOUN
ma-80	779	12	w	w	NOUN
ma-80	779	13	y	y	NOUN
ma-80	779	14			PROPN
ma-80	779	15	d1	d1	VERB
ma-80	779	16	y	y	NOUN
ma-80	779	17			PROPN
ma-80	779	18	1	1	NUM
ma-80	779	19	10	10	NUM
ma-80	779	20	-----u	-----u	PROPN
ma-80	780	1	y	y	NOUN
ma-80	780	2	w	w	NOUN
ma-80	780	3	y	y	NOUN
ma-80	781	1			PROPN
ma-80	782	1	k	k	PROPN
ma-80	783	1	10	10	NUM
ma-80	783	2	------+	------+	NOUN
ma-80	783	3	w	w	ADP
ma-80	783	4	y	y	NOUN
ma-80	783	5			PROPN
ma-80	783	6	k	k	PROPN
ma-80	783	7	10	10	NUM
ma-80	783	8	------+exp	------+exp	PROPN
ma-80	783	9	–	–	PUNCT
ma-80	783	10	k	k	NOUN
ma-80	783	11	1=	1=	NUM
ma-80	783	12	10	10	NUM
ma-80	783	13	=	=	PROPN
ma-80	783	14			NUM
ma-80	783	15	d2	d2	PROPN
ma-80	783	16	y	y	NOUN
ma-80	783	17			PROPN
ma-80	783	18	1	1	NUM
ma-80	783	19	100	100	NUM
ma-80	783	20	--------u	--------u	NOUN
ma-80	784	1	y	y	NOUN
ma-80	784	2	w	w	NOUN
ma-80	784	3	y	y	NOUN
ma-80	784	4			PROPN
ma-80	784	5	d1	d1	VERB
ma-80	784	6	y	y	NOUN
ma-80	784	7			PROPN
ma-80	784	8	k	k	PROPN
ma-80	784	9	100	100	NUM
ma-80	784	10	---------+	---------+	NOUN
ma-80	785	1	+	+	X
ma-80	785	2	w	w	ADJ
ma-80	785	3	y	y	NOUN
ma-80	785	4			PROPN
ma-80	785	5	d1	d1	PROPN
ma-80	785	6	y	y	NOUN
ma-80	785	7			PROPN
ma-80	785	8	k	k	PROPN
ma-80	785	9	100	100	NUM
ma-80	785	10	---------+	---------+	NOUN
ma-80	785	11	+	+	NOUN
ma-80	785	12	exp	exp	NOUN
ma-80	785	13	–	–	PUNCT
ma-80	785	14	k	k	NOUN
ma-80	785	15	1=	1=	NUM
ma-80	785	16	10	10	NUM
ma-80	785	17			NUM
ma-80	785	18	=	=	NOUN
ma-80	785	19			NOUN
ma-80	785	20	dq	dq	ADP
ma-80	785	21	y	y	NOUN
ma-80	785	22			NOUN
ma-80	785	23	1	1	NUM
ma-80	785	24	10	10	NUM
ma-80	785	25	q	q	NOUN
ma-80	785	26	-------u	-------u	PUNCT
ma-80	786	1	y	y	NOUN
ma-80	786	2	w	w	NOUN
ma-80	786	3	y	y	PROPN
ma-80	786	4			PROPN
ma-80	786	5	di	di	NOUN
ma-80	786	6	y	y	NOUN
ma-80	786	7			PUNCT
ma-80	787	1	i	i	PRON
ma-80	787	2	1=	1=	X
ma-80	787	3	q	q	NOUN
ma-80	787	4	1	1	NUM
ma-80	787	5	–	–	PUNCT
ma-80	787	6			X
ma-80	787	7	k	k	NOUN
ma-80	787	8	10	10	NUM
ma-80	787	9	q	q	NOUN
ma-80	787	10	--------+	--------+	NOUN
ma-80	788	1	+	+	CCONJ
ma-80	788	2	w	w	NOUN
ma-80	788	3	y	y	NOUN
ma-80	788	4			PROPN
ma-80	788	5	di	di	NOUN
ma-80	788	6	y	y	NOUN
ma-80	788	7			PUNCT
ma-80	789	1	i	i	PRON
ma-80	789	2	1=	1=	X
ma-80	789	3	q	q	NOUN
ma-80	789	4	1	1	NUM
ma-80	789	5	–	–	PUNCT
ma-80	789	6			X
ma-80	789	7	k	k	NOUN
ma-80	789	8	10	10	NUM
ma-80	789	9	q	q	NOUN
ma-80	789	10	--------+	--------+	NOUN
ma-80	789	11	+	+	NOUN
ma-80	789	12	exp	exp	NOUN
ma-80	789	13	–	–	PUNCT
ma-80	789	14	k	k	NOUN
ma-80	789	15	1=	1=	NUM
ma-80	789	16	10	10	NUM
ma-80	789	17			NUM
ma-80	789	18	.=	.=	PUNCT
ma-80	790	1	w	w	PRON
ma-80	790	2	y	y	NOUN
ma-80	790	3			PROPN
ma-80	790	4	w	w	NOUN
ma-80	790	5	y	y	NOUN
ma-80	790	6			PROPN
ma-80	790	7	d1	d1	PROPN
ma-80	790	8	y	y	NOUN
ma-80	790	9			PROPN
ma-80	790	10	d2	d2	VERB
ma-80	790	11	y	y	NOUN
ma-80	790	12			PUNCT
ma-80	790	13	+	+	PROPN
ma-80	791	1	+	+	CCONJ
ma-80	792	1	+	+	NOUN
ma-80	792	2	=	=	NOUN
ma-80	792	3	dq	dq	NUM
ma-80	792	4	y	y	NOUN
ma-80	792	5			NOUN
ma-80	792	6	qth	qth	NOUN
ma-80	792	7	d1	d1	VERB
ma-80	792	8	y	y	NOUN
ma-80	792	9			PROPN
ma-80	792	10	1	1	NUM
ma-80	792	11	10	10	NUM
ma-80	792	12	-----u	-----u	PROPN
ma-80	793	1	y	y	NOUN
ma-80	793	2	w	w	NOUN
ma-80	793	3	y	y	NOUN
ma-80	794	1			PROPN
ma-80	795	1	k	k	PROPN
ma-80	796	1	10	10	NUM
ma-80	796	2	------+	------+	NOUN
ma-80	796	3	w	w	ADP
ma-80	796	4	y	y	NOUN
ma-80	796	5			PROPN
ma-80	796	6	k	k	PROPN
ma-80	796	7	10	10	NUM
ma-80	796	8	------+exp	------+exp	PROPN
ma-80	796	9	–	–	PUNCT
ma-80	796	10	.	.	PUNCT
ma-80	797	1	k	k	X
ma-80	797	2	1=	1=	NUM
ma-80	798	1	10	10	NUM
ma-80	798	2	=	=	PROPN
ma-80	798	3	w	w	NOUN
ma-80	798	4	y	y	NOUN
ma-80	798	5			PROPN
ma-80	798	6	d1	d1	PROPN
ma-80	798	7	y	y	NOUN
ma-80	798	8	+	+	PUNCT
ma-80	798	9	d2	d2	ADJ
ma-80	798	10	y	y	NOUN
ma-80	798	11			PROPN
ma-80	798	12	figure	figure	NOUN
ma-80	798	13	27	27	NUM
ma-80	798	14	.	.	PUNCT
ma-80	799	1	illustration	illustration	NOUN
ma-80	799	2	of	of	ADP
ma-80	799	3	demarcation	demarcation	NOUN
ma-80	799	4	that	that	PRON
ma-80	799	5	underpins	underpin	VERB
ma-80	799	6	determination	determination	NOUN
ma-80	799	7	of	of	ADP
ma-80	799	8	,	,	PUNCT
ma-80	799	9	to	to	ADP
ma-80	799	10	a	a	DET
ma-80	799	11	set	set	ADJ
ma-80	799	12	resolution	resolution	NOUN
ma-80	799	13	of	of	ADP
ma-80	799	14	,	,	PUNCT
ma-80	799	15	between	between	ADP
ma-80	799	16	and	and	CCONJ
ma-80	799	17	.	.	PUNCT
ma-80	800	1	w	w	NOUN
ma-80	800	2	y	y	NOUN
ma-80	800	3			PROPN
ma-80	800	4			NOUN
ma-80	801	1	ke	ke	NOUN
ma-80	801	2	k	k	PROPN
ma-80	802	1	k	k	PROPN
ma-80	802	2	1+	1+	PROPN
ma-80	802	3	ek	ek	PROPN
ma-80	802	4	1	1	NUM
ma-80	803	1	+	+	NUM
ma-80	803	2	y	y	PROPN
ma-80	803	3	k	k	PROPN
ma-80	803	4	+	+	PROPN
ma-80	804	1	k	k	PROPN
ma-80	804	2	1	1	NUM
ma-80	804	3	+	+	NUM
ma-80	804	4	k	k	X
ma-80	804	5	+	+	PROPN
ma-80	804	6	ek	ek	PROPN
ma-80	804	7	+	+	PROPN
ma-80	805	1	k	k	PROPN
ma-80	805	2	ke	ke	PROPN
ma-80	805	3	k	k	PROPN
ma-80	805	4	w	w	PROPN
ma-80	805	5	y	y	NOUN
ma-80	805	6			PUNCT
ma-80	806	1	k	k	PROPN
ma-80	807	1	2+	2+	NUM
ma-80	807	2	k	k	X
ma-80	807	3	2+	2+	NUM
ma-80	807	4	ek	ek	PUNCT
ma-80	807	5	2+	2+	NUM
ma-80	808	1	k	k	X
ma-80	809	1	1+	1+	NUM
ma-80	809	2	ek	ek	NOUN
ma-80	809	3	1	1	NUM
ma-80	809	4	+	+	SYM
ma-80	809	5	k	k	PROPN
ma-80	809	6	1	1	NUM
ma-80	809	7	–+	–+	PROPN
ma-80	809	8	ek	ek	ADV
ma-80	810	1	1	1	NUM
ma-80	810	2	–+	–+	SYM
ma-80	810	3	k	k	NOUN
ma-80	811	1	1	1	NUM
ma-80	811	2	–+	–+	NUM
ma-80	811	3	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	NOUN
ma-80	811	4	the	the	DET
ma-80	811	5	number	number	NOUN
ma-80	811	6	of	of	ADP
ma-80	811	7	terms	term	NOUN
ma-80	811	8	in	in	ADP
ma-80	811	9	the	the	DET
ma-80	811	10	summation	summation	NOUN
ma-80	811	11	defined	define	VERB
ma-80	811	12	by	by	ADP
ma-80	811	13	equation	equation	NOUN
ma-80	811	14	109	109	NUM
ma-80	811	15	comprises	comprise	NOUN
ma-80	811	16	approximately	approximately	ADV
ma-80	811	17	terms	term	NOUN
ma-80	811	18	for	for	ADP
ma-80	811	19	the	the	DET
ma-80	811	20	evaluation	evaluation	NOUN
ma-80	811	21	of	of	ADP
ma-80	811	22	,	,	PUNCT
ma-80	811	23	plus	plus	CCONJ
ma-80	811	24	terms	term	NOUN
ma-80	811	25	for	for	ADP
ma-80	811	26	the	the	DET
ma-80	811	27	summations	summation	NOUN
ma-80	811	28	comprising	comprising	NOUN
ma-80	811	29	and	and	CCONJ
ma-80	811	30	terms	term	NOUN
ma-80	811	31	for	for	ADP
ma-80	811	32	the	the	DET
ma-80	811	33	summation	summation	NOUN
ma-80	811	34	of	of	ADP
ma-80	811	35	,	,	PUNCT
ma-80	811	36	,	,	PUNCT
ma-80	811	37	.	.	PUNCT
ma-80	812	1	7.6.2	7.6.2	X
ma-80	812	2	.	.	PUNCT
ma-80	812	3	note	note	NOUN
ma-80	812	4	.	.	PUNCT
ma-80	813	1	theorem	theorem	VERB
ma-80	813	2	7.4	7.4	NUM
ma-80	813	3	defines	define	VERB
ma-80	813	4	a	a	DET
ma-80	813	5	series	series	NOUN
ma-80	813	6	for	for	ADP
ma-80	813	7	the	the	DET
ma-80	813	8	lambert	lambert	PROPN
ma-80	813	9	w	w	PROPN
ma-80	813	10	function	function	PROPN
ma-80	813	11	,	,	PUNCT
ma-80	813	12	which	which	PRON
ma-80	813	13	,	,	PUNCT
ma-80	813	14	by	by	ADP
ma-80	813	15	construction	construction	NOUN
ma-80	813	16	is	be	AUX
ma-80	813	17	convergent	convergent	ADJ
ma-80	813	18	,	,	PUNCT
ma-80	813	19	i.e.	i.e.	X
ma-80	813	20	(	(	PUNCT
ma-80	813	21	113	113	NUM
ma-80	813	22	)	)	PUNCT
ma-80	813	23	and	and	CCONJ
ma-80	813	24	is	be	AUX
ma-80	813	25	such	such	ADJ
ma-80	813	26	that	that	SCONJ
ma-80	813	27	(	(	PUNCT
ma-80	813	28	114	114	NUM
ma-80	813	29	)	)	PUNCT
ma-80	813	30	8	8	NUM
ma-80	813	31	.	.	PUNCT
ma-80	814	1	conclusion	conclusion	NOUN
ma-80	814	2	a	a	DET
ma-80	814	3	geometric	geometric	ADJ
ma-80	814	4	based	base	VERB
ma-80	814	5	approach	approach	NOUN
ma-80	814	6	for	for	ADP
ma-80	814	7	iteratively	iteratively	ADV
ma-80	814	8	specifying	specify	VERB
ma-80	814	9	approximations	approximation	NOUN
ma-80	814	10	to	to	ADP
ma-80	814	11	the	the	DET
ma-80	814	12	lambert	lambert	PROPN
ma-80	814	13	w	w	PROPN
ma-80	814	14	function	function	PROPN
ma-80	814	15	,	,	PUNCT
ma-80	814	16	which	which	PRON
ma-80	814	17	can	can	AUX
ma-80	814	18	achieve	achieve	VERB
ma-80	814	19	any	any	DET
ma-80	814	20	set	set	ADJ
ma-80	814	21	relative	relative	ADJ
ma-80	814	22	error	error	NOUN
ma-80	814	23	bound	bind	VERB
ma-80	814	24	over	over	ADP
ma-80	814	25	the	the	DET
ma-80	814	26	interval	interval	NOUN
ma-80	814	27	,	,	PUNCT
ma-80	814	28	was	be	AUX
ma-80	814	29	detailed	detail	VERB
ma-80	814	30	.	.	PUNCT
ma-80	815	1	the	the	DET
ma-80	815	2	approximations	approximation	NOUN
ma-80	815	3	are	be	AUX
ma-80	815	4	also	also	ADV
ma-80	815	5	valid	valid	ADJ
ma-80	815	6	for	for	ADP
ma-80	815	7	the	the	DET
ma-80	815	8	interval	interval	NOUN
ma-80	815	9	but	but	CCONJ
ma-80	815	10	are	be	AUX
ma-80	815	11	not	not	PART
ma-80	815	12	sharp	sharp	ADJ
ma-80	815	13	at	at	ADP
ma-80	815	14	the	the	DET
ma-80	815	15	point	point	NOUN
ma-80	815	16	.	.	PUNCT
ma-80	816	1	convergence	convergence	NOUN
ma-80	816	2	was	be	AUX
ma-80	816	3	proved	prove	VERB
ma-80	816	4	.	.	PUNCT
ma-80	817	1	for	for	ADP
ma-80	817	2	the	the	DET
ma-80	817	3	interval	interval	NOUN
ma-80	817	4	,	,	PUNCT
ma-80	817	5	arbitrarily	arbitrarily	ADV
ma-80	817	6	accurate	accurate	ADJ
ma-80	817	7	approximations	approximation	NOUN
ma-80	817	8	,	,	PUNCT
ma-80	817	9	based	base	VERB
ma-80	817	10	on	on	ADP
ma-80	817	11	a	a	DET
ma-80	817	12	two	two	NUM
ma-80	817	13	point	point	NOUN
ma-80	817	14	spline	spline	NOUN
ma-80	817	15	approximation	approximation	NOUN
ma-80	817	16	,	,	PUNCT
ma-80	817	17	were	be	AUX
ma-80	817	18	specified	specify	VERB
ma-80	817	19	.	.	PUNCT
ma-80	818	1	iteration	iteration	NOUN
ma-80	818	2	,	,	PUNCT
ma-80	818	3	either	either	CCONJ
ma-80	818	4	by	by	ADP
ma-80	818	5	using	use	VERB
ma-80	818	6	the	the	DET
ma-80	818	7	iteration	iteration	NOUN
ma-80	818	8	structure	structure	NOUN
ma-80	818	9	inherent	inherent	ADJ
ma-80	818	10	in	in	ADP
ma-80	818	11	the	the	DET
ma-80	818	12	definition	definition	NOUN
ma-80	818	13	of	of	ADP
ma-80	818	14	the	the	DET
ma-80	818	15	lambert	lambert	PROPN
ma-80	818	16	w	w	PROPN
ma-80	818	17	function	function	PROPN
ma-80	818	18	,	,	PUNCT
ma-80	818	19	or	or	CCONJ
ma-80	818	20	via	via	ADP
ma-80	818	21	the	the	DET
ma-80	818	22	newton	newton	PROPN
ma-80	818	23	-	-	PUNCT
ma-80	818	24	raphson	raphson	PROPN
ma-80	818	25	method	method	NOUN
ma-80	818	26	,	,	PUNCT
ma-80	818	27	leads	lead	VERB
ma-80	818	28	to	to	ADP
ma-80	818	29	significantly	significantly	ADV
ma-80	818	30	improved	improve	VERB
ma-80	818	31	approximations	approximation	NOUN
ma-80	818	32	albeit	albeit	SCONJ
ma-80	818	33	with	with	ADP
ma-80	818	34	increasing	increase	VERB
ma-80	818	35	complex	complex	ADJ
ma-80	818	36	functional	functional	ADJ
ma-80	818	37	forms	form	NOUN
ma-80	818	38	.	.	PUNCT
ma-80	819	1	applications	application	NOUN
ma-80	819	2	of	of	ADP
ma-80	819	3	the	the	DET
ma-80	819	4	approximations	approximation	NOUN
ma-80	819	5	were	be	AUX
ma-80	819	6	detailed	detail	VERB
ma-80	819	7	and	and	CCONJ
ma-80	819	8	include	include	VERB
ma-80	819	9	,	,	PUNCT
ma-80	819	10	first	first	ADV
ma-80	819	11	,	,	PUNCT
ma-80	819	12	analytical	analytical	ADJ
ma-80	819	13	expressions	expression	NOUN
ma-80	819	14	for	for	ADP
ma-80	819	15	the	the	DET
ma-80	819	16	lambert	lambert	PROPN
ma-80	819	17	w	w	PROPN
ma-80	819	18	function	function	NOUN
ma-80	819	19	that	that	PRON
ma-80	819	20	achieve	achieve	VERB
ma-80	819	21	set	set	ADJ
ma-80	819	22	relative	relative	ADJ
ma-80	819	23	error	error	NOUN
ma-80	819	24	bounds	bound	NOUN
ma-80	819	25	over	over	ADP
ma-80	819	26	the	the	DET
ma-80	819	27	interval	interval	NOUN
ma-80	819	28	.	.	PUNCT
ma-80	820	1	second	second	ADJ
ma-80	820	2	,	,	PUNCT
ma-80	820	3	based	base	VERB
ma-80	820	4	on	on	ADP
ma-80	820	5	the	the	DET
ma-80	820	6	geometry	geometry	NOUN
ma-80	820	7	inherent	inherent	ADJ
ma-80	820	8	in	in	ADP
ma-80	820	9	the	the	DET
ma-80	820	10	approximations	approximation	NOUN
ma-80	820	11	,	,	PUNCT
ma-80	820	12	upper	upper	ADJ
ma-80	820	13	and	and	CCONJ
ma-80	820	14	lower	low	ADJ
ma-80	820	15	bounds	bound	NOUN
ma-80	820	16	for	for	ADP
ma-80	820	17	the	the	DET
ma-80	820	18	lambert	lambert	PROPN
ma-80	820	19	w	w	PROPN
ma-80	820	20	function	function	NOUN
ma-80	820	21	that	that	PRON
ma-80	820	22	can	can	AUX
ma-80	820	23	be	be	AUX
ma-80	820	24	made	make	VERB
ma-80	820	25	arbitrary	arbitrary	ADJ
ma-80	820	26	accurate	accurate	ADJ
ma-80	820	27	.	.	PUNCT
ma-80	821	1	third	third	ADJ
ma-80	821	2	,	,	PUNCT
ma-80	821	3	higher	high	ADJ
ma-80	821	4	accuracy	accuracy	NOUN
ma-80	821	5	spline	spline	NOUN
ma-80	821	6	based	base	VERB
ma-80	821	7	approximations	approximation	NOUN
ma-80	821	8	for	for	ADP
ma-80	821	9	the	the	DET
ma-80	821	10	lambert	lambert	PROPN
ma-80	821	11	w	w	PROPN
ma-80	821	12	function	function	NOUN
ma-80	821	13	based	base	VERB
ma-80	821	14	on	on	ADP
ma-80	821	15	the	the	DET
ma-80	821	16	defined	define	VERB
ma-80	821	17	upper	upper	ADJ
ma-80	821	18	and	and	CCONJ
ma-80	821	19	lower	low	ADJ
ma-80	821	20	bounded	bounded	ADJ
ma-80	821	21	functions	function	NOUN
ma-80	821	22	.	.	PUNCT
ma-80	822	1	fourth	fourth	ADJ
ma-80	822	2	,	,	PUNCT
ma-80	822	3	analytical	analytical	ADJ
ma-80	822	4	expressions	expression	NOUN
ma-80	822	5	for	for	ADP
ma-80	822	6	the	the	DET
ma-80	822	7	evaluation	evaluation	NOUN
ma-80	822	8	of	of	ADP
ma-80	822	9	,	,	PUNCT
ma-80	822	10	and	and	CCONJ
ma-80	822	11	the	the	DET
ma-80	822	12	integral	integral	ADJ
ma-80	822	13	of	of	ADP
ma-80	822	14	,	,	PUNCT
ma-80	822	15	without	without	ADP
ma-80	822	16	knowledge	knowledge	NOUN
ma-80	822	17	of	of	ADP
ma-80	822	18	for	for	ADP
ma-80	822	19	.	.	PUNCT
ma-80	823	1	finally	finally	ADV
ma-80	823	2	,	,	PUNCT
ma-80	823	3	a	a	DET
ma-80	823	4	direct	direct	ADJ
ma-80	823	5	approach	approach	NOUN
ma-80	823	6	for	for	ADP
ma-80	823	7	evaluating	evaluate	VERB
ma-80	823	8	the	the	DET
ma-80	823	9	lambert	lambert	PROPN
ma-80	823	10	w	w	PROPN
ma-80	823	11	function	function	NOUN
ma-80	823	12	to	to	PART
ma-80	823	13	achieve	achieve	VERB
ma-80	823	14	a	a	DET
ma-80	823	15	prior	prior	ADJ
ma-80	823	16	defined	define	VERB
ma-80	823	17	error	error	NOUN
ma-80	823	18	.	.	PUNCT
ma-80	824	1	acknowledgement	acknowledgement	NOUN
ma-80	824	2	:	:	PUNCT
ma-80	824	3	the	the	DET
ma-80	824	4	author	author	NOUN
ma-80	824	5	is	be	AUX
ma-80	824	6	pleased	pleased	ADJ
ma-80	824	7	to	to	PART
ma-80	824	8	acknowledge	acknowledge	VERB
ma-80	824	9	the	the	DET
ma-80	824	10	support	support	NOUN
ma-80	824	11	of	of	ADP
ma-80	824	12	prof	prof	PROPN
ma-80	824	13	.	.	PUNCT
ma-80	825	1	a.	a.	NOUN
ma-80	825	2	zoubir	zoubir	PROPN
ma-80	825	3	,	,	PUNCT
ma-80	825	4	spg	spg	INTJ
ma-80	825	5	,	,	PUNCT
ma-80	825	6	technische	technische	PROPN
ma-80	825	7	universität	universität	PROPN
ma-80	825	8	darmstadt	darmstadt	PROPN
ma-80	825	9	,	,	PUNCT
ma-80	825	10	darmstadt	darmstadt	PROPN
ma-80	825	11	,	,	PUNCT
ma-80	825	12	germany	germany	PROPN
ma-80	825	13	,	,	PUNCT
ma-80	825	14	who	who	PRON
ma-80	825	15	hosted	host	VERB
ma-80	825	16	a	a	DET
ma-80	825	17	visit	visit	NOUN
ma-80	825	18	where	where	SCONJ
ma-80	825	19	the	the	DET
ma-80	825	20	research	research	NOUN
ma-80	825	21	,	,	PUNCT
ma-80	825	22	underpinning	underpin	VERB
ma-80	825	23	this	this	DET
ma-80	825	24	paper	paper	NOUN
ma-80	825	25	,	,	PUNCT
ma-80	825	26	was	be	AUX
ma-80	825	27	completed	complete	VERB
ma-80	825	28	.	.	PUNCT
ma-80	826	1	appendix	appendix	VERB
ma-80	826	2	a.	a.	NOUN
ma-80	826	3	properties	property	NOUN
ma-80	826	4	of	of	ADP
ma-80	826	5	lambert	lambert	PROPN
ma-80	826	6	w	w	PROPN
ma-80	826	7	function	function	VERB
ma-80	826	8	the	the	DET
ma-80	826	9	following	follow	VERB
ma-80	826	10	are	be	AUX
ma-80	826	11	useful	useful	ADJ
ma-80	826	12	properties	property	NOUN
ma-80	826	13	of	of	ADP
ma-80	826	14	the	the	DET
ma-80	826	15	lambert	lambert	PROPN
ma-80	826	16	w	w	PROPN
ma-80	826	17	function	function	PROPN
ma-80	826	18	:	:	PUNCT
ma-80	826	19	(	(	PUNCT
ma-80	826	20	115	115	NUM
ma-80	826	21	)	)	PUNCT
ma-80	826	22	(	(	PUNCT
ma-80	826	23	116	116	NUM
ma-80	826	24	)	)	PUNCT
ma-80	826	25	the	the	DET
ma-80	826	26	latter	latter	ADJ
ma-80	826	27	formula	formula	NOUN
ma-80	826	28	underpins	underpin	VERB
ma-80	826	29	the	the	DET
ma-80	826	30	iteration	iteration	NOUN
ma-80	826	31	:	:	PUNCT
ma-80	826	32	w	w	NOUN
ma-80	826	33	y	y	NOUN
ma-80	826	34			PROPN
ma-80	827	1	w	w	NOUN
ma-80	827	2	y	y	NOUN
ma-80	827	3			PROPN
ma-80	827	4	10q	10q	NOUN
ma-80	827	5	d1	d1	VERB
ma-80	827	6	y	y	NOUN
ma-80	827	7			PROPN
ma-80	827	8	d2	d2	NOUN
ma-80	827	9	y	y	NOUN
ma-80	827	10			ADP
ma-80	827	11			NOUN
ma-80	827	12	dq	dq	ADP
ma-80	827	13	y	y	NOUN
ma-80	827	14			ADP
ma-80	827	15			NUM
ma-80	827	16	q	q	PROPN
ma-80	827	17	1	1	NUM
ma-80	827	18	–	–	PUNCT
ma-80	827	19	d1	d1	PROPN
ma-80	827	20	y	y	NOUN
ma-80	827	21			PROPN
ma-80	827	22	d2	d2	NOUN
ma-80	827	23	y	y	NOUN
ma-80	827	24	+	+	PUNCT
ma-80	828	1			NOUN
ma-80	828	2	d1	d1	PROPN
ma-80	828	3	y	y	NOUN
ma-80	828	4			PROPN
ma-80	828	5	d2	d2	VERB
ma-80	828	6	y	y	NOUN
ma-80	828	7			PROPN
ma-80	828	8			NOUN
ma-80	828	9	dq	dq	NOUN
ma-80	828	10	y	y	NOUN
ma-80	828	11	+	+	PUNCT
ma-80	829	1	+	+	PUNCT
ma-80	830	1	+	+	NUM
ma-80	830	2	w	w	ADJ
ma-80	830	3	y	y	NOUN
ma-80	830	4			PROPN
ma-80	830	5	w	w	NOUN
ma-80	830	6	y	y	NOUN
ma-80	830	7			PROPN
ma-80	830	8	d1	d1	PROPN
ma-80	830	9	y	y	NOUN
ma-80	830	10			PROPN
ma-80	830	11	d2	d2	VERB
ma-80	830	12	y	y	NOUN
ma-80	831	1			PUNCT
ma-80	831	2	+	+	PROPN
ma-80	832	1	+	+	CCONJ
ma-80	832	2	+	+	PROPN
ma-80	832	3	=	=	SYM
ma-80	832	4	y	y	PROPN
ma-80	832	5	0	0	NUM
ma-80	832	6			NUM
ma-80	832	7	w	w	PROPN
ma-80	832	8	y	y	X
ma-80	832	9			PROPN
ma-80	832	10	w	w	NOUN
ma-80	832	11	y	y	NOUN
ma-80	832	12			PROPN
ma-80	832	13	d1	d1	VERB
ma-80	832	14	y	y	NOUN
ma-80	832	15			PROPN
ma-80	832	16			NOUN
ma-80	832	17	dq	dq	NOUN
ma-80	832	18	y	y	NOUN
ma-80	832	19	+	+	PUNCT
ma-80	833	1	+	+	PUNCT
ma-80	834	1	+	+	ADJ
ma-80	834	2	–	–	PUNCT
ma-80	834	3	10	10	NUM
ma-80	834	4	q	q	NOUN
ma-80	834	5	–	–	PUNCT
ma-80	834	6	.	.	NOUN
ma-80	834	7	0	0	NUM
ma-80	835	1			NUM
ma-80	835	2			NOUN
ma-80	835	3	1	1	NUM
ma-80	835	4	e	e	ADV
ma-80	835	5	–	–	PUNCT
ma-80	835	6	0	0	INTJ
ma-80	835	7			NOUN
ma-80	835	8	1	1	NUM
ma-80	835	9	e	e	NOUN
ma-80	835	10	–	–	PUNCT
ma-80	835	11	1	1	NUM
ma-80	835	12	e	e	NOUN
ma-80	835	13	–	–	PUNCT
ma-80	835	14	0	0	NUM
ma-80	835	15			NOUN
ma-80	835	16	0	0	NUM
ma-80	835	17			VERB
ma-80	835	18	w	w	NOUN
ma-80	835	19	y	y	NOUN
ma-80	835	20			PROPN
ma-80	835	21	w	w	NOUN
ma-80	835	22	y	y	NOUN
ma-80	835	23			PROPN
ma-80	835	24	w	w	NOUN
ma-80	835	25	y	y	NOUN
ma-80	835	26			PUNCT
ma-80	835	27	y	y	PROPN
ma-80	835	28	0	0	NUM
ma-80	835	29			NUM
ma-80	835	30			NUM
ma-80	835	31	w	w	ADP
ma-80	835	32	z	z	PROPN
ma-80	835	33	z	z	PROPN
ma-80	835	34	ln	ln	NOUN
ma-80	835	35			PROPN
ma-80	835	36	z	z	PROPN
ma-80	835	37	ln	ln	PROPN
ma-80	835	38	=	=	PROPN
ma-80	835	39	z	z	NOUN
ma-80	835	40	0	0	PUNCT
ma-80	835	41	w	w	ADJ
ma-80	835	42	y	y	NOUN
ma-80	835	43			PUNCT
ma-80	835	44	y	y	PROPN
ma-80	835	45	w	w	NOUN
ma-80	835	46	y	y	NOUN
ma-80	836	1			PROPN
ma-80	836	2	------------ln	------------ln	VERB
ma-80	836	3	y	y	NOUN
ma-80	836	4	ln	ln	PROPN
ma-80	836	5	w	w	NOUN
ma-80	836	6	y	y	NOUN
ma-80	836	7			X
ma-80	836	8	ln	ln	NOUN
ma-80	836	9	–	–	PUNCT
ma-80	836	10	=	=	NOUN
ma-80	836	11	=	=	SYM
ma-80	836	12	y	y	PROPN
ma-80	836	13	0.	0.	NUM
ma-80	836	14	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	PROPN
ma-80	836	15	(	(	PUNCT
ma-80	836	16	117	117	NUM
ma-80	836	17	)	)	PUNCT
ma-80	836	18	to	to	PART
ma-80	836	19	prove	prove	VERB
ma-80	836	20	that	that	SCONJ
ma-80	836	21	,	,	PUNCT
ma-80	836	22	consider	consider	VERB
ma-80	836	23	which	which	PRON
ma-80	836	24	implies	imply	VERB
ma-80	836	25	and	and	CCONJ
ma-80	836	26	,	,	PUNCT
ma-80	836	27	thus	thus	ADV
ma-80	836	28	,	,	PUNCT
ma-80	836	29	.	.	PUNCT
ma-80	837	1	the	the	DET
ma-80	837	2	relationship	relationship	NOUN
ma-80	837	3	follows	follow	VERB
ma-80	837	4	from	from	ADP
ma-80	837	5	the	the	DET
ma-80	837	6	definitions	definition	NOUN
ma-80	837	7	,	,	PUNCT
ma-80	837	8	which	which	PRON
ma-80	837	9	implies	imply	VERB
ma-80	837	10	and	and	CCONJ
ma-80	837	11	,	,	PUNCT
ma-80	837	12	thus	thus	ADV
ma-80	837	13	,	,	PUNCT
ma-80	837	14	.	.	PUNCT
ma-80	838	1	a.1	a.1	X
ma-80	838	2	.	.	PUNCT
ma-80	839	1	differentiation	differentiation	NOUN
ma-80	839	2	.	.	PUNCT
ma-80	840	1	the	the	DET
ma-80	840	2	derivatives	derivative	NOUN
ma-80	840	3	of	of	ADP
ma-80	840	4	the	the	DET
ma-80	840	5	lambert	lambert	PROPN
ma-80	840	6	w	w	PROPN
ma-80	840	7	function	function	NOUN
ma-80	840	8	are	be	AUX
ma-80	840	9	defined	define	VERB
ma-80	840	10	according	accord	VERB
ma-80	840	11	to	to	ADP
ma-80	840	12	(	(	PUNCT
ma-80	840	13	118	118	NUM
ma-80	840	14	)	)	PUNCT
ma-80	840	15	(	(	PUNCT
ma-80	840	16	119	119	NUM
ma-80	840	17	)	)	PUNCT
ma-80	840	18	where	where	SCONJ
ma-80	840	19	the	the	DET
ma-80	840	20	second	second	ADJ
ma-80	840	21	inequalities	inequality	NOUN
ma-80	840	22	follow	follow	VERB
ma-80	840	23	from	from	ADP
ma-80	840	24	the	the	DET
ma-80	840	25	relationship	relationship	NOUN
ma-80	840	26	and	and	CCONJ
ma-80	840	27	the	the	DET
ma-80	840	28	polynomial	polynomial	NOUN
ma-80	840	29	is	be	AUX
ma-80	840	30	defined	define	VERB
ma-80	840	31	according	accord	VERB
ma-80	840	32	to	to	ADP
ma-80	840	33	(	(	PUNCT
ma-80	840	34	120	120	NUM
ma-80	840	35	)	)	PUNCT
ma-80	840	36	the	the	DET
ma-80	840	37	coefficients	coefficient	NOUN
ma-80	840	38	in	in	ADP
ma-80	840	39	this	this	DET
ma-80	840	40	expression	expression	NOUN
ma-80	840	41	are	be	AUX
ma-80	840	42	defined	define	VERB
ma-80	840	43	according	accord	VERB
ma-80	840	44	to	to	ADP
ma-80	840	45	(	(	PUNCT
ma-80	840	46	https://oeis.org/a042977	https://oeis.org/a042977	X
ma-80	840	47	;	;	PUNCT
ma-80	840	48	[	[	X
ma-80	840	49	7	7	NUM
ma-80	840	50	]	]	PUNCT
ma-80	840	51	,	,	PUNCT
ma-80	840	52	eqn	eqn	PROPN
ma-80	840	53	3.4	3.4	NUM
ma-80	840	54	;	;	PUNCT
ma-80	840	55	[	[	X
ma-80	840	56	23	23	NUM
ma-80	840	57	]	]	PUNCT
ma-80	840	58	,	,	PUNCT
ma-80	840	59	p.	p.	NOUN
ma-80	840	60	1370	1370	NUM
ma-80	840	61	):	):	PUNCT
ma-80	840	62	(	(	PUNCT
ma-80	840	63	121	121	NUM
ma-80	840	64	)	)	PUNCT
ma-80	840	65	explicit	explicit	ADJ
ma-80	840	66	expressions	expression	NOUN
ma-80	840	67	are	be	AUX
ma-80	840	68	:	:	PUNCT
ma-80	840	69	(	(	PUNCT
ma-80	840	70	122	122	X
ma-80	840	71	)	)	PUNCT
ma-80	840	72	appendix	appendix	NOUN
ma-80	840	73	b.	b.	PROPN
ma-80	840	74	proof	proof	NOUN
ma-80	840	75	of	of	ADP
ma-80	840	76	theorem	theorem	ADJ
ma-80	840	77	3.2	3.2	NUM
ma-80	840	78	the	the	DET
ma-80	840	79	iteration	iteration	NOUN
ma-80	840	80	formula	formula	NOUN
ma-80	840	81	,	,	PUNCT
ma-80	840	82	as	as	SCONJ
ma-80	840	83	specified	specify	VERB
ma-80	840	84	in	in	ADP
ma-80	840	85	theorem	theorem	ADJ
ma-80	840	86	3.1	3.1	NUM
ma-80	840	87	,	,	PUNCT
ma-80	840	88	yields	yield	VERB
ma-80	840	89	the	the	DET
ma-80	840	90	first	first	ADJ
ma-80	840	91	order	order	NOUN
ma-80	840	92	approximations	approximation	NOUN
ma-80	840	93	as	as	SCONJ
ma-80	840	94	stated	state	VERB
ma-80	840	95	in	in	ADP
ma-80	840	96	equation	equation	NOUN
ma-80	840	97	30	30	NUM
ma-80	840	98	:	:	PUNCT
ma-80	840	99	(	(	PUNCT
ma-80	840	100	123	123	NUM
ma-80	840	101	)	)	PUNCT
ma-80	840	102	w	w	ADP
ma-80	840	103	y	y	NOUN
ma-80	840	104			PROPN
ma-80	840	105	y	y	NOUN
ma-80	841	1	ln	ln	PRON
ma-80	841	2	y	y	NOUN
ma-80	841	3	ln	ln	PRON
ma-80	842	1	w	w	NOUN
ma-80	842	2	y	y	NOUN
ma-80	842	3			PUNCT
ma-80	842	4	ln–	ln–	VERB
ma-80	842	5	ln	ln	NOUN
ma-80	842	6	–	–	PUNCT
ma-80	842	7	=	=	AUX
ma-80	842	8	w	w	ADP
ma-80	842	9	y	y	NOUN
ma-80	843	1			PROPN
ma-80	844	1	y	y	NOUN
ma-80	845	1	ln	ln	DET
ma-80	845	2	y	y	NOUN
ma-80	846	1	ln	ln	DET
ma-80	846	2	y	y	NOUN
ma-80	846	3	ln	ln	PRON
ma-80	847	1	w	w	NOUN
ma-80	847	2	y	y	NOUN
ma-80	847	3			PUNCT
ma-80	847	4	ln–	ln–	VERB
ma-80	847	5	ln–	ln–	PROPN
ma-80	847	6	ln	ln	NOUN
ma-80	847	7	–	–	PUNCT
ma-80	847	8	=	=	NUM
ma-80	847	9			NOUN
ma-80	847	10	w	w	PROPN
ma-80	847	11	z	z	PROPN
ma-80	847	12	z	z	PROPN
ma-80	847	13	ln	ln	NOUN
ma-80	847	14			PROPN
ma-80	848	1	z	z	PROPN
ma-80	848	2	ln=	ln=	PUNCT
ma-80	849	1	f	f	PROPN
ma-80	849	2	x	x	PROPN
ma-80	850	1			PUNCT
ma-80	850	2	xe	xe	PROPN
ma-80	850	3	x	x	X
ma-80	850	4	=	=	PUNCT
ma-80	850	5	f	f	PROPN
ma-80	850	6	z	z	PROPN
ma-80	850	7	ln	ln	PROPN
ma-80	850	8			PROPN
ma-80	850	9	z	z	PROPN
ma-80	850	10	z	z	PROPN
ma-80	850	11	ln=	ln=	PUNCT
ma-80	851	1	z	z	PROPN
ma-80	851	2	ln	ln	PROPN
ma-80	852	1	f	f	PROPN
ma-80	852	2	1	1	NUM
ma-80	852	3	–	–	PUNCT
ma-80	852	4	z	z	NOUN
ma-80	852	5	z	z	PROPN
ma-80	852	6	ln	ln	NOUN
ma-80	852	7			PROPN
ma-80	852	8	w	w	PROPN
ma-80	852	9	z	z	PROPN
ma-80	852	10	z	z	PROPN
ma-80	852	11	ln	ln	NOUN
ma-80	852	12	=	=	NOUN
ma-80	852	13	=	=	NOUN
ma-80	852	14	w	w	NOUN
ma-80	852	15	y	y	NOUN
ma-80	852	16			PROPN
ma-80	852	17	y	y	NOUN
ma-80	852	18	ln	ln	NOUN
ma-80	852	19	w	w	NOUN
ma-80	852	20	y	y	NOUN
ma-80	852	21			PUNCT
ma-80	853	1	ln–=	ln–=	VERB
ma-80	853	2	y	y	PROPN
ma-80	853	3	xe	xe	PROPN
ma-80	853	4	x	x	PUNCT
ma-80	854	1	=	=	PUNCT
ma-80	854	2	x	x	PUNCT
ma-80	854	3	w	w	X
ma-80	854	4	y	y	NOUN
ma-80	854	5	=	=	NOUN
ma-80	854	6	y	y	NOUN
ma-80	854	7	ln	ln	NOUN
ma-80	855	1	x	x	PUNCT
ma-80	855	2	x	x	X
ma-80	855	3	ln+=	ln+=	NOUN
ma-80	855	4	x	x	X
ma-80	855	5	y	y	NOUN
ma-80	855	6	ln	ln	PROPN
ma-80	855	7	w	w	NOUN
ma-80	855	8	y	y	NOUN
ma-80	855	9			PUNCT
ma-80	856	1	ln–=	ln–=	PRON
ma-80	856	2	w	w	ADJ
ma-80	856	3	1	1	NUM
ma-80	856	4			PROPN
ma-80	856	5	y	y	NOUN
ma-80	856	6			PUNCT
ma-80	856	7	e	e	NOUN
ma-80	856	8	w	w	NOUN
ma-80	856	9	y	y	PROPN
ma-80	856	10			PROPN
ma-80	856	11	–	–	PUNCT
ma-80	856	12	1	1	NUM
ma-80	856	13	w	w	NOUN
ma-80	856	14	y	y	NOUN
ma-80	856	15	+	+	CCONJ
ma-80	856	16	---------------------w	---------------------w	PUNCT
ma-80	857	1	y	y	NOUN
ma-80	857	2			PUNCT
ma-80	857	3	y	y	PROPN
ma-80	857	4	1	1	NUM
ma-80	857	5	w	w	NOUN
ma-80	857	6	y	y	NOUN
ma-80	857	7	+	+	PROPN
ma-80	857	8			NOUN
ma-80	857	9	------------------------------=	------------------------------=	PUNCT
ma-80	858	1	=	=	PUNCT
ma-80	858	2	w	w	NOUN
ma-80	858	3	k	k	NOUN
ma-80	858	4			PROPN
ma-80	858	5	y	y	NOUN
ma-80	858	6			PROPN
ma-80	858	7	w	w	PROPN
ma-80	858	8	k	k	PROPN
ma-80	858	9	y	y	PROPN
ma-80	858	10	pk	pk	NOUN
ma-80	858	11	w	w	NOUN
ma-80	858	12	y	y	NOUN
ma-80	858	13			PUNCT
ma-80	858	14			NOUN
ma-80	858	15	y	y	PROPN
ma-80	858	16	k	k	PROPN
ma-80	858	17	1	1	NUM
ma-80	858	18	w	w	NOUN
ma-80	858	19	y	y	NOUN
ma-80	858	20	+	+	ADP
ma-80	858	21			NOUN
ma-80	858	22	2k	2k	NUM
ma-80	858	23	1	1	NUM
ma-80	858	24	–	–	PUNCT
ma-80	858	25	-------------------------------------------pk	-------------------------------------------pk	NOUN
ma-80	858	26	w	w	PROPN
ma-80	858	27	y	y	NOUN
ma-80	858	28			NOUN
ma-80	858	29	e	e	NOUN
ma-80	858	30	kw	kw	PROPN
ma-80	858	31	–	–	PUNCT
ma-80	858	32	y	y	NOUN
ma-80	858	33			PROPN
ma-80	858	34	1	1	NUM
ma-80	858	35	w	w	NOUN
ma-80	858	36	y	y	NOUN
ma-80	858	37	+	+	ADP
ma-80	858	38	2k	2k	ADP
ma-80	858	39	1	1	NUM
ma-80	858	40	–	–	PUNCT
ma-80	858	41	------------------------------------------=	------------------------------------------=	PUNCT
ma-80	859	1	=	=	PUNCT
ma-80	859	2	y	y	PROPN
ma-80	859	3	w	w	PROPN
ma-80	859	4	y	y	PROPN
ma-80	859	5	ew	ew	NOUN
ma-80	859	6	y	y	NOUN
ma-80	859	7			PUNCT
ma-80	860	1	=	=	SYM
ma-80	860	2	pk	pk	NOUN
ma-80	860	3	pk	pk	NOUN
ma-80	860	4	r	r	PROPN
ma-80	860	5			PROPN
ma-80	860	6	ck	ck	INTJ
ma-80	860	7	0	0	ADJ
ma-80	860	8	ck	ck	INTJ
ma-80	860	9	1	1	NOUN
ma-80	860	10	r	r	NOUN
ma-80	860	11	ck	ck	NOUN
ma-80	860	12	2	2	NOUN
ma-80	860	13	r	r	NOUN
ma-80	860	14	2	2	NUM
ma-80	860	15			NOUN
ma-80	860	16	ck	ck	PROPN
ma-80	861	1	k	k	NOUN
ma-80	861	2	1–	1–	NUM
ma-80	861	3	r	r	NOUN
ma-80	861	4	k	k	NOUN
ma-80	861	5	1	1	NUM
ma-80	861	6	–	–	PUNCT
ma-80	861	7	.+	.+	PROPN
ma-80	861	8	+	+	PUNCT
ma-80	862	1	+	+	PUNCT
ma-80	863	1	+	+	ADJ
ma-80	863	2	=	=	ADJ
ma-80	863	3	cn	cn	X
ma-80	863	4	k	k	NOUN
ma-80	863	5	0	0	PUNCT
ma-80	864	1	k	k	X
ma-80	864	2	0	0	PROPN
ma-80	864	3	1–	1–	NUM
ma-80	864	4	n	n	VERB
ma-80	864	5	1	1	NUM
ma-80	864	6	+	+	NUM
ma-80	864	7	n	n	CCONJ
ma-80	864	8	n	n	DET
ma-80	864	9	1	1	NUM
ma-80	864	10	–	–	PUNCT
ma-80	864	11	k	k	NOUN
ma-80	864	12	0=	0=	NOUN
ma-80	865	1	n	n	PROPN
ma-80	865	2	1–	1–	NUM
ma-80	865	3	cn	cn	NOUN
ma-80	865	4	1	1	NUM
ma-80	865	5	–	–	PUNCT
ma-80	865	6	k	k	NOUN
ma-80	865	7	1–	1–	NUM
ma-80	865	8	–	–	PUNCT
ma-80	865	9	3	3	NUM
ma-80	865	10	n	n	NOUN
ma-80	865	11	1–	1–	NUM
ma-80	865	12			PUNCT
ma-80	865	13	k	k	PROPN
ma-80	866	1	1+	1+	PROPN
ma-80	866	2	–	–	PROPN
ma-80	866	3	cn	cn	ADJ
ma-80	866	4	1	1	NUM
ma-80	866	5	–	–	PUNCT
ma-80	866	6	k	k	NUM
ma-80	866	7	–	–	PUNCT
ma-80	866	8	k	k	PROPN
ma-80	866	9	1+	1+	NUM
ma-80	866	10	cn	cn	NOUN
ma-80	866	11	1	1	NUM
ma-80	866	12	–	–	PUNCT
ma-80	866	13	k	k	NOUN
ma-80	866	14	1++	1++	NUM
ma-80	866	15	1	1	NUM
ma-80	866	16	k	k	PROPN
ma-80	866	17	n	n	PROPN
ma-80	866	18	3–	3–	NUM
ma-80	866	19			NOUN
ma-80	866	20	n	n	PRON
ma-80	866	21	1–	1–	NUM
ma-80	866	22	cn	cn	NOUN
ma-80	866	23	1	1	NUM
ma-80	866	24	–	–	PUNCT
ma-80	866	25	k	k	NOUN
ma-80	866	26	1–	1–	NUM
ma-80	866	27	–	–	PUNCT
ma-80	866	28	3	3	NUM
ma-80	866	29	n	n	NOUN
ma-80	866	30	1–	1–	NUM
ma-80	866	31			PUNCT
ma-80	866	32	k	k	PROPN
ma-80	867	1	1+	1+	PROPN
ma-80	867	2	–	–	PROPN
ma-80	867	3	cn	cn	ADJ
ma-80	867	4	1	1	NUM
ma-80	867	5	–	–	PUNCT
ma-80	867	6	k	k	NOUN
ma-80	867	7	–	–	PUNCT
ma-80	867	8	k	k	PROPN
ma-80	867	9	n	n	CCONJ
ma-80	867	10	2–=	2–=	NUM
ma-80	867	11	n	n	NUM
ma-80	867	12	1–	1–	NUM
ma-80	867	13	cn	cn	NOUN
ma-80	867	14	1	1	NUM
ma-80	867	15	–	–	PUNCT
ma-80	867	16	k	k	NOUN
ma-80	867	17	1–	1–	NUM
ma-80	867	18	–	–	PUNCT
ma-80	867	19	n	n	NOUN
ma-80	867	20	1–	1–	NUM
ma-80	867	21	!=	!=	PUNCT
ma-80	868	1	k	k	PROPN
ma-80	868	2	n	n	CCONJ
ma-80	868	3	1–=	1–=	NUM
ma-80	868	4			NUM
ma-80	868	5			NUM
ma-80	868	6			NUM
ma-80	868	7			NUM
ma-80	868	8			NUM
ma-80	868	9			NUM
ma-80	868	10			NUM
ma-80	868	11			NOUN
ma-80	868	12	=	=	SYM
ma-80	868	13	p1	p1	NOUN
ma-80	868	14	r	r	PROPN
ma-80	868	15			PROPN
ma-80	868	16	1=	1=	NUM
ma-80	868	17	p2	p2	PROPN
ma-80	868	18	r	r	PROPN
ma-80	868	19			PROPN
ma-80	868	20	2	2	NUM
ma-80	868	21	r+	r+	NOUN
ma-80	868	22			PROPN
ma-80	868	23	–	–	PUNCT
ma-80	868	24	=	=	NUM
ma-80	868	25	p3	p3	NOUN
ma-80	868	26	r	r	VERB
ma-80	868	27			PROPN
ma-80	868	28	9	9	NUM
ma-80	868	29	8r	8r	NUM
ma-80	868	30	2r	2r	NUM
ma-80	868	31	2	2	NUM
ma-80	869	1	+	+	CCONJ
ma-80	869	2	+	+	NUM
ma-80	869	3	=	=	NOUN
ma-80	869	4	p4	p4	ADJ
ma-80	869	5	r	r	NOUN
ma-80	869	6			PROPN
ma-80	869	7	64	64	NUM
ma-80	869	8	79r	79r	NOUN
ma-80	869	9	36r	36r	NUM
ma-80	869	10	2	2	NUM
ma-80	869	11	6r	6r	NUM
ma-80	869	12	3	3	NUM
ma-80	869	13	+	+	CCONJ
ma-80	870	1	+	+	CCONJ
ma-80	870	2	+	+	ADJ
ma-80	870	3			ADJ
ma-80	870	4			NOUN
ma-80	870	5	–	–	PUNCT
ma-80	870	6	=	=	NUM
ma-80	870	7	p5	p5	ADJ
ma-80	870	8	r	r	PROPN
ma-80	870	9			PROPN
ma-80	870	10	625	625	NUM
ma-80	870	11	974r	974r	PROPN
ma-80	870	12	622r	622r	ADP
ma-80	870	13	2	2	NUM
ma-80	870	14	192r	192r	NUM
ma-80	870	15	3	3	NUM
ma-80	870	16	24r	24r	NOUN
ma-80	870	17	4	4	NUM
ma-80	870	18	+	+	CCONJ
ma-80	871	1	+	+	PUNCT
ma-80	871	2	+	+	CCONJ
ma-80	871	3	+	+	NUM
ma-80	871	4	=	=	NOUN
ma-80	871	5	p6	p6	ADJ
ma-80	871	6	r	r	PROPN
ma-80	871	7			PROPN
ma-80	871	8	7776	7776	NUM
ma-80	871	9	14543r	14543r	NUM
ma-80	871	10	11758r	11758r	NUM
ma-80	871	11	2	2	NUM
ma-80	871	12	5126r	5126r	NOUN
ma-80	871	13	3	3	NUM
ma-80	871	14	1200r	1200r	NUM
ma-80	871	15	4	4	NUM
ma-80	871	16	120r	120r	NUM
ma-80	871	17	5	5	NUM
ma-80	871	18	+	+	CCONJ
ma-80	872	1	+	+	PUNCT
ma-80	872	2	+	+	PUNCT
ma-80	872	3	+	+	CCONJ
ma-80	872	4	+	+	ADJ
ma-80	872	5			ADJ
ma-80	872	6	.–=	.–=	PROPN
ma-80	872	7	wl1	wl1	PROPN
ma-80	872	8	y	y	PROPN
ma-80	872	9			PUNCT
ma-80	872	10	y	y	PROPN
ma-80	872	11	1	1	NUM
ma-80	872	12	y+	y+	NUM
ma-80	872	13	-----------n1	-----------n1	PUNCT
ma-80	872	14	y	y	PROPN
ma-80	872	15			PROPN
ma-80	872	16	d1	d1	PROPN
ma-80	872	17	y	y	NOUN
ma-80	872	18			PUNCT
ma-80	872	19	-------------=	-------------=	NOUN
ma-80	873	1	=	=	PUNCT
ma-80	873	2	wu1	wu1	NOUN
ma-80	873	3	y	y	NOUN
ma-80	873	4			PROPN
ma-80	873	5	1	1	NUM
ma-80	873	6	y+	y+	NOUN
ma-80	873	7	ln	ln	PROPN
ma-80	874	1	1	1	NUM
ma-80	874	2	ln	ln	PROPN
ma-80	874	3	–	–	PUNCT
ma-80	874	4	d1	d1	PROPN
ma-80	874	5	y	y	NOUN
ma-80	874	6			X
ma-80	874	7	ln	ln	NOUN
ma-80	874	8	n1	n1	PROPN
ma-80	874	9	y	y	NOUN
ma-80	874	10			PROPN
ma-80	874	11	y	y	PROPN
ma-80	874	12	-------------ln	-------------ln	NOUN
ma-80	874	13	–	–	PUNCT
ma-80	874	14	=	=	NUM
ma-80	874	15	=	=	SYM
ma-80	874	16	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	NOUN
ma-80	874	17	where	where	SCONJ
ma-80	874	18	and	and	CCONJ
ma-80	874	19	.	.	PUNCT
ma-80	875	1	the	the	DET
ma-80	875	2	second	second	ADJ
ma-80	875	3	order	order	NOUN
ma-80	875	4	approximations	approximation	NOUN
ma-80	875	5	,	,	PUNCT
ma-80	875	6	as	as	SCONJ
ma-80	875	7	specified	specify	VERB
ma-80	875	8	by	by	ADP
ma-80	875	9	equation	equation	NOUN
ma-80	875	10	31	31	NUM
ma-80	875	11	,	,	PUNCT
ma-80	875	12	can	can	AUX
ma-80	875	13	be	be	AUX
ma-80	875	14	written	write	VERB
ma-80	875	15	in	in	ADP
ma-80	875	16	the	the	DET
ma-80	875	17	form	form	NOUN
ma-80	875	18	(	(	PUNCT
ma-80	875	19	124	124	NUM
ma-80	875	20	)	)	PUNCT
ma-80	875	21	where	where	SCONJ
ma-80	875	22	(	(	PUNCT
ma-80	875	23	125	125	NUM
ma-80	875	24	)	)	PUNCT
ma-80	875	25	the	the	DET
ma-80	875	26	third	third	ADJ
ma-80	875	27	order	order	NOUN
ma-80	875	28	approximations	approximation	NOUN
ma-80	875	29	,	,	PUNCT
ma-80	875	30	as	as	SCONJ
ma-80	875	31	specified	specify	VERB
ma-80	875	32	by	by	ADP
ma-80	875	33	equation	equation	NOUN
ma-80	875	34	32	32	NUM
ma-80	875	35	and	and	CCONJ
ma-80	875	36	equation	equation	NOUN
ma-80	875	37	33	33	NUM
ma-80	875	38	,	,	PUNCT
ma-80	875	39	can	can	AUX
ma-80	875	40	be	be	AUX
ma-80	875	41	written	write	VERB
ma-80	875	42	in	in	ADP
ma-80	875	43	the	the	DET
ma-80	875	44	form	form	NOUN
ma-80	875	45	:	:	PUNCT
ma-80	875	46	(	(	PUNCT
ma-80	875	47	126	126	NUM
ma-80	875	48	)	)	PUNCT
ma-80	875	49	(	(	PUNCT
ma-80	875	50	127	127	NUM
ma-80	875	51	)	)	PUNCT
ma-80	875	52	where	where	SCONJ
ma-80	875	53	(	(	PUNCT
ma-80	875	54	128	128	NUM
ma-80	875	55	)	)	PUNCT
ma-80	875	56	thus	thus	ADV
ma-80	875	57	,	,	PUNCT
ma-80	875	58	iteration	iteration	NOUN
ma-80	875	59	yields	yield	VERB
ma-80	875	60	the	the	DET
ma-80	875	61	general	general	ADJ
ma-80	875	62	formulas	formula	NOUN
ma-80	875	63	:	:	PUNCT
ma-80	875	64	(	(	PUNCT
ma-80	875	65	129	129	NUM
ma-80	875	66	)	)	PUNCT
ma-80	875	67	where	where	SCONJ
ma-80	875	68	(	(	PUNCT
ma-80	875	69	130	130	NUM
ma-80	875	70	)	)	PUNCT
ma-80	875	71	appendix	appendix	VERB
ma-80	875	72	c.	c.	NOUN
ma-80	875	73	proof	proof	NOUN
ma-80	875	74	of	of	ADP
ma-80	875	75	theorem	theorem	ADJ
ma-80	875	76	3.5	3.5	NUM
ma-80	875	77	consider	consider	VERB
ma-80	875	78	the	the	DET
ma-80	875	79	geometry	geometry	NOUN
ma-80	875	80	illustrated	illustrate	VERB
ma-80	875	81	in	in	ADP
ma-80	875	82	figure	figure	NOUN
ma-80	875	83	15	15	NUM
ma-80	875	84	and	and	CCONJ
ma-80	875	85	an	an	DET
ma-80	875	86	initial	initial	ADJ
ma-80	875	87	approximation	approximation	NOUN
ma-80	875	88	for	for	ADP
ma-80	875	89	,	,	PUNCT
ma-80	875	90	based	base	VERB
ma-80	875	91	on	on	ADP
ma-80	875	92	the	the	DET
ma-80	875	93	intersection	intersection	NOUN
ma-80	875	94	of	of	ADP
ma-80	875	95	the	the	DET
ma-80	875	96	second	second	ADJ
ma-80	875	97	order	order	NOUN
ma-80	875	98	taylor	taylor	PROPN
ma-80	875	99	series	series	PROPN
ma-80	875	100	for	for	ADP
ma-80	875	101	at	at	ADP
ma-80	875	102	the	the	DET
ma-80	875	103	origin	origin	NOUN
ma-80	875	104	,	,	PUNCT
ma-80	875	105	i.e.	i.e.	X
ma-80	875	106	n1	n1	ADJ
ma-80	875	107	y	y	NOUN
ma-80	875	108			PROPN
ma-80	875	109	y=	y=	PRON
ma-80	875	110	d1	d1	VERB
ma-80	875	111	y	y	NOUN
ma-80	875	112			PROPN
ma-80	875	113	1	1	NUM
ma-80	876	1	y+=	y+=	PROPN
ma-80	876	2	wl2	wl2	PROPN
ma-80	876	3	y	y	PROPN
ma-80	876	4			PROPN
ma-80	876	5	y	y	PROPN
ma-80	876	6	1	1	NUM
ma-80	876	7	1	1	NUM
ma-80	876	8	y+	y+	NOUN
ma-80	876	9	ln+	ln+	PUNCT
ma-80	876	10			NOUN
ma-80	876	11	1	1	NUM
ma-80	876	12	2y+	2y+	NUM
ma-80	876	13	--------------------------------------n2	--------------------------------------n2	X
ma-80	876	14	y	y	X
ma-80	876	15			PROPN
ma-80	876	16	d2	d2	NOUN
ma-80	876	17	y	y	NOUN
ma-80	876	18			PROPN
ma-80	876	19	-------------=	-------------=	NOUN
ma-80	876	20	=	=	PUNCT
ma-80	876	21	wu2	wu2	VERB
ma-80	876	22	y	y	NOUN
ma-80	876	23			PROPN
ma-80	876	24	1	1	NUM
ma-80	876	25	2y+	2y+	NUM
ma-80	876	26	ln	ln	NOUN
ma-80	876	27	1	1	NUM
ma-80	876	28	1	1	NUM
ma-80	876	29	y+	y+	NOUN
ma-80	876	30	ln+	ln+	SYM
ma-80	876	31	ln	ln	NOUN
ma-80	876	32	–	–	PUNCT
ma-80	876	33	d2	d2	NOUN
ma-80	876	34	y	y	NOUN
ma-80	876	35			NOUN
ma-80	876	36	ln	ln	NOUN
ma-80	876	37	n2	n2	NOUN
ma-80	876	38	y	y	PROPN
ma-80	876	39			PROPN
ma-80	876	40	y	y	PROPN
ma-80	876	41	-------------ln	-------------ln	NOUN
ma-80	876	42	–	–	PUNCT
ma-80	876	43	=	=	NOUN
ma-80	876	44	=	=	SYM
ma-80	876	45	n2	n2	ADJ
ma-80	876	46	y	y	NOUN
ma-80	876	47			PUNCT
ma-80	876	48	y	y	NOUN
ma-80	876	49	1	1	NUM
ma-80	876	50	1	1	NUM
ma-80	876	51	y+	y+	NOUN
ma-80	876	52	ln+	ln+	PUNCT
ma-80	876	53			NOUN
ma-80	876	54	n1	n1	ADJ
ma-80	876	55	y	y	NOUN
ma-80	876	56			PROPN
ma-80	876	57	1	1	NUM
ma-80	876	58	d1	d1	NOUN
ma-80	876	59	y	y	NOUN
ma-80	876	60			NOUN
ma-80	876	61	ln+	ln+	SYM
ma-80	876	62	=	=	PROPN
ma-80	876	63	=	=	SYM
ma-80	876	64	d2	d2	PROPN
ma-80	876	65	y	y	NOUN
ma-80	876	66			PROPN
ma-80	876	67	1	1	NUM
ma-80	876	68	2y+	2y+	NUM
ma-80	876	69	n1	n1	ADJ
ma-80	876	70	y	y	NOUN
ma-80	877	1			PROPN
ma-80	877	2	d1	d1	VERB
ma-80	877	3	y	y	NOUN
ma-80	878	1	.+=	.+=	PUNCT
ma-80	878	2	=	=	PUNCT
ma-80	878	3	wl3	wl3	NOUN
ma-80	878	4	y	y	NOUN
ma-80	878	5			PUNCT
ma-80	878	6	y	y	PROPN
ma-80	878	7	1	1	NUM
ma-80	878	8	1	1	NUM
ma-80	878	9	y+	y+	NOUN
ma-80	878	10	ln+	ln+	PUNCT
ma-80	878	11			NOUN
ma-80	878	12	1	1	NUM
ma-80	878	13	1	1	NUM
ma-80	878	14	2y+	2y+	NUM
ma-80	878	15	ln	ln	NOUN
ma-80	878	16	1	1	NUM
ma-80	878	17	1	1	NUM
ma-80	878	18	y+	y+	NOUN
ma-80	878	19	ln+	ln+	PUNCT
ma-80	878	20	ln–+	ln–+	NOUN
ma-80	878	21	1	1	NUM
ma-80	878	22	3y	3y	NUM
ma-80	878	23	y	y	PROPN
ma-80	878	24	1	1	NUM
ma-80	878	25	y+	y+	NOUN
ma-80	878	26	ln+	ln+	PROPN
ma-80	879	1	+	+	CCONJ
ma-80	879	2	-----------------------------------------------------------------------------------------------------------------------------------n3	-----------------------------------------------------------------------------------------------------------------------------------n3	PROPN
ma-80	879	3	y	y	PROPN
ma-80	879	4			PROPN
ma-80	879	5	d3	d3	VERB
ma-80	879	6	y	y	NOUN
ma-80	879	7			PROPN
ma-80	879	8	-------------=	-------------=	NOUN
ma-80	880	1	=	=	NOUN
ma-80	880	2	wu3	wu3	VERB
ma-80	880	3	y	y	NOUN
ma-80	880	4			PROPN
ma-80	880	5	1	1	NUM
ma-80	880	6	3y	3y	NUM
ma-80	880	7	y	y	PROPN
ma-80	880	8	1	1	NUM
ma-80	880	9	y+	y+	NOUN
ma-80	880	10	ln+	ln+	PROPN
ma-80	881	1	+	+	PROPN
ma-80	881	2			ADJ
ma-80	881	3	ln	ln	NOUN
ma-80	881	4	1	1	NUM
ma-80	881	5	1	1	NUM
ma-80	881	6	y+	y+	NOUN
ma-80	881	7	ln+	ln+	PUNCT
ma-80	881	8			NOUN
ma-80	881	9	1	1	NUM
ma-80	881	10	1	1	NUM
ma-80	881	11	2y+	2y+	NUM
ma-80	881	12	ln	ln	NOUN
ma-80	881	13	1	1	NUM
ma-80	881	14	1	1	NUM
ma-80	881	15	y+	y+	NOUN
ma-80	881	16	ln+	ln+	PUNCT
ma-80	881	17	ln–+ln–=	ln–+ln–=	PROPN
ma-80	881	18	d3	d3	VERB
ma-80	881	19	y	y	PROPN
ma-80	881	20			NOUN
ma-80	881	21	ln	ln	NOUN
ma-80	881	22	n3	n3	VERB
ma-80	881	23	y	y	PROPN
ma-80	881	24			PROPN
ma-80	881	25	y	y	PROPN
ma-80	881	26	-------------ln	-------------ln	NOUN
ma-80	881	27	–	–	PUNCT
ma-80	881	28	=	=	NOUN
ma-80	881	29	n3	n3	VERB
ma-80	881	30	y	y	NOUN
ma-80	881	31			PROPN
ma-80	881	32	y	y	NOUN
ma-80	881	33	1	1	NUM
ma-80	881	34	1	1	NUM
ma-80	881	35	y+	y+	NOUN
ma-80	881	36	ln+	ln+	PUNCT
ma-80	881	37			NOUN
ma-80	881	38	1	1	NUM
ma-80	881	39	1	1	NUM
ma-80	881	40	2y+	2y+	NUM
ma-80	881	41	ln	ln	NOUN
ma-80	881	42	1	1	NUM
ma-80	881	43	1	1	NUM
ma-80	881	44	y+	y+	NOUN
ma-80	881	45	ln+	ln+	PUNCT
ma-80	881	46	ln–+=	ln–+=	NOUN
ma-80	881	47	n2	n2	ADJ
ma-80	881	48	y	y	PROPN
ma-80	881	49			PROPN
ma-80	881	50	1	1	NUM
ma-80	881	51	d2	d2	NOUN
ma-80	881	52	y	y	NOUN
ma-80	881	53			NOUN
ma-80	881	54	ln	ln	NOUN
ma-80	881	55	n2	n2	PROPN
ma-80	881	56	y	y	PROPN
ma-80	881	57			PROPN
ma-80	881	58	y	y	PROPN
ma-80	881	59	-------------ln–+	-------------ln–+	PUNCT
ma-80	881	60	=	=	PROPN
ma-80	881	61	d3	d3	VERB
ma-80	881	62	y	y	NOUN
ma-80	881	63			PROPN
ma-80	881	64	1	1	NUM
ma-80	881	65	3y	3y	NUM
ma-80	881	66	y	y	PROPN
ma-80	881	67	1	1	NUM
ma-80	881	68	y+	y+	NOUN
ma-80	881	69	ln+	ln+	PROPN
ma-80	881	70	+	+	CCONJ
ma-80	881	71	n2	n2	ADJ
ma-80	881	72	y	y	NOUN
ma-80	881	73			PROPN
ma-80	881	74	d2	d2	NOUN
ma-80	881	75	y	y	NOUN
ma-80	882	1	.+=	.+=	PROPN
ma-80	882	2	=	=	SYM
ma-80	882	3	wli	wli	PROPN
ma-80	882	4	ni	ni	PROPN
ma-80	882	5	y	y	PROPN
ma-80	882	6			PROPN
ma-80	882	7	di	di	NOUN
ma-80	882	8	y	y	NOUN
ma-80	882	9			PROPN
ma-80	882	10	------------=	------------=	X
ma-80	882	11	wui	wui	PROPN
ma-80	882	12	di	di	X
ma-80	882	13	y	y	NOUN
ma-80	882	14			X
ma-80	882	15	ln	ln	NOUN
ma-80	882	16	ni	ni	PROPN
ma-80	882	17	y	y	PROPN
ma-80	882	18			PROPN
ma-80	882	19	y	y	PROPN
ma-80	882	20	------------ln	------------ln	PROPN
ma-80	882	21	–	–	PUNCT
ma-80	882	22	=	=	NUM
ma-80	882	23	ni	ni	NOUN
ma-80	882	24	y	y	NOUN
ma-80	882	25			PROPN
ma-80	882	26	ni	ni	PROPN
ma-80	882	27	1	1	NUM
ma-80	882	28	–	–	PUNCT
ma-80	882	29	y	y	NOUN
ma-80	882	30			PROPN
ma-80	882	31	1	1	NUM
ma-80	882	32	di	di	NOUN
ma-80	882	33	1	1	NUM
ma-80	882	34	–	–	PUNCT
ma-80	882	35	y	y	NOUN
ma-80	882	36			NOUN
ma-80	882	37	ln	ln	NOUN
ma-80	882	38	ni	ni	PROPN
ma-80	882	39	1	1	NUM
ma-80	882	40	–	–	PUNCT
ma-80	882	41	y	y	NOUN
ma-80	882	42			PROPN
ma-80	882	43	y	y	PROPN
ma-80	882	44	-------------------ln–+	-------------------ln–+	PUNCT
ma-80	882	45	=	=	PROPN
ma-80	882	46	n0	n0	ADJ
ma-80	882	47	y	y	NOUN
ma-80	882	48			PROPN
ma-80	882	49	y=	y=	SYM
ma-80	882	50	d0	d0	VERB
ma-80	882	51	y	y	PROPN
ma-80	882	52			PROPN
ma-80	882	53	1=	1=	PROPN
ma-80	882	54			NUM
ma-80	882	55	di	di	X
ma-80	882	56	y	y	PROPN
ma-80	882	57			PROPN
ma-80	882	58	ni	ni	PROPN
ma-80	882	59	1	1	NUM
ma-80	882	60	–	–	PUNCT
ma-80	882	61	y	y	NOUN
ma-80	882	62			PROPN
ma-80	882	63	di	di	NOUN
ma-80	882	64	1	1	NUM
ma-80	882	65	–	–	PUNCT
ma-80	882	66	y	y	X
ma-80	883	1	.+=	.+=	PROPN
ma-80	883	2	xo	xo	NOUN
ma-80	883	3	ye	ye	PROPN
ma-80	883	4	x	x	PROPN
ma-80	883	5	–	–	PUNCT
ma-80	883	6	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	NOUN
ma-80	883	7	,	,	PUNCT
ma-80	883	8	and	and	CCONJ
ma-80	883	9	which	which	PRON
ma-80	883	10	is	be	AUX
ma-80	883	11	.	.	PUNCT
ma-80	884	1	the	the	DET
ma-80	884	2	problem	problem	NOUN
ma-80	884	3	with	with	ADP
ma-80	884	4	such	such	DET
ma-80	884	5	an	an	DET
ma-80	884	6	approximation	approximation	NOUN
ma-80	884	7	is	be	AUX
ma-80	884	8	that	that	SCONJ
ma-80	884	9	it	it	PRON
ma-80	884	10	only	only	ADV
ma-80	884	11	yields	yield	VERB
ma-80	884	12	a	a	DET
ma-80	884	13	real	real	ADJ
ma-80	884	14	solution	solution	NOUN
ma-80	884	15	for	for	ADP
ma-80	884	16	.	.	PUNCT
ma-80	885	1	a	a	DET
ma-80	885	2	practical	practical	ADJ
ma-80	885	3	approach	approach	NOUN
ma-80	885	4	is	be	AUX
ma-80	885	5	to	to	PART
ma-80	885	6	utilize	utilize	VERB
ma-80	885	7	an	an	DET
ma-80	885	8	affine	affine	NOUN
ma-80	885	9	approximation	approximation	NOUN
ma-80	885	10	at	at	ADP
ma-80	885	11	the	the	DET
ma-80	885	12	origin	origin	NOUN
ma-80	885	13	of	of	ADP
ma-80	885	14	leading	lead	VERB
ma-80	885	15	to	to	ADP
ma-80	885	16	the	the	DET
ma-80	885	17	first	first	ADJ
ma-80	885	18	approximation	approximation	NOUN
ma-80	885	19	of	of	ADP
ma-80	885	20	.	.	PUNCT
ma-80	886	1	to	to	PART
ma-80	886	2	establish	establish	VERB
ma-80	886	3	a	a	DET
ma-80	886	4	further	further	ADJ
ma-80	886	5	approximation	approximation	NOUN
ma-80	886	6	,	,	PUNCT
ma-80	886	7	consider	consider	VERB
ma-80	886	8	the	the	DET
ma-80	886	9	point	point	NOUN
ma-80	886	10	where	where	SCONJ
ma-80	886	11	the	the	DET
ma-80	886	12	level	level	NOUN
ma-80	886	13	intersects	intersect	NOUN
ma-80	886	14	which	which	PRON
ma-80	886	15	is	be	AUX
ma-80	886	16	(	(	PUNCT
ma-80	886	17	131	131	NUM
ma-80	886	18	)	)	PUNCT
ma-80	886	19	a	a	DET
ma-80	886	20	second	second	ADJ
ma-80	886	21	level	level	NOUN
ma-80	886	22	approximation	approximation	NOUN
ma-80	886	23	follows	follow	VERB
ma-80	886	24	by	by	ADP
ma-80	886	25	finding	find	VERB
ma-80	886	26	the	the	DET
ma-80	886	27	intersection	intersection	NOUN
ma-80	886	28	of	of	ADP
ma-80	886	29	a	a	DET
ma-80	886	30	second	second	ADJ
ma-80	886	31	order	order	NOUN
ma-80	886	32	taylor	taylor	PROPN
ma-80	886	33	series	series	PROPN
ma-80	886	34	at	at	ADP
ma-80	886	35	the	the	DET
ma-80	886	36	point	point	NOUN
ma-80	886	37	,	,	PUNCT
ma-80	886	38	which	which	PRON
ma-80	886	39	is	be	AUX
ma-80	886	40	(	(	PUNCT
ma-80	886	41	132	132	NUM
ma-80	886	42	)	)	PUNCT
ma-80	886	43	with	with	ADP
ma-80	886	44	to	to	PART
ma-80	886	45	yield	yield	VERB
ma-80	886	46	(	(	PUNCT
ma-80	886	47	133	133	NUM
ma-80	886	48	)	)	PUNCT
ma-80	886	49	and	and	CCONJ
ma-80	886	50	(	(	PUNCT
ma-80	886	51	134	134	NUM
ma-80	886	52	)	)	PUNCT
ma-80	886	53	iteration	iteration	NOUN
ma-80	886	54	in	in	ADP
ma-80	886	55	this	this	DET
ma-80	886	56	manner	manner	NOUN
ma-80	886	57	leads	lead	VERB
ma-80	886	58	to	to	ADP
ma-80	886	59	the	the	DET
ma-80	886	60	general	general	ADJ
ma-80	886	61	iteration	iteration	NOUN
ma-80	886	62	formulas	formula	NOUN
ma-80	886	63	:	:	PUNCT
ma-80	886	64	(	(	PUNCT
ma-80	886	65	135	135	NUM
ma-80	886	66	)	)	PUNCT
ma-80	886	67	simulation	simulation	NOUN
ma-80	886	68	results	result	NOUN
ma-80	886	69	(	(	PUNCT
ma-80	886	70	see	see	VERB
ma-80	886	71	figure	figure	NOUN
ma-80	886	72	16	16	NUM
ma-80	886	73	)	)	PUNCT
ma-80	886	74	indicate	indicate	VERB
ma-80	886	75	that	that	SCONJ
ma-80	886	76	the	the	DET
ma-80	886	77	approximations	approximation	NOUN
ma-80	886	78	also	also	ADV
ma-80	886	79	have	have	VERB
ma-80	886	80	good	good	ADJ
ma-80	886	81	convergence	convergence	NOUN
ma-80	886	82	for	for	ADP
ma-80	886	83	the	the	DET
ma-80	886	84	interval	interval	NOUN
ma-80	886	85	but	but	CCONJ
ma-80	886	86	the	the	DET
ma-80	886	87	approximations	approximation	NOUN
ma-80	886	88	are	be	AUX
ma-80	886	89	not	not	PART
ma-80	886	90	sharp	sharp	ADJ
ma-80	886	91	at	at	ADP
ma-80	886	92	.	.	PUNCT
ma-80	887	1	appendix	appendix	VERB
ma-80	887	2	d.	d.	PROPN
ma-80	887	3	proof	proof	NOUN
ma-80	887	4	of	of	ADP
ma-80	887	5	theorem	theorem	ADJ
ma-80	887	6	4.1	4.1	NUM
ma-80	887	7	consider	consider	VERB
ma-80	887	8	the	the	DET
ma-80	887	9	case	case	NOUN
ma-80	887	10	of	of	ADP
ma-80	887	11	fixed	fix	VERB
ma-80	887	12	,	,	PUNCT
ma-80	887	13	,	,	PUNCT
ma-80	887	14	and	and	CCONJ
ma-80	887	15	the	the	DET
ma-80	887	16	illustration	illustration	NOUN
ma-80	887	17	shown	show	VERB
ma-80	887	18	in	in	ADP
ma-80	887	19	figure	figure	NOUN
ma-80	887	20	18	18	NUM
ma-80	887	21	.	.	PUNCT
ma-80	888	1	by	by	ADP
ma-80	888	2	construction	construction	NOUN
ma-80	888	3	,	,	PUNCT
ma-80	888	4	,	,	PUNCT
ma-80	888	5	and	and	CCONJ
ma-80	888	6	for	for	ADP
ma-80	888	7	.	.	PUNCT
ma-80	889	1	further	far	ADV
ma-80	889	2	,	,	PUNCT
ma-80	889	3	(	(	PUNCT
ma-80	889	4	see	see	VERB
ma-80	889	5	equation	equation	NOUN
ma-80	889	6	25	25	NUM
ma-80	889	7	)	)	PUNCT
ma-80	889	8	(	(	PUNCT
ma-80	889	9	136	136	NUM
ma-80	889	10	)	)	PUNCT
ma-80	889	11	and	and	CCONJ
ma-80	889	12	it	it	PRON
ma-80	889	13	follows	follow	VERB
ma-80	889	14	that	that	SCONJ
ma-80	889	15	,	,	PUNCT
ma-80	889	16	,	,	PUNCT
ma-80	889	17	is	be	AUX
ma-80	889	18	a	a	DET
ma-80	889	19	monotonically	monotonically	ADV
ma-80	889	20	increasing	increase	VERB
ma-80	889	21	sequence	sequence	NOUN
ma-80	889	22	.	.	PUNCT
ma-80	890	1	using	use	VERB
ma-80	890	2	equation	equation	NOUN
ma-80	890	3	136	136	NUM
ma-80	890	4	it	it	PRON
ma-80	890	5	follows	follow	VERB
ma-80	890	6	that	that	SCONJ
ma-80	890	7	y	y	PROPN
ma-80	890	8	1	1	NUM
ma-80	890	9	x	x	NOUN
ma-80	890	10	–	–	PUNCT
ma-80	890	11	x	x	SYM
ma-80	890	12	2	2	NUM
ma-80	890	13	2+	2+	NUM
ma-80	890	14			NOUN
ma-80	890	15	x	x	SYM
ma-80	890	16	wl1	wl1	PROPN
ma-80	890	17	1	1	NUM
ma-80	890	18	y	y	PROPN
ma-80	890	19	--1	--1	NOUN
ma-80	890	20	y	y	PROPN
ma-80	890	21	1	1	NUM
ma-80	890	22	2y	2y	NUM
ma-80	890	23	y	y	PROPN
ma-80	890	24	2	2	NUM
ma-80	890	25	–	–	PUNCT
ma-80	890	26	+	+	NOUN
ma-80	890	27	+=	+=	NUM
ma-80	890	28	1	1	NUM
ma-80	890	29	2	2	NUM
ma-80	890	30	–	–	PUNCT
ma-80	890	31	y	y	PROPN
ma-80	890	32	1	1	NUM
ma-80	890	33	2+	2+	NUM
ma-80	890	34			PROPN
ma-80	891	1	y	y	NOUN
ma-80	891	2	1	1	NUM
ma-80	891	3	x–	x–	X
ma-80	891	4			PUNCT
ma-80	891	5	wl1	wl1	PROPN
ma-80	891	6	y	y	PROPN
ma-80	891	7	1	1	NUM
ma-80	891	8	y+	y+	NOUN
ma-80	891	9	=	=	NOUN
ma-80	891	10	wl1	wl1	PROPN
ma-80	891	11	ye	ye	NUM
ma-80	891	12	x	x	PROPN
ma-80	891	13	–	–	PUNCT
ma-80	891	14	wu1	wu1	NOUN
ma-80	891	15	y	y	PROPN
ma-80	891	16	wl1	wl1	PROPN
ma-80	891	17	---------ln	---------ln	VERB
ma-80	891	18	1	1	NUM
ma-80	891	19	y+	y+	NOUN
ma-80	891	20	.ln=	.ln=	NUM
ma-80	892	1	=	=	PUNCT
ma-80	892	2	wu1	wu1	ADJ
ma-80	892	3	wl1	wl1	ADJ
ma-80	892	4	x	x	X
ma-80	892	5	wu1	wu1	ADJ
ma-80	892	6	–	–	PUNCT
ma-80	892	7			ADJ
ma-80	892	8	wl1	wl1	PROPN
ma-80	892	9	–	–	PUNCT
ma-80	892	10	x	x	SYM
ma-80	892	11	wu1	wu1	NOUN
ma-80	892	12	–	–	PUNCT
ma-80	892	13			NOUN
ma-80	892	14	2wl1	2wl1	ADJ
ma-80	892	15	2	2	NUM
ma-80	892	16	-------------------------------------+	-------------------------------------+	NOUN
ma-80	892	17			NUM
ma-80	892	18	x	x	SYM
ma-80	892	19	wl2	wl2	PROPN
ma-80	892	20	1	1	NUM
ma-80	892	21	wl1	wl1	PROPN
ma-80	892	22	--------1	--------1	INTJ
ma-80	892	23	wl1	wl1	VERB
ma-80	892	24	1	1	NUM
ma-80	892	25	wu1	wu1	NOUN
ma-80	892	26	+	+	ADJ
ma-80	892	27			ADJ
ma-80	892	28			NOUN
ma-80	892	29	1	1	NUM
ma-80	892	30	wl1	wl1	PROPN
ma-80	892	31	2	2	NUM
ma-80	892	32	–	–	PUNCT
ma-80	892	33	2wl1	2wl1	NUM
ma-80	892	34	1	1	NUM
ma-80	892	35	wu1	wu1	ADJ
ma-80	892	36	+	+	ADJ
ma-80	892	37			ADJ
ma-80	892	38	+–+=	+–+=	NOUN
ma-80	892	39	wu2	wu2	NOUN
ma-80	892	40	y	y	PROPN
ma-80	892	41	wl2	wl2	PROPN
ma-80	892	42	--------.ln=	--------.ln=	PROPN
ma-80	892	43	wli	wli	PROPN
ma-80	892	44	1	1	NUM
ma-80	892	45	wli	wli	PROPN
ma-80	892	46	1	1	NUM
ma-80	892	47	–	–	PUNCT
ma-80	892	48	-------------1	-------------1	PROPN
ma-80	892	49	wli	wli	PROPN
ma-80	892	50	1	1	NUM
ma-80	892	51	–	–	SYM
ma-80	892	52	1	1	NUM
ma-80	892	53	wui	wui	NOUN
ma-80	892	54	1	1	NUM
ma-80	892	55	–	–	PUNCT
ma-80	892	56	+	+	NOUN
ma-80	892	57			ADJ
ma-80	892	58			NOUN
ma-80	892	59	1	1	NUM
ma-80	892	60	wli	wli	PROPN
ma-80	892	61	1	1	NUM
ma-80	892	62	–	–	SYM
ma-80	892	63	2	2	NUM
ma-80	892	64	–	–	PUNCT
ma-80	892	65	2wli	2wli	NUM
ma-80	892	66	1	1	NUM
ma-80	892	67	–	–	SYM
ma-80	892	68	1	1	NUM
ma-80	892	69	wui	wui	NOUN
ma-80	892	70	1	1	NUM
ma-80	892	71	–	–	PUNCT
ma-80	892	72	+	+	NUM
ma-80	892	73			ADJ
ma-80	892	74	+–+	+–+	NOUN
ma-80	892	75	=	=	AUX
ma-80	892	76	wui	wui	NOUN
ma-80	892	77	y	y	PROPN
ma-80	892	78	wli	wli	PROPN
ma-80	892	79	---------ln	---------ln	PROPN
ma-80	892	80	.=	.=	VERB
ma-80	892	81	1	1	NUM
ma-80	892	82	e	e	ADV
ma-80	892	83	–	–	PUNCT
ma-80	892	84	0	0	PUNCT
ma-80	892	85			PUNCT
ma-80	892	86	y	y	PROPN
ma-80	892	87	1	1	NUM
ma-80	892	88	e–=	e–=	NOUN
ma-80	892	89	y	y	PROPN
ma-80	892	90	y	y	PROPN
ma-80	892	91	0	0	NUM
ma-80	893	1	li	li	ADJ
ma-80	893	2	0	0	PUNCT
ma-80	893	3	ui	ui	PROPN
ma-80	893	4	0	0	NUM
ma-80	893	5	wui	wui	PROPN
ma-80	893	6	wli	wli	PROPN
ma-80	893	7			PROPN
ma-80	893	8	i	i	PRON
ma-80	893	9	1	1	NUM
ma-80	893	10	2	2	NUM
ma-80	893	11			NOUN
ma-80	893	12			X
ma-80	894	1			VERB
ma-80	894	2	wli	wli	NOUN
ma-80	894	3	1	1	NUM
ma-80	894	4	+	+	NUM
ma-80	894	5	wli	wli	PROPN
ma-80	894	6	1	1	NUM
ma-80	894	7	wui	wui	NOUN
ma-80	894	8	+	+	CCONJ
ma-80	894	9	1	1	NUM
ma-80	894	10	wli	wli	NOUN
ma-80	894	11	+	+	CCONJ
ma-80	894	12	-------------------	-------------------	PROPN
ma-80	894	13	=	=	PROPN
ma-80	894	14	wli	wli	NOUN
ma-80	895	1	i	i	NOUN
ma-80	895	2	1	1	NUM
ma-80	895	3	2	2	NUM
ma-80	895	4			NOUN
ma-80	895	5			X
ma-80	895	6			NUM
ma-80	895	7	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	NOUN
ma-80	895	8	(	(	PUNCT
ma-80	895	9	137	137	NUM
ma-80	895	10	)	)	PUNCT
ma-80	895	11	as	as	ADP
ma-80	895	12	,	,	PUNCT
ma-80	895	13	and	and	CCONJ
ma-80	895	14	,	,	PUNCT
ma-80	895	15	it	it	PRON
ma-80	895	16	follows	follow	VERB
ma-80	895	17	that	that	SCONJ
ma-80	895	18	(	(	PUNCT
ma-80	895	19	138	138	NUM
ma-80	895	20	)	)	PUNCT
ma-80	895	21	where	where	SCONJ
ma-80	895	22	.	.	PUNCT
ma-80	896	1	thus	thus	ADV
ma-80	896	2	,	,	PUNCT
ma-80	896	3	as	as	SCONJ
ma-80	896	4	monotonically	monotonically	ADV
ma-80	896	5	increases	increase	VERB
ma-80	896	6	with	with	ADP
ma-80	896	7	,	,	PUNCT
ma-80	896	8	it	it	PRON
ma-80	896	9	follows	follow	VERB
ma-80	896	10	that	that	SCONJ
ma-80	896	11	monotonically	monotonically	ADV
ma-80	896	12	decreases	decrease	VERB
ma-80	896	13	with	with	ADP
ma-80	896	14	,	,	PUNCT
ma-80	896	15	i.e.	i.e.	X
ma-80	896	16	.	.	PUNCT
ma-80	897	1	it	it	PRON
ma-80	897	2	then	then	ADV
ma-80	897	3	follows	follow	VERB
ma-80	897	4	that	that	SCONJ
ma-80	897	5	(	(	PUNCT
ma-80	897	6	139	139	NUM
ma-80	897	7	)	)	PUNCT
ma-80	897	8	hence	hence	ADV
ma-80	897	9	,	,	PUNCT
ma-80	897	10	convergence	convergence	NOUN
ma-80	897	11	is	be	AUX
ma-80	897	12	guaranteed	guarantee	VERB
ma-80	897	13	as	as	ADP
ma-80	897	14	.	.	PUNCT
ma-80	898	1	thus	thus	ADV
ma-80	898	2	:	:	PUNCT
ma-80	898	3	and	and	CCONJ
ma-80	898	4	.	.	PUNCT
ma-80	899	1	the	the	DET
ma-80	899	2	result	result	NOUN
ma-80	899	3	implies	imply	VERB
ma-80	899	4	that	that	SCONJ
ma-80	899	5	and	and	CCONJ
ma-80	899	6	,	,	PUNCT
ma-80	899	7	thus	thus	ADV
ma-80	899	8	,	,	PUNCT
ma-80	899	9	.	.	PUNCT
ma-80	900	1	appendix	appendix	VERB
ma-80	900	2	e.	e.	PROPN
ma-80	900	3	alternative	alternative	PROPN
ma-80	900	4	form	form	NOUN
ma-80	900	5	for	for	ADP
ma-80	900	6	spline	spline	NOUN
ma-80	900	7	approximation	approximation	NOUN
ma-80	900	8	the	the	DET
ma-80	900	9	general	general	ADJ
ma-80	900	10	form	form	NOUN
ma-80	900	11	for	for	ADP
ma-80	900	12	a	a	DET
ma-80	900	13	order	order	NOUN
ma-80	900	14	,	,	PUNCT
ma-80	900	15	two	two	NUM
ma-80	900	16	point	point	NOUN
ma-80	900	17	,	,	PUNCT
ma-80	900	18	spline	spline	NOUN
ma-80	900	19	approximation	approximation	NOUN
ma-80	900	20	for	for	ADP
ma-80	900	21	a	a	DET
ma-80	900	22	function	function	NOUN
ma-80	900	23	,	,	PUNCT
ma-80	900	24	over	over	ADP
ma-80	900	25	the	the	DET
ma-80	900	26	interval	interval	NOUN
ma-80	900	27	,	,	PUNCT
ma-80	900	28	has	have	AUX
ma-80	900	29	been	be	AUX
ma-80	900	30	detailed	detail	VERB
ma-80	900	31	in	in	ADP
ma-80	900	32	howard	howard	PROPN
ma-80	900	33	,	,	PUNCT
ma-80	901	1	[	[	X
ma-80	901	2	16	16	NUM
ma-80	901	3	]	]	PUNCT
ma-80	901	4	,	,	PUNCT
ma-80	901	5	eqn	eqn	PROPN
ma-80	901	6	.	.	PUNCT
ma-80	902	1	40	40	NUM
ma-80	902	2	.	.	PUNCT
ma-80	903	1	the	the	DET
ma-80	903	2	assumption	assumption	NOUN
ma-80	903	3	is	be	AUX
ma-80	903	4	that	that	SCONJ
ma-80	903	5	the	the	DET
ma-80	903	6	function	function	NOUN
ma-80	903	7	is	be	AUX
ma-80	903	8	at	at	ADP
ma-80	903	9	least	least	ADJ
ma-80	903	10	order	order	NOUN
ma-80	903	11	differentiable	differentiable	ADJ
ma-80	903	12	over	over	ADP
ma-80	903	13	the	the	DET
ma-80	903	14	interval	interval	NOUN
ma-80	903	15	.	.	PUNCT
ma-80	904	1	the	the	DET
ma-80	904	2	approximation	approximation	NOUN
ma-80	904	3	,	,	PUNCT
ma-80	904	4	denoted	denote	VERB
ma-80	904	5	,	,	PUNCT
ma-80	904	6	can	can	AUX
ma-80	904	7	be	be	AUX
ma-80	904	8	written	write	VERB
ma-80	904	9	in	in	ADP
ma-80	904	10	the	the	DET
ma-80	904	11	modified	modify	VERB
ma-80	904	12	form	form	NOUN
ma-80	904	13	:	:	PUNCT
ma-80	904	14	(	(	PUNCT
ma-80	904	15	140	140	NUM
ma-80	904	16	)	)	PUNCT
ma-80	904	17	in	in	ADP
ma-80	904	18	this	this	DET
ma-80	904	19	equation	equation	NOUN
ma-80	904	20	,	,	PUNCT
ma-80	904	21	the	the	DET
ma-80	904	22	double	double	ADJ
ma-80	904	23	summation	summation	NOUN
ma-80	904	24	can	can	AUX
ma-80	904	25	be	be	AUX
ma-80	904	26	rewritten	rewrite	VERB
ma-80	904	27	by	by	ADP
ma-80	904	28	utilizing	utilize	VERB
ma-80	904	29	the	the	DET
ma-80	904	30	transformations	transformation	NOUN
ma-80	904	31	and	and	CCONJ
ma-80	904	32	,	,	PUNCT
ma-80	904	33	,	,	PUNCT
ma-80	904	34	.	.	PUNCT
ma-80	905	1	the	the	DET
ma-80	905	2	possible	possible	ADJ
ma-80	905	3	values	value	NOUN
ma-80	905	4	of	of	ADP
ma-80	905	5	are	be	AUX
ma-80	905	6	detailed	detail	VERB
ma-80	905	7	in	in	ADP
ma-80	905	8	table	table	NOUN
ma-80	905	9	8	8	NUM
ma-80	905	10	and	and	CCONJ
ma-80	905	11	for	for	ADP
ma-80	905	12	fixed	fix	VERB
ma-80	905	13	,	,	PUNCT
ma-80	905	14	the	the	DET
ma-80	905	15	valid	valid	ADJ
ma-80	905	16	values	value	NOUN
ma-80	905	17	for	for	ADP
ma-80	905	18	are	be	AUX
ma-80	905	19	from	from	ADP
ma-80	905	20	the	the	DET
ma-80	905	21	set	set	NOUN
ma-80	905	22	.	.	PUNCT
ma-80	906	1	table	table	NOUN
ma-80	906	2	8	8	NUM
ma-80	906	3	.	.	PUNCT
ma-80	906	4	valid	valid	ADJ
ma-80	906	5	values	value	NOUN
ma-80	906	6	of	of	ADP
ma-80	906	7	for	for	ADP
ma-80	906	8	,	,	PUNCT
ma-80	906	9	.	.	PUNCT
ma-80	907	1	i	i	PRON
ma-80	907	2	k	k	NOUN
ma-80	908	1	0	0	NUM
ma-80	908	2	1	1	NUM
ma-80	908	3	2	2	NUM
ma-80	908	4	3	3	NUM
ma-80	908	5	...	...	PUNCT
ma-80	908	6	n-2	n-2	X
ma-80	908	7	n-1	n-1	NOUN
ma-80	908	8	n	n	PRON
ma-80	908	9	0	0	NUM
ma-80	908	10	0	0	NUM
ma-80	908	11	1	1	NUM
ma-80	908	12	2	2	NUM
ma-80	908	13	3	3	NUM
ma-80	908	14	n-2	n-2	NOUN
ma-80	908	15	n-1	n-1	NOUN
ma-80	908	16	n	n	ADV
ma-80	908	17	1	1	NUM
ma-80	908	18	1	1	NUM
ma-80	908	19	2	2	NUM
ma-80	908	20	3	3	NUM
ma-80	908	21	4	4	NUM
ma-80	908	22	n-1	n-1	NOUN
ma-80	908	23	n	n	ADV
ma-80	908	24	2	2	NUM
ma-80	908	25	2	2	NUM
ma-80	908	26	3	3	NUM
ma-80	908	27	4	4	NUM
ma-80	908	28	5	5	NUM
ma-80	908	29	n	n	NUM
ma-80	908	30	3	3	NUM
ma-80	908	31	3	3	NUM
ma-80	908	32	4	4	NUM
ma-80	908	33	5	5	NUM
ma-80	908	34	6	6	NUM
ma-80	908	35	li	li	VERB
ma-80	908	36	li	li	VERB
ma-80	908	37	1	1	NUM
ma-80	908	38	+	+	CCONJ
ma-80	908	39	–	–	PUNCT
ma-80	908	40	xo	xo	PROPN
ma-80	908	41	wli	wli	PROPN
ma-80	908	42	–	–	PUNCT
ma-80	908	43			PROPN
ma-80	908	44			PROPN
ma-80	908	45	xo	xo	PROPN
ma-80	908	46	wli	wli	PROPN
ma-80	908	47	1	1	NUM
ma-80	908	48	wui	wui	PROPN
ma-80	908	49	+	+	ADJ
ma-80	908	50			ADJ
ma-80	908	51			ADP
ma-80	908	52	1	1	NUM
ma-80	908	53	wli	wli	NOUN
ma-80	908	54	+	+	CCONJ
ma-80	908	55	---------------------------------	---------------------------------	PROPN
ma-80	908	56	–	–	PUNCT
ma-80	908	57	–	–	PUNCT
ma-80	908	58	wli	wli	PROPN
ma-80	908	59	wui	wui	PROPN
ma-80	908	60	wli	wli	PROPN
ma-80	908	61	–	–	PUNCT
ma-80	908	62			PROPN
ma-80	908	63			PROPN
ma-80	908	64	1	1	NUM
ma-80	908	65	wli	wli	NOUN
ma-80	908	66	+	+	CCONJ
ma-80	908	67	---------------------------------------.=	---------------------------------------.=	NOUN
ma-80	908	68	=	=	SYM
ma-80	908	69	wui	wui	PROPN
ma-80	908	70	wli	wli	PROPN
ma-80	908	71	–	–	PUNCT
ma-80	908	72	li	li	VERB
ma-80	908	73	ui	ui	NOUN
ma-80	908	74	+	+	NOUN
ma-80	908	75	=	=	ADJ
ma-80	908	76	ui	ui	PROPN
ma-80	908	77	0	0	NUM
ma-80	908	78	li	li	ADJ
ma-80	908	79	1	1	NUM
ma-80	908	80	+	+	NUM
ma-80	908	81	li	li	ADJ
ma-80	908	82	wli	wli	NOUN
ma-80	908	83	1	1	NUM
ma-80	908	84	wli	wli	PROPN
ma-80	908	85	+	+	CCONJ
ma-80	908	86	------------------	------------------	PUNCT
ma-80	908	87	–	–	PUNCT
ma-80	908	88	li	li	ADJ
ma-80	908	89	ui	ui	PROPN
ma-80	908	90	+	+	PROPN
ma-80	908	91			ADJ
ma-80	908	92			PROPN
ma-80	908	93	1	1	NUM
ma-80	908	94	wli	wli	NOUN
ma-80	908	95	1	1	NUM
ma-80	908	96	wli	wli	PROPN
ma-80	908	97	+	+	CCONJ
ma-80	908	98	------------------	------------------	PUNCT
ma-80	908	99	–	–	PUNCT
ma-80	908	100	li	li	SYM
ma-80	908	101	rili=	rili=	VERB
ma-80	908	102	=	=	SYM
ma-80	908	103	ri	ri	PROPN
ma-80	908	104	1	1	NUM
ma-80	908	105	1	1	NUM
ma-80	908	106	wli	wli	NOUN
ma-80	908	107	+	+	CCONJ
ma-80	908	108	------------------=	------------------=	VERB
ma-80	908	109	wli	wli	PROPN
ma-80	908	110	i	i	PRON
ma-80	908	111	ri	ri	VERB
ma-80	909	1	i	i	ADV
ma-80	909	2	0	0	NUM
ma-80	909	3	ri	ri	PROPN
ma-80	909	4	1	1	NUM
ma-80	909	5	+	+	NUM
ma-80	909	6	r	r	PROPN
ma-80	909	7	i	i	PRON
ma-80	909	8	1	1	NUM
ma-80	909	9			PROPN
ma-80	909	10	0	0	NUM
ma-80	910	1	li	li	VERB
ma-80	910	2	1	1	NUM
ma-80	910	3	+	+	NUM
ma-80	910	4	l1	l1	NOUN
ma-80	910	5	rk	rk	NOUN
ma-80	910	6	k	k	NOUN
ma-80	910	7	1=	1=	NUM
ma-80	910	8	i	i	PRON
ma-80	910	9			PROPN
ma-80	910	10	l1	l1	VERB
ma-80	910	11	r1	r1	NOUN
ma-80	911	1	i	i	PRON
ma-80	911	2	.	.	PROPN
ma-80	912	1			PROPN
ma-80	912	2			PROPN
ma-80	912	3	0	0	NUM
ma-80	913	1	r1	r1	NOUN
ma-80	913	2	1	1	NUM
ma-80	913	3	1	1	NUM
ma-80	913	4	y	y	PROPN
ma-80	913	5	1	1	NUM
ma-80	913	6	y+	y+	NOUN
ma-80	913	7	+	+	PROPN
ma-80	913	8	--------------------------------=	--------------------------------=	PUNCT
ma-80	913	9	1	1	NUM
ma-80	913	10			PROPN
ma-80	913	11	lii	lii	ADJ
ma-80	913	12			PROPN
ma-80	913	13	lim	lim	PROPN
ma-80	913	14	0=	0=	NUM
ma-80	913	15	wlii	wlii	PROPN
ma-80	913	16			PROPN
ma-80	913	17	lim	lim	PROPN
ma-80	913	18	xo=	xo=	PROPN
ma-80	914	1	li	li	VERB
ma-80	914	2	1	1	NUM
ma-80	914	3	+	+	CCONJ
ma-80	914	4	li	li	ADJ
ma-80	914	5	wli	wli	NOUN
ma-80	914	6	1	1	NUM
ma-80	914	7	wli	wli	PROPN
ma-80	914	8	+	+	CCONJ
ma-80	914	9	------------------	------------------	PUNCT
ma-80	914	10	–	–	PUNCT
ma-80	914	11	li	li	ADJ
ma-80	914	12	ui	ui	NOUN
ma-80	914	13	+	+	NOUN
ma-80	914	14			ADJ
ma-80	914	15	=	=	ADJ
ma-80	914	16	uii	uii	PROPN
ma-80	914	17			PROPN
ma-80	914	18	lim	lim	PROPN
ma-80	914	19	0=	0=	PROPN
ma-80	914	20	wuii	wuii	PROPN
ma-80	915	1			PROPN
ma-80	915	2	lim	lim	PROPN
ma-80	915	3	xo=	xo=	PROPN
ma-80	916	1	nth	nth	PROPN
ma-80	916	2	f	f	PROPN
ma-80	916	3			X
ma-80	916	4			PRON
ma-80	916	5			PROPN
ma-80	916	6	f	f	PROPN
ma-80	916	7	nth	nth	PROPN
ma-80	916	8			NUM
ma-80	916	9			NOUN
ma-80	916	10			PROPN
ma-80	916	11	fn	fn	NOUN
ma-80	916	12	fn	fn	NOUN
ma-80	917	1	x	x	PROPN
ma-80	917	2			PROPN
ma-80	917	3			NOUN
ma-80	917	4	x–	x–	NOUN
ma-80	917	5	n	n	PROPN
ma-80	918	1	1	1	NUM
ma-80	918	2	+	+	NUM
ma-80	918	3			NOUN
ma-80	918	4	–	–	NOUN
ma-80	918	5	n	n	PROPN
ma-80	918	6	1	1	NUM
ma-80	918	7	+	+	CCONJ
ma-80	918	8	---------------------------f	---------------------------f	NOUN
ma-80	918	9	k	k	NOUN
ma-80	918	10			PROPN
ma-80	918	11			NOUN
ma-80	918	12			PROPN
ma-80	918	13	k	k	X
ma-80	918	14	!	!	PUNCT
ma-80	918	15	---------------n	---------------n	PUNCT
ma-80	919	1	i+	i+	PROPN
ma-80	919	2			PROPN
ma-80	919	3	!	!	PUNCT
ma-80	920	1	i!n	i!n	PROPN
ma-80	920	2	!	!	PUNCT
ma-80	921	1	-----------------	-----------------	PUNCT
ma-80	921	2	i	i	PRON
ma-80	921	3	0=	0=	NUM
ma-80	922	1	n	n	CCONJ
ma-80	922	2	k	k	X
ma-80	922	3	–	–	PUNCT
ma-80	922	4			X
ma-80	923	1	x	x	PUNCT
ma-80	923	2	–	–	NOUN
ma-80	923	3	k	k	X
ma-80	923	4	i+	i+	NUM
ma-80	923	5			NOUN
ma-80	923	6	–	–	NOUN
ma-80	923	7	i	i	PROPN
ma-80	924	1	--------------------------	--------------------------	PROPN
ma-80	924	2	k	k	PROPN
ma-80	924	3	0=	0=	PUNCT
ma-80	925	1	n	n	PRON
ma-80	925	2			VERB
ma-80	926	1	+	+	X
ma-80	926	2	=	=	X
ma-80	926	3	x	x	SYM
ma-80	926	4	–	–	NOUN
ma-80	926	5	n	n	PROPN
ma-80	926	6	1	1	NUM
ma-80	926	7	+	+	NUM
ma-80	926	8			NOUN
ma-80	926	9	–	–	NOUN
ma-80	926	10	n	n	PROPN
ma-80	926	11	1	1	NUM
ma-80	926	12	+	+	CCONJ
ma-80	926	13	---------------------------1–	---------------------------1–	ADJ
ma-80	926	14	kf	kf	NOUN
ma-80	927	1	k	k	NOUN
ma-80	927	2			PROPN
ma-80	927	3			NOUN
ma-80	927	4			PUNCT
ma-80	927	5	k	k	X
ma-80	927	6	!	!	PUNCT
ma-80	927	7	-----------------------------n	-----------------------------n	PUNCT
ma-80	928	1	i+	i+	PROPN
ma-80	929	1			PROPN
ma-80	929	2	!	!	PUNCT
ma-80	930	1	i!n	i!n	PROPN
ma-80	930	2	!	!	PUNCT
ma-80	931	1	-----------------	-----------------	PUNCT
ma-80	931	2	i	i	PRON
ma-80	931	3	0=	0=	NUM
ma-80	932	1	n	n	CCONJ
ma-80	932	2	k	k	X
ma-80	932	3	–	–	PUNCT
ma-80	932	4			X
ma-80	932	5			PROPN
ma-80	932	6	x–	x–	PROPN
ma-80	932	7	k	k	X
ma-80	933	1	i+	i+	NUM
ma-80	933	2			NOUN
ma-80	933	3	–	–	NOUN
ma-80	933	4	i	i	PROPN
ma-80	934	1	-------------------------	-------------------------	NUM
ma-80	934	2	.	.	PUNCT
ma-80	935	1	k	k	X
ma-80	936	1	0=	0=	NOUN
ma-80	937	1	n	n	PRON
ma-80	937	2			NOUN
ma-80	938	1	r	r	NOUN
ma-80	938	2	i	i	PRON
ma-80	938	3	k+=	k+=	VERB
ma-80	938	4	u	u	NOUN
ma-80	938	5	i=	i=	PROPN
ma-80	938	6	k	k	NOUN
ma-80	938	7	0	0	NUM
ma-80	938	8	1	1	NUM
ma-80	938	9			NOUN
ma-80	938	10	n	n	X
ma-80	938	11			NUM
ma-80	938	12			VERB
ma-80	939	1			VERB
ma-80	939	2	i	i	NOUN
ma-80	939	3	0	0	NUM
ma-80	939	4	1	1	NUM
ma-80	939	5			PROPN
ma-80	939	6	n	n	PART
ma-80	939	7	k–	k–	X
ma-80	939	8			NUM
ma-80	939	9			NOUN
ma-80	940	1			PUNCT
ma-80	940	2	r	r	NOUN
ma-80	940	3	i	i	PRON
ma-80	940	4	k+=	k+=	INTJ
ma-80	940	5	r	r	NOUN
ma-80	940	6	i	i	NOUN
ma-80	940	7	0	0	NUM
ma-80	940	8	1	1	NUM
ma-80	940	9			NOUN
ma-80	940	10	r	r	VERB
ma-80	940	11			NUM
ma-80	940	12			X
ma-80	940	13			PROPN
ma-80	940	14	r	r	NOUN
ma-80	941	1	i	i	PRON
ma-80	941	2	k+=	k+=	PROPN
ma-80	941	3	k	k	NOUN
ma-80	941	4	0	0	NUM
ma-80	941	5	1	1	NUM
ma-80	941	6			NOUN
ma-80	941	7	n	n	X
ma-80	941	8			NUM
ma-80	941	9			VERB
ma-80	942	1			VERB
ma-80	942	2	i	i	NOUN
ma-80	942	3	0	0	NUM
ma-80	942	4	1	1	NUM
ma-80	942	5			PROPN
ma-80	942	6	n	n	PART
ma-80	942	7	k–	k–	X
ma-80	942	8			NUM
ma-80	942	9			VERB
ma-80	942	10			PROPN
ma-80	942	11	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	NOUN
ma-80	942	12	with	with	ADP
ma-80	942	13	,	,	PUNCT
ma-80	942	14	and	and	CCONJ
ma-80	942	15	,	,	PUNCT
ma-80	942	16	,	,	PUNCT
ma-80	942	17	equation	equation	NOUN
ma-80	942	18	140	140	NUM
ma-80	942	19	can	can	AUX
ma-80	942	20	be	be	AUX
ma-80	942	21	written	write	VERB
ma-80	942	22	as	as	ADP
ma-80	942	23	(	(	PUNCT
ma-80	942	24	141	141	NUM
ma-80	942	25	)	)	PUNCT
ma-80	942	26	thus	thus	ADV
ma-80	942	27	:	:	PUNCT
ma-80	942	28	(	(	PUNCT
ma-80	942	29	142	142	NUM
ma-80	942	30	)	)	PUNCT
ma-80	942	31	where	where	SCONJ
ma-80	942	32	(	(	PUNCT
ma-80	942	33	143	143	NUM
ma-80	942	34	)	)	PUNCT
ma-80	942	35	appendix	appendix	VERB
ma-80	942	36	f.	f.	NOUN
ma-80	942	37	proof	proof	NOUN
ma-80	942	38	of	of	ADP
ma-80	942	39	lemma	lemma	PROPN
ma-80	942	40	1	1	NUM
ma-80	942	41	first	first	ADV
ma-80	942	42	,	,	PUNCT
ma-80	942	43	the	the	DET
ma-80	942	44	definitions	definition	NOUN
ma-80	942	45	of	of	ADP
ma-80	942	46	,	,	PUNCT
ma-80	942	47	and	and	CCONJ
ma-80	942	48	with	with	ADP
ma-80	942	49	,	,	PUNCT
ma-80	942	50	imply	imply	INTJ
ma-80	942	51	:	:	PUNCT
ma-80	942	52	(	(	PUNCT
ma-80	942	53	144	144	NUM
ma-80	942	54	)	)	PUNCT
ma-80	942	55	it	it	PRON
ma-80	942	56	then	then	ADV
ma-80	942	57	follows	follow	VERB
ma-80	942	58	that	that	SCONJ
ma-80	942	59	which	which	PRON
ma-80	942	60	implies	imply	VERB
ma-80	942	61	.	.	PUNCT
ma-80	943	1	with	with	ADP
ma-80	943	2	and	and	CCONJ
ma-80	943	3	,	,	PUNCT
ma-80	943	4	the	the	DET
ma-80	943	5	required	require	VERB
ma-80	943	6	result	result	NOUN
ma-80	943	7	of	of	ADP
ma-80	943	8	then	then	ADV
ma-80	943	9	follows	follow	VERB
ma-80	943	10	.	.	PUNCT
ma-80	944	1	second	second	ADV
ma-80	944	2	,	,	PUNCT
ma-80	944	3	the	the	DET
ma-80	944	4	transformation	transformation	NOUN
ma-80	944	5	of	of	ADP
ma-80	944	6	,	,	PUNCT
ma-80	944	7	,	,	PUNCT
ma-80	944	8	results	result	NOUN
ma-80	944	9	in	in	ADP
ma-80	944	10	(	(	PUNCT
ma-80	944	11	145	145	NUM
ma-80	944	12	)	)	PUNCT
ma-80	944	13	as	as	SCONJ
ma-80	944	14	it	it	PRON
ma-80	944	15	then	then	ADV
ma-80	944	16	follows	follow	VERB
ma-80	944	17	that	that	PRON
ma-80	944	18	and	and	CCONJ
ma-80	944	19	the	the	DET
ma-80	944	20	final	final	ADJ
ma-80	944	21	result	result	NOUN
ma-80	944	22	follows	follow	VERB
ma-80	944	23	:	:	PUNCT
ma-80	944	24	(	(	PUNCT
ma-80	944	25	146	146	NUM
ma-80	944	26	)	)	PUNCT
ma-80	944	27	n-2	n-2	PROPN
ma-80	944	28	n-2	n-2	NOUN
ma-80	944	29	n-1	n-1	NOUN
ma-80	944	30	n	n	PRON
ma-80	944	31	n-1	n-1	NOUN
ma-80	944	32	n-1	n-1	VERB
ma-80	944	33	n	n	CCONJ
ma-80	944	34	n	n	CCONJ
ma-80	944	35	n	n	PRON
ma-80	944	36	table	table	NOUN
ma-80	944	37	8	8	NUM
ma-80	944	38	.	.	PUNCT
ma-80	944	39	valid	valid	ADJ
ma-80	944	40	values	value	NOUN
ma-80	944	41	of	of	ADP
ma-80	944	42	for	for	ADP
ma-80	944	43	,	,	PUNCT
ma-80	944	44	.	.	PUNCT
ma-80	945	1	i	i	PRON
ma-80	945	2	k	k	NOUN
ma-80	946	1	0	0	NUM
ma-80	946	2	1	1	NUM
ma-80	946	3	2	2	NUM
ma-80	946	4	3	3	NUM
ma-80	946	5	...	...	PUNCT
ma-80	946	6	n-2	n-2	X
ma-80	946	7	n-1	n-1	NOUN
ma-80	946	8	n	n	ADP
ma-80	946	9	r	r	NOUN
ma-80	946	10	i	i	PRON
ma-80	946	11	k+=	k+=	PROPN
ma-80	946	12	k	k	NOUN
ma-80	946	13	0	0	NUM
ma-80	946	14	1	1	NUM
ma-80	946	15			NOUN
ma-80	946	16	n	n	X
ma-80	946	17			NUM
ma-80	946	18			VERB
ma-80	946	19			VERB
ma-80	946	20	i	i	NOUN
ma-80	946	21	0	0	NUM
ma-80	946	22	1	1	NUM
ma-80	946	23			PROPN
ma-80	946	24	n	n	PART
ma-80	946	25	k–	k–	X
ma-80	946	26			NUM
ma-80	946	27			VERB
ma-80	946	28			NUM
ma-80	946	29			ADP
ma-80	946	30	r	r	NOUN
ma-80	946	31	0	0	NUM
ma-80	946	32	1	1	NUM
ma-80	946	33			NOUN
ma-80	946	34	n	n	X
ma-80	946	35			NUM
ma-80	946	36			VERB
ma-80	946	37			NUM
ma-80	946	38	u	u	NOUN
ma-80	946	39	0	0	NUM
ma-80	946	40	1	1	NUM
ma-80	946	41			NOUN
ma-80	946	42	r	r	VERB
ma-80	946	43			NUM
ma-80	946	44			VERB
ma-80	947	1			VERB
ma-80	947	2	i	i	PRON
ma-80	947	3	u=	u=	ADV
ma-80	948	1	k	k	NOUN
ma-80	948	2	r	r	NOUN
ma-80	948	3	u–=	u–=	PROPN
ma-80	948	4	fn	fn	NOUN
ma-80	948	5	x	x	PROPN
ma-80	949	1			PROPN
ma-80	949	2			NOUN
ma-80	949	3	x–	x–	NOUN
ma-80	949	4	n	n	PROPN
ma-80	950	1	1	1	NUM
ma-80	950	2	+	+	NUM
ma-80	950	3			NOUN
ma-80	950	4	–	–	NOUN
ma-80	950	5	n	n	PROPN
ma-80	950	6	1	1	NUM
ma-80	950	7	+	+	NUM
ma-80	950	8	---------------------------x	---------------------------x	PUNCT
ma-80	950	9	–	–	NOUN
ma-80	950	10	r	r	X
ma-80	950	11	f	f	X
ma-80	951	1	r	r	NOUN
ma-80	951	2	u–	u–	NOUN
ma-80	951	3			PUNCT
ma-80	951	4			NOUN
ma-80	951	5			NOUN
ma-80	951	6	r	r	NOUN
ma-80	951	7	u–	u–	NOUN
ma-80	951	8			PROPN
ma-80	951	9	!	!	PUNCT
ma-80	951	10	----------------------n	----------------------n	PUNCT
ma-80	952	1	u+	u+	PROPN
ma-80	952	2			PROPN
ma-80	952	3	!	!	PUNCT
ma-80	953	1	u!n	u!n	PROPN
ma-80	953	2	!	!	PUNCT
ma-80	953	3	-------------------	-------------------	PROPN
ma-80	953	4	u	u	NOUN
ma-80	954	1	0=	0=	NOUN
ma-80	954	2	r	r	NOUN
ma-80	954	3			X
ma-80	954	4	1	1	NUM
ma-80	954	5			NOUN
ma-80	954	6	–	–	NOUN
ma-80	954	7	u	u	ADJ
ma-80	954	8	--------------------	--------------------	PUNCT
ma-80	954	9	r	r	NOUN
ma-80	954	10	0=	0=	NOUN
ma-80	954	11	n	n	PRON
ma-80	954	12			VERB
ma-80	955	1	+	+	X
ma-80	955	2	=	=	X
ma-80	955	3	x	x	SYM
ma-80	955	4	–	–	NOUN
ma-80	955	5	n	n	PROPN
ma-80	955	6	1	1	NUM
ma-80	955	7	+	+	NUM
ma-80	955	8			NOUN
ma-80	955	9	–	–	NOUN
ma-80	955	10	n	n	PROPN
ma-80	955	11	1	1	NUM
ma-80	955	12	+	+	NUM
ma-80	955	13	---------------------------	---------------------------	NUM
ma-80	955	14	x–	x–	PUNCT
ma-80	956	1	r	r	X
ma-80	956	2	1–	1–	NUM
ma-80	956	3	r	r	DET
ma-80	956	4	u	u	NOUN
ma-80	956	5	–	–	PUNCT
ma-80	956	6	f	f	PROPN
ma-80	956	7	r	r	NOUN
ma-80	956	8	u–	u–	NOUN
ma-80	956	9			NUM
ma-80	956	10			NOUN
ma-80	956	11			PUNCT
ma-80	957	1	r	r	NOUN
ma-80	957	2	u–	u–	NOUN
ma-80	957	3			PROPN
ma-80	957	4	!	!	PUNCT
ma-80	957	5	-------------------------------------------n	-------------------------------------------n	PUNCT
ma-80	958	1	u+	u+	PROPN
ma-80	958	2			PROPN
ma-80	958	3	!	!	PUNCT
ma-80	959	1	u!n	u!n	PROPN
ma-80	959	2	!	!	PUNCT
ma-80	959	3	-------------------	-------------------	PROPN
ma-80	959	4	u	u	NOUN
ma-80	960	1	0=	0=	NOUN
ma-80	960	2	r	r	NOUN
ma-80	960	3			X
ma-80	960	4	1	1	NUM
ma-80	960	5			NOUN
ma-80	960	6	–	–	NOUN
ma-80	960	7	u	u	PROPN
ma-80	960	8	--------------------	--------------------	PUNCT
ma-80	960	9	.	.	PUNCT
ma-80	961	1	r	r	NOUN
ma-80	961	2	0=	0=	NOUN
ma-80	962	1	n	n	DET
ma-80	962	2			NOUN
ma-80	962	3	fn	fn	NOUN
ma-80	962	4	x	x	PROPN
ma-80	963	1			PROPN
ma-80	963	2			NOUN
ma-80	963	3	x–	x–	NOUN
ma-80	963	4	n	n	PROPN
ma-80	964	1	1	1	NUM
ma-80	964	2	+	+	ADP
ma-80	964	3	an	an	DET
ma-80	964	4	r	r	ADJ
ma-80	964	5	x	x	NOUN
ma-80	964	6	–	–	NOUN
ma-80	964	7	r	r	NOUN
ma-80	964	8	r	r	NOUN
ma-80	964	9	0=	0=	NOUN
ma-80	965	1	n	n	NOUN
ma-80	965	2			X
ma-80	966	1	x	x	PUNCT
ma-80	966	2	–	–	NOUN
ma-80	966	3	n	n	PROPN
ma-80	966	4	1	1	NUM
ma-80	966	5	+	+	NUM
ma-80	966	6	bn	bn	NUM
ma-80	966	7	r	r	ADJ
ma-80	966	8			NOUN
ma-80	966	9	x–	x–	PUNCT
ma-80	967	1	r	r	X
ma-80	967	2	r	r	NOUN
ma-80	967	3	0=	0=	NOUN
ma-80	968	1	n	n	NOUN
ma-80	968	2	+=	+=	NOUN
ma-80	968	3	an	an	DET
ma-80	968	4	r	r	PROPN
ma-80	968	5	1	1	NUM
ma-80	968	6			NOUN
ma-80	968	7	–	–	NOUN
ma-80	968	8	n	n	PROPN
ma-80	968	9	1	1	NUM
ma-80	968	10	+	+	NUM
ma-80	968	11	---------------------------f	---------------------------f	NOUN
ma-80	968	12	r	r	NOUN
ma-80	968	13	u–	u–	NOUN
ma-80	968	14			PUNCT
ma-80	968	15			NOUN
ma-80	968	16			NOUN
ma-80	968	17	r	r	NOUN
ma-80	968	18	u–	u–	NOUN
ma-80	968	19			PROPN
ma-80	968	20	!	!	PUNCT
ma-80	968	21	----------------------n	----------------------n	PUNCT
ma-80	969	1	u+	u+	PROPN
ma-80	969	2			PROPN
ma-80	969	3	!	!	PUNCT
ma-80	970	1	u!n	u!n	PROPN
ma-80	970	2	!	!	PUNCT
ma-80	970	3	-------------------	-------------------	PROPN
ma-80	970	4	u	u	NOUN
ma-80	971	1	0=	0=	NOUN
ma-80	971	2	r	r	NOUN
ma-80	971	3			X
ma-80	971	4	1	1	NUM
ma-80	971	5			NOUN
ma-80	971	6	–	–	NOUN
ma-80	971	7	u	u	PROPN
ma-80	971	8	--------------------	--------------------	PROPN
ma-80	972	1	=	=	PROPN
ma-80	972	2	bn	bn	NUM
ma-80	972	3	r	r	PROPN
ma-80	972	4	1	1	NUM
ma-80	972	5			NOUN
ma-80	972	6	–	–	NOUN
ma-80	972	7	n	n	PROPN
ma-80	972	8	1	1	NUM
ma-80	972	9	+	+	CCONJ
ma-80	972	10	---------------------------1–	---------------------------1–	PROPN
ma-80	972	11	r	r	DET
ma-80	972	12	u	u	NOUN
ma-80	972	13	–	–	PUNCT
ma-80	972	14	f	f	PROPN
ma-80	972	15	r	r	NOUN
ma-80	972	16	u–	u–	NOUN
ma-80	972	17			NUM
ma-80	972	18			NOUN
ma-80	973	1			PUNCT
ma-80	973	2	r	r	NOUN
ma-80	973	3	u–	u–	NOUN
ma-80	973	4			PROPN
ma-80	973	5	!	!	PUNCT
ma-80	973	6	-------------------------------------------n	-------------------------------------------n	PUNCT
ma-80	973	7	u+	u+	PROPN
ma-80	973	8			PROPN
ma-80	973	9	!	!	PUNCT
ma-80	973	10	u!n	u!n	PROPN
ma-80	973	11	!	!	PUNCT
ma-80	973	12	-------------------	-------------------	PROPN
ma-80	973	13	u	u	NOUN
ma-80	973	14	0=	0=	NOUN
ma-80	973	15	r	r	NOUN
ma-80	973	16			X
ma-80	973	17	1	1	NUM
ma-80	973	18			NOUN
ma-80	973	19	–	–	NOUN
ma-80	973	20	u	u	PROPN
ma-80	974	1	--------------------.	--------------------.	PUNCT
ma-80	975	1	=	=	PROPN
ma-80	975	2	f	f	PROPN
ma-80	975	3	g1	g1	PROPN
ma-80	975	4	x	x	PUNCT
ma-80	976	1	x1	x1	PROPN
ma-80	976	2	1–=	1–=	NUM
ma-80	976	3	x	x	SYM
ma-80	976	4	1–	1–	NUM
ma-80	976	5	y1	y1	NOUN
ma-80	976	6	g1	g1	NOUN
ma-80	976	7	x1	x1	PUNCT
ma-80	977	1			PROPN
ma-80	977	2	1	1	NUM
ma-80	977	3	e	e	X
ma-80	977	4	--x1	--x1	NOUN
ma-80	977	5	1–	1–	NUM
ma-80	977	6	e	e	PROPN
ma-80	977	7	x1	x1	NUM
ma-80	977	8	1	1	NUM
ma-80	977	9	–	–	PUNCT
ma-80	977	10	+	+	NUM
ma-80	977	11	=	=	NUM
ma-80	978	1	x1	x1	NUM
ma-80	978	2	0.=	0.=	NOUN
ma-80	978	3	y1	y1	NOUN
ma-80	978	4	1	1	NUM
ma-80	978	5	e	e	NOUN
ma-80	978	6	–	–	PUNCT
ma-80	979	1	f	f	X
ma-80	979	2	x1	x1	PROPN
ma-80	979	3	1–	1–	NUM
ma-80	979	4	=	=	X
ma-80	979	5	f	f	PROPN
ma-80	979	6	1	1	NUM
ma-80	979	7	–	–	PUNCT
ma-80	979	8	y1	y1	NOUN
ma-80	979	9	1	1	NUM
ma-80	979	10	e–	e–	NOUN
ma-80	979	11			ADP
ma-80	980	1	x1	x1	PROPN
ma-80	980	2	1–=	1–=	NUM
ma-80	980	3	x1	x1	PROPN
ma-80	980	4	g1	g1	PROPN
ma-80	980	5	1	1	NUM
ma-80	980	6	–	–	PUNCT
ma-80	980	7	y1	y1	PROPN
ma-80	980	8	=	=	NOUN
ma-80	980	9	y	y	PROPN
ma-80	980	10	y1	y1	PROPN
ma-80	980	11	1	1	NUM
ma-80	980	12	e–=	e–=	NOUN
ma-80	980	13	f	f	PROPN
ma-80	980	14	1	1	NUM
ma-80	980	15	–	–	PUNCT
ma-80	980	16	y	y	NOUN
ma-80	980	17			PROPN
ma-80	980	18	g1	g1	NOUN
ma-80	980	19	1	1	NUM
ma-80	980	20	–	–	PUNCT
ma-80	980	21	y	y	PROPN
ma-80	980	22	1	1	NUM
ma-80	980	23	e+	e+	NOUN
ma-80	980	24			NOUN
ma-80	980	25	1–=	1–=	NUM
ma-80	980	26	y2	y2	NOUN
ma-80	980	27	g	g	NOUN
ma-80	980	28	x1	x1	PROPN
ma-80	981	1			PROPN
ma-80	981	2	g1	g1	PROPN
ma-80	981	3	x1	x1	PUNCT
ma-80	982	1			PROPN
ma-80	982	2	y1=	y1=	NOUN
ma-80	982	3	=	=	PUNCT
ma-80	983	1	=	=	SYM
ma-80	983	2	x1	x1	NUM
ma-80	983	3	0	0	NOUN
ma-80	983	4	g	g	NOUN
ma-80	983	5	1	1	NUM
ma-80	983	6	–	–	PUNCT
ma-80	983	7	y2	y2	ADV
ma-80	983	8			PROPN
ma-80	983	9	x1	x1	PRON
ma-80	983	10	g	g	PROPN
ma-80	983	11	1	1	NUM
ma-80	983	12	–	–	PUNCT
ma-80	983	13	y1	y1	NOUN
ma-80	983	14	.=	.=	X
ma-80	983	15	=	=	SYM
ma-80	983	16	x1	x1	PROPN
ma-80	983	17	g1	g1	PROPN
ma-80	983	18	1	1	NUM
ma-80	983	19	–	–	PUNCT
ma-80	983	20	y1	y1	PROPN
ma-80	983	21	=	=	PROPN
ma-80	983	22	g1	g1	PROPN
ma-80	983	23	1	1	NUM
ma-80	983	24	–	–	PUNCT
ma-80	983	25	y1	y1	PROPN
ma-80	983	26			PROPN
ma-80	983	27	g	g	PROPN
ma-80	983	28	1	1	NUM
ma-80	983	29	–	–	PUNCT
ma-80	983	30	y1	y1	PROPN
ma-80	983	31	=	=	NOUN
ma-80	983	32	f	f	PROPN
ma-80	983	33	1	1	NUM
ma-80	983	34	–	–	PUNCT
ma-80	983	35	y	y	NOUN
ma-80	983	36			PROPN
ma-80	983	37	g1	g1	NOUN
ma-80	983	38	1	1	NUM
ma-80	983	39	–	–	PUNCT
ma-80	983	40	y	y	NOUN
ma-80	983	41	1	1	NUM
ma-80	983	42	e	e	NOUN
ma-80	983	43	---+	---+	PROPN
ma-80	983	44	1	1	NUM
ma-80	983	45	–	–	PUNCT
ma-80	983	46	g	g	PROPN
ma-80	983	47	1	1	NUM
ma-80	983	48	–	–	PUNCT
ma-80	983	49	y	y	NOUN
ma-80	983	50	1	1	NUM
ma-80	983	51	e	e	NOUN
ma-80	983	52	---+	---+	NUM
ma-80	983	53	1.–=	1.–=	NUM
ma-80	983	54	=	=	SYM
ma-80	983	55	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	NOUN
ma-80	983	56	appendix	appendix	ADJ
ma-80	983	57	g.	g.	NOUN
ma-80	983	58	proof	proof	NOUN
ma-80	983	59	of	of	ADP
ma-80	983	60	theorem	theorem	ADJ
ma-80	983	61	5.1	5.1	NUM
ma-80	983	62	with	with	ADP
ma-80	983	63	denoting	denote	VERB
ma-80	983	64	the	the	DET
ma-80	983	65	differentiation	differentiation	NOUN
ma-80	983	66	operator	operator	NOUN
ma-80	983	67	,	,	PUNCT
ma-80	983	68	the	the	DET
ma-80	983	69	following	follow	VERB
ma-80	983	70	well	well	ADV
ma-80	983	71	known	know	VERB
ma-80	983	72	results	result	NOUN
ma-80	983	73	apply	apply	VERB
ma-80	983	74	for	for	ADP
ma-80	983	75	an	an	DET
ma-80	983	76	arbitrary	arbitrary	ADJ
ma-80	983	77	function	function	NOUN
ma-80	983	78	:	:	PUNCT
ma-80	983	79	(	(	PUNCT
ma-80	983	80	147	147	NUM
ma-80	983	81	)	)	PUNCT
ma-80	983	82	(	(	PUNCT
ma-80	983	83	148	148	NUM
ma-80	983	84	)	)	PUNCT
ma-80	983	85	(	(	PUNCT
ma-80	983	86	149	149	NUM
ma-80	983	87	)	)	PUNCT
ma-80	983	88	etc	etc	X
ma-80	983	89	.	.	X
ma-80	983	90	consider	consider	VERB
ma-80	983	91	,	,	PUNCT
ma-80	983	92	as	as	SCONJ
ma-80	983	93	defined	define	VERB
ma-80	983	94	by	by	ADP
ma-80	983	95	equation	equation	NOUN
ma-80	983	96	75	75	NUM
ma-80	983	97	,	,	PUNCT
ma-80	983	98	over	over	ADP
ma-80	983	99	the	the	DET
ma-80	983	100	interval	interval	NOUN
ma-80	983	101	.	.	PUNCT
ma-80	984	1	a	a	DET
ma-80	984	2	spline	spline	NOUN
ma-80	984	3	approximation	approximation	NOUN
ma-80	984	4	(	(	PUNCT
ma-80	984	5	see	see	VERB
ma-80	984	6	equation	equation	NOUN
ma-80	984	7	70	70	NUM
ma-80	984	8	)	)	PUNCT
ma-80	984	9	for	for	ADP
ma-80	984	10	,	,	PUNCT
ma-80	984	11	of	of	ADP
ma-80	984	12	order	order	NOUN
ma-80	984	13	,	,	PUNCT
ma-80	984	14	requires	require	VERB
ma-80	984	15	derivatives	derivative	NOUN
ma-80	984	16	,	,	PUNCT
ma-80	984	17	of	of	ADP
ma-80	984	18	orders	order	NOUN
ma-80	984	19	zero	zero	NUM
ma-80	984	20	to	to	ADP
ma-80	984	21	at	at	ADP
ma-80	984	22	the	the	DET
ma-80	984	23	points	point	NOUN
ma-80	984	24	and	and	CCONJ
ma-80	984	25	,	,	PUNCT
ma-80	984	26	to	to	PART
ma-80	984	27	be	be	AUX
ma-80	984	28	determined	determine	VERB
ma-80	984	29	.	.	PUNCT
ma-80	985	1	using	use	VERB
ma-80	985	2	the	the	DET
ma-80	985	3	above	above	ADJ
ma-80	985	4	formulas	formula	NOUN
ma-80	985	5	,	,	PUNCT
ma-80	985	6	such	such	ADJ
ma-80	985	7	values	value	NOUN
ma-80	985	8	can	can	AUX
ma-80	985	9	be	be	AUX
ma-80	985	10	determined	determine	VERB
ma-80	985	11	from	from	ADP
ma-80	985	12	the	the	DET
ma-80	985	13	derivatives	derivative	NOUN
ma-80	985	14	of	of	ADP
ma-80	985	15	at	at	ADP
ma-80	985	16	the	the	DET
ma-80	985	17	points	point	NOUN
ma-80	985	18	and	and	CCONJ
ma-80	985	19	and	and	CCONJ
ma-80	985	20	values	value	NOUN
ma-80	985	21	of	of	ADP
ma-80	985	22	these	these	DET
ma-80	985	23	derivatives	derivative	NOUN
ma-80	985	24	are	be	AUX
ma-80	985	25	tabulated	tabulate	VERB
ma-80	985	26	in	in	ADP
ma-80	985	27	table	table	NOUN
ma-80	985	28	9	9	NUM
ma-80	985	29	.	.	PUNCT
ma-80	985	30	to	to	PART
ma-80	985	31	determine	determine	VERB
ma-80	985	32	the	the	DET
ma-80	985	33	derivative	derivative	ADJ
ma-80	985	34	values	value	NOUN
ma-80	985	35	at	at	ADP
ma-80	985	36	zero	zero	NUM
ma-80	985	37	,	,	PUNCT
ma-80	985	38	the	the	DET
ma-80	985	39	standard	standard	PROPN
ma-80	985	40	taylor	taylor	PROPN
ma-80	985	41	series	series	PROPN
ma-80	985	42	expansion	expansion	NOUN
ma-80	985	43	for	for	ADP
ma-80	985	44	the	the	DET
ma-80	985	45	exponential	exponential	ADJ
ma-80	985	46	function	function	NOUN
ma-80	985	47	can	can	AUX
ma-80	985	48	be	be	AUX
ma-80	985	49	used	use	VERB
ma-80	985	50	to	to	PART
ma-80	985	51	yield	yield	VERB
ma-80	985	52	the	the	DET
ma-80	985	53	alternative	alternative	ADJ
ma-80	985	54	form	form	NOUN
ma-80	985	55	for	for	ADP
ma-80	985	56	of	of	ADP
ma-80	985	57	(	(	PUNCT
ma-80	985	58	150	150	NUM
ma-80	985	59	)	)	PUNCT
ma-80	985	60	using	use	VERB
ma-80	985	61	equation	equation	NOUN
ma-80	985	62	70	70	NUM
ma-80	985	63	,	,	PUNCT
ma-80	985	64	and	and	CCONJ
ma-80	985	65	the	the	DET
ma-80	985	66	derivative	derivative	ADJ
ma-80	985	67	values	value	NOUN
ma-80	985	68	given	give	VERB
ma-80	985	69	in	in	ADP
ma-80	985	70	table	table	NOUN
ma-80	985	71	9	9	NUM
ma-80	985	72	,	,	PUNCT
ma-80	985	73	the	the	DET
ma-80	985	74	spline	spline	NOUN
ma-80	985	75	approximations	approximation	VERB
ma-80	985	76	for	for	ADP
ma-80	985	77	,	,	PUNCT
ma-80	985	78	based	base	VERB
ma-80	985	79	on	on	ADP
ma-80	985	80	the	the	DET
ma-80	985	81	points	point	NOUN
ma-80	985	82	and	and	CCONJ
ma-80	985	83	and	and	CCONJ
ma-80	985	84	for	for	ADP
ma-80	985	85	orders	order	NOUN
ma-80	985	86	one	one	NUM
ma-80	985	87	to	to	ADP
ma-80	985	88	four	four	NUM
ma-80	985	89	,	,	PUNCT
ma-80	985	90	are	be	AUX
ma-80	985	91	:	:	PUNCT
ma-80	985	92	(	(	PUNCT
ma-80	985	93	151	151	NUM
ma-80	985	94	)	)	PUNCT
ma-80	985	95	(	(	PUNCT
ma-80	985	96	152	152	NUM
ma-80	985	97	)	)	PUNCT
ma-80	986	1	d	d	NOUN
ma-80	986	2	f	f	X
ma-80	986	3	d	d	X
ma-80	986	4	f	f	PROPN
ma-80	986	5	1	1	NUM
ma-80	986	6	–	–	PUNCT
ma-80	986	7	z	z	PROPN
ma-80	986	8			SYM
ma-80	986	9			ADP
ma-80	986	10	1	1	NUM
ma-80	986	11	f	f	NOUN
ma-80	986	12	1	1	NUM
ma-80	986	13			PUNCT
ma-80	986	14	x	x	PUNCT
ma-80	986	15			PROPN
ma-80	986	16	---------------x	---------------x	PUNCT
ma-80	987	1	f	f	PROPN
ma-80	987	2	1	1	NUM
ma-80	987	3	–	–	PUNCT
ma-80	987	4	z	z	PROPN
ma-80	987	5	=	=	NOUN
ma-80	987	6	=	=	PUNCT
ma-80	987	7	d	d	X
ma-80	987	8	2	2	PROPN
ma-80	987	9			PROPN
ma-80	987	10	f	f	PROPN
ma-80	987	11	1	1	NUM
ma-80	987	12	–	–	PUNCT
ma-80	987	13	z	z	PROPN
ma-80	987	14			PUNCT
ma-80	987	15			NOUN
ma-80	987	16	f	f	X
ma-80	987	17	2	2	PROPN
ma-80	987	18			PROPN
ma-80	987	19	x	x	X
ma-80	988	1			PROPN
ma-80	988	2	–	–	PUNCT
ma-80	988	3	f	f	NOUN
ma-80	989	1	1	1	NUM
ma-80	989	2			PUNCT
ma-80	989	3	x	x	PUNCT
ma-80	989	4			X
ma-80	990	1			NOUN
ma-80	990	2	3	3	NUM
ma-80	990	3	----------------------x	----------------------x	NUM
ma-80	990	4	f	f	PROPN
ma-80	990	5	1	1	NUM
ma-80	990	6	–	–	PUNCT
ma-80	990	7	z	z	PROPN
ma-80	990	8	=	=	NOUN
ma-80	990	9	=	=	PUNCT
ma-80	991	1	d	d	NUM
ma-80	991	2	3	3	NUM
ma-80	991	3			PROPN
ma-80	991	4	f	f	PROPN
ma-80	991	5	1	1	NUM
ma-80	991	6	–	–	PUNCT
ma-80	991	7	z	z	PROPN
ma-80	991	8			PUNCT
ma-80	991	9			PROPN
ma-80	991	10	f	f	PROPN
ma-80	991	11	3	3	PROPN
ma-80	991	12			PROPN
ma-80	991	13	x	x	PROPN
ma-80	992	1			PROPN
ma-80	992	2	–	–	PUNCT
ma-80	992	3	f	f	NOUN
ma-80	993	1	1	1	NUM
ma-80	993	2			PUNCT
ma-80	993	3	x	x	PUNCT
ma-80	993	4			X
ma-80	993	5			NOUN
ma-80	993	6	4	4	NUM
ma-80	993	7	----------------------3	----------------------3	PROPN
ma-80	993	8	f	f	X
ma-80	993	9	2	2	PROPN
ma-80	993	10			PROPN
ma-80	993	11	x	x	X
ma-80	993	12			X
ma-80	993	13			NOUN
ma-80	993	14	2	2	NUM
ma-80	993	15	f	f	NOUN
ma-80	993	16	1	1	NUM
ma-80	993	17			PUNCT
ma-80	993	18	x	x	PUNCT
ma-80	993	19			X
ma-80	993	20			NOUN
ma-80	993	21	5	5	NUM
ma-80	993	22	--------------------------+	--------------------------+	NOUN
ma-80	993	23	x	x	X
ma-80	993	24	f	f	PROPN
ma-80	993	25	1	1	NUM
ma-80	993	26	–	–	PUNCT
ma-80	993	27	z	z	PROPN
ma-80	993	28	=	=	NOUN
ma-80	993	29	=	=	PUNCT
ma-80	994	1	d	d	X
ma-80	994	2	4	4	PROPN
ma-80	994	3			PUNCT
ma-80	994	4	f	f	PROPN
ma-80	994	5	1	1	NUM
ma-80	994	6	–	–	PUNCT
ma-80	994	7	z	z	PROPN
ma-80	994	8			PUNCT
ma-80	994	9			NOUN
ma-80	994	10	f	f	PROPN
ma-80	994	11	4	4	PROPN
ma-80	994	12			PROPN
ma-80	994	13	x	x	PUNCT
ma-80	995	1			PROPN
ma-80	995	2	–	–	PUNCT
ma-80	995	3	f	f	NOUN
ma-80	996	1	1	1	NUM
ma-80	996	2			PUNCT
ma-80	996	3	x	x	PUNCT
ma-80	996	4			X
ma-80	996	5			PROPN
ma-80	996	6	5	5	NUM
ma-80	997	1	----------------------10f	----------------------10f	NUM
ma-80	997	2	3	3	PROPN
ma-80	997	3			PUNCT
ma-80	997	4	x	x	PROPN
ma-80	997	5	f	f	X
ma-80	997	6	2	2	PROPN
ma-80	997	7			PUNCT
ma-80	997	8	x	x	PUNCT
ma-80	998	1			PUNCT
ma-80	998	2	f	f	X
ma-80	998	3	1	1	NUM
ma-80	998	4			PUNCT
ma-80	998	5	x	x	PUNCT
ma-80	998	6			X
ma-80	998	7			PROPN
ma-80	999	1	6	6	NUM
ma-80	999	2	-------------------------------------15	-------------------------------------15	PROPN
ma-80	999	3	f	f	X
ma-80	999	4	2	2	PROPN
ma-80	999	5			PROPN
ma-80	999	6	x	x	X
ma-80	999	7			X
ma-80	999	8			NOUN
ma-80	999	9	3	3	NUM
ma-80	999	10	f	f	NOUN
ma-80	999	11	1	1	NUM
ma-80	999	12			PUNCT
ma-80	999	13	x	x	PUNCT
ma-80	999	14			X
ma-80	999	15			NOUN
ma-80	999	16	7	7	NUM
ma-80	999	17	-----------------------------–+	-----------------------------–+	NOUN
ma-80	999	18	x	x	SYM
ma-80	999	19	f	f	PROPN
ma-80	999	20	1	1	NUM
ma-80	999	21	–	–	PUNCT
ma-80	999	22	z	z	PROPN
ma-80	999	23	=	=	NOUN
ma-80	999	24	=	=	PUNCT
ma-80	999	25	g	g	NOUN
ma-80	999	26	0	0	NUM
ma-80	999	27	1	1	NUM
ma-80	999	28			NOUN
ma-80	999	29	g	g	PROPN
ma-80	999	30	1	1	NUM
ma-80	999	31	–	–	PUNCT
ma-80	999	32	n	n	CCONJ
ma-80	999	33	n	n	NOUN
ma-80	999	34	0	0	NUM
ma-80	999	35	1	1	NUM
ma-80	999	36	e	e	ADP
ma-80	999	37	g	g	PROPN
ma-80	999	38	0	0	NUM
ma-80	999	39	1	1	NUM
ma-80	999	40	g	g	NOUN
ma-80	999	41	g	g	PROPN
ma-80	999	42	x1	x1	PROPN
ma-80	1000	1			PUNCT
ma-80	1001	1	x1	x1	DET
ma-80	1001	2	2e	2e	PROPN
ma-80	1001	3	---------1	---------1	NOUN
ma-80	1001	4	2	2	NUM
ma-80	1001	5	i	i	PRON
ma-80	1001	6	1+	1+	NUM
ma-80	1001	7	x1	x1	VERB
ma-80	1002	1	i	i	PRON
ma-80	1002	2	i	i	PRON
ma-80	1002	3	2+	2+	NUM
ma-80	1002	4			PROPN
ma-80	1002	5	!	!	PUNCT
ma-80	1003	1	--------------------i	--------------------i	PROPN
ma-80	1003	2	1=	1=	NUM
ma-80	1003	3			PROPN
ma-80	1003	4	+	+	NUM
ma-80	1004	1	.=	.=	PROPN
ma-80	1004	2	g	g	PROPN
ma-80	1004	3	1	1	NUM
ma-80	1004	4	–	–	PUNCT
ma-80	1004	5	y2	y2	PROPN
ma-80	1004	6			PROPN
ma-80	1004	7	0	0	NUM
ma-80	1004	8	1	1	NUM
ma-80	1004	9	e	e	ADV
ma-80	1004	10	g1	g1	PROPN
ma-80	1004	11	1	1	NUM
ma-80	1004	12	–	–	PUNCT
ma-80	1004	13	y2	y2	ADJ
ma-80	1004	14			PROPN
ma-80	1004	15	2ey2	2ey2	NUM
ma-80	1004	16	1	1	NUM
ma-80	1004	17	2	2	NUM
ma-80	1004	18	ey2	ey2	NOUN
ma-80	1004	19	1	1	NUM
ma-80	1004	20	1	1	NUM
ma-80	1004	21	2e	2e	NUM
ma-80	1004	22	---------3	---------3	NOUN
ma-80	1004	23	2	2	NUM
ma-80	1004	24	2	2	NUM
ma-80	1004	25	----------–+	----------–+	NOUN
ma-80	1004	26	–	–	PUNCT
ma-80	1004	27	ey2	ey2	NOUN
ma-80	1004	28	2	2	NUM
ma-80	1004	29	1	1	NUM
ma-80	1004	30	2	2	NUM
ma-80	1004	31	–	–	PUNCT
ma-80	1004	32	2	2	NUM
ma-80	1004	33	e	e	NOUN
ma-80	1004	34	-------++=	-------++=	PUNCT
ma-80	1004	35	g2	g2	PROPN
ma-80	1004	36	1	1	NUM
ma-80	1004	37	–	–	PUNCT
ma-80	1004	38	y2	y2	ADJ
ma-80	1004	39			PROPN
ma-80	1004	40	2ey2	2ey2	NUM
ma-80	1004	41	1	1	NUM
ma-80	1004	42	2ey2	2ey2	NUM
ma-80	1004	43	3	3	NUM
ma-80	1004	44	---------------	---------------	PUNCT
ma-80	1004	45	–	–	PUNCT
ma-80	1004	46	6e	6e	NUM
ma-80	1004	47	2	2	NUM
ma-80	1004	48	1–	1–	NUM
ma-80	1004	49			PROPN
ma-80	1004	50	7	7	NUM
ma-80	1004	51	2	2	NUM
ma-80	1004	52	-------	-------	PUNCT
ma-80	1004	53	–	–	PUNCT
ma-80	1004	54	2	2	NUM
ma-80	1004	55	2	2	NUM
ma-80	1004	56	e	e	NOUN
ma-80	1004	57	----------	----------	PUNCT
ma-80	1004	58	–	–	PUNCT
ma-80	1004	59	y2	y2	NOUN
ma-80	1004	60	2	2	NUM
ma-80	1004	61	–	–	PUNCT
ma-80	1004	62	+	+	NUM
ma-80	1004	63	e	e	X
ma-80	1004	64	3	3	NUM
ma-80	1004	65	2	2	NUM
ma-80	1004	66	17	17	NUM
ma-80	1004	67	2	2	NUM
ma-80	1004	68	------8	------8	PROPN
ma-80	1004	69	–	–	PUNCT
ma-80	1004	70	6	6	NUM
ma-80	1004	71	2e	2e	NUM
ma-80	1004	72	–	–	PUNCT
ma-80	1004	73	4	4	NUM
ma-80	1004	74	2	2	NUM
ma-80	1004	75	e	e	NOUN
ma-80	1004	76	----------	----------	PUNCT
ma-80	1004	77	–	–	PUNCT
ma-80	1004	78	y2	y2	NOUN
ma-80	1004	79	3	3	NUM
ma-80	1004	80	e	e	NOUN
ma-80	1004	81	2	2	NUM
ma-80	1004	82	10	10	NUM
ma-80	1004	83	2	2	NUM
ma-80	1004	84	3	3	NUM
ma-80	1004	85	------------3	------------3	NOUN
ma-80	1004	86	–	–	PUNCT
ma-80	1004	87	5e	5e	NOUN
ma-80	1004	88	2	2	NUM
ma-80	1004	89	-------	-------	PUNCT
ma-80	1004	90	–	–	PUNCT
ma-80	1004	91	2	2	NUM
ma-80	1004	92	2	2	NUM
ma-80	1004	93	–	–	PUNCT
ma-80	1004	94	y2	y2	NOUN
ma-80	1004	95	4	4	NUM
ma-80	1004	96	+	+	NOUN
ma-80	1004	97	=	=	SYM
ma-80	1004	98	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	NOUN
ma-80	1004	99	(	(	PUNCT
ma-80	1004	100	153	153	NUM
ma-80	1004	101	)	)	PUNCT
ma-80	1004	102	(	(	PUNCT
ma-80	1004	103	154	154	NUM
ma-80	1004	104	)	)	PUNCT
ma-80	1004	105	in	in	ADP
ma-80	1004	106	general	general	ADJ
ma-80	1004	107	:	:	PUNCT
ma-80	1004	108	(	(	PUNCT
ma-80	1004	109	155	155	NUM
ma-80	1004	110	)	)	PUNCT
ma-80	1004	111	table	table	NOUN
ma-80	1004	112	9	9	NUM
ma-80	1004	113	.	.	PUNCT
ma-80	1005	1	values	value	NOUN
ma-80	1005	2	of	of	ADP
ma-80	1005	3	the	the	DET
ma-80	1005	4	derivatives	derivative	NOUN
ma-80	1005	5	of	of	ADP
ma-80	1005	6	at	at	ADP
ma-80	1005	7	the	the	DET
ma-80	1005	8	points	point	NOUN
ma-80	1005	9	zero	zero	NUM
ma-80	1005	10	and	and	CCONJ
ma-80	1005	11	one	one	NUM
ma-80	1005	12	.	.	PUNCT
ma-80	1006	1	order	order	NOUN
ma-80	1006	2	0	0	NUM
ma-80	1006	3	0	0	NUM
ma-80	1006	4	1	1	NUM
ma-80	1006	5	2	2	NUM
ma-80	1006	6	3	3	NUM
ma-80	1006	7	4	4	NUM
ma-80	1006	8	5	5	NUM
ma-80	1006	9	g	g	NOUN
ma-80	1006	10	x1	x1	PROPN
ma-80	1007	1			PROPN
ma-80	1007	2	g	g	NOUN
ma-80	1007	3	i	i	NOUN
ma-80	1007	4			PROPN
ma-80	1007	5	0	0	PROPN
ma-80	1008	1			PROPN
ma-80	1008	2	g	g	NOUN
ma-80	1008	3	i	i	NOUN
ma-80	1009	1			PROPN
ma-80	1009	2	1	1	NUM
ma-80	1009	3			PROPN
ma-80	1009	4	1	1	NUM
ma-80	1009	5	e	e	NOUN
ma-80	1009	6	-----1	-----1	DET
ma-80	1009	7	2e	2e	NOUN
ma-80	1009	8	---------e	---------e	ADJ
ma-80	1009	9	2	2	NUM
ma-80	1009	10	-----2	-----2	SYM
ma-80	1009	11	3	3	NUM
ma-80	1009	12	e	e	NOUN
ma-80	1009	13	---------e	---------e	PROPN
ma-80	1009	14	1	1	NUM
ma-80	1009	15	e	e	NOUN
ma-80	1009	16	4	4	NUM
ma-80	1009	17	---	---	PUNCT
ma-80	1009	18	–	–	PUNCT
ma-80	1009	19	5	5	NUM
ma-80	1009	20	12	12	NUM
ma-80	1009	21	2e	2e	NOUN
ma-80	1009	22	---------------3	---------------3	PROPN
ma-80	1009	23	e	e	NOUN
ma-80	1009	24	2	2	NUM
ma-80	1009	25	---------1	---------1	NOUN
ma-80	1009	26	e	e	NOUN
ma-80	1009	27	–	–	PUNCT
ma-80	1009	28	e	e	NOUN
ma-80	1009	29	2	2	NUM
ma-80	1009	30	4	4	NUM
ma-80	1009	31	-----+	-----+	PROPN
ma-80	1009	32	11	11	NUM
ma-80	1009	33	45	45	NUM
ma-80	1009	34	2e	2e	NOUN
ma-80	1009	35	---------------2	---------------2	X
ma-80	1009	36	e	e	PROPN
ma-80	1009	37	1	1	NUM
ma-80	1009	38	3e	3e	NOUN
ma-80	1009	39	–	–	PUNCT
ma-80	1009	40	9e	9e	NOUN
ma-80	1009	41	2	2	NUM
ma-80	1009	42	4	4	NUM
ma-80	1009	43	-------15e	-------15e	NUM
ma-80	1009	44	3	3	NUM
ma-80	1009	45	32	32	NUM
ma-80	1009	46	-----------–+	-----------–+	NOUN
ma-80	1009	47	59	59	NUM
ma-80	1009	48	432	432	NUM
ma-80	1009	49	2e	2e	NOUN
ma-80	1009	50	------------------5	------------------5	PROPN
ma-80	1009	51	e	e	PROPN
ma-80	1009	52	2	2	NUM
ma-80	1009	53	---------1	---------1	NOUN
ma-80	1009	54	8e	8e	NUM
ma-80	1009	55	–	–	PUNCT
ma-80	1009	56	27e	27e	NUM
ma-80	1009	57	2	2	NUM
ma-80	1009	58	2	2	NUM
ma-80	1009	59	----------15e	----------15e	NOUN
ma-80	1009	60	3	3	NUM
ma-80	1009	61	2	2	NUM
ma-80	1009	62	-----------	-----------	PUNCT
ma-80	1009	63	–	–	PUNCT
ma-80	1009	64	21e	21e	NUM
ma-80	1009	65	4	4	NUM
ma-80	1009	66	16	16	NUM
ma-80	1009	67	-----------+	-----------+	ADJ
ma-80	1009	68	+	+	CCONJ
ma-80	1009	69	g3	g3	PROPN
ma-80	1009	70	1	1	NUM
ma-80	1009	71	–	–	PUNCT
ma-80	1009	72	y2	y2	ADJ
ma-80	1009	73			PROPN
ma-80	1009	74	2ey2	2ey2	NUM
ma-80	1009	75	1	1	NUM
ma-80	1009	76	2ey2	2ey2	NUM
ma-80	1009	77	3	3	NUM
ma-80	1009	78	---------------	---------------	PUNCT
ma-80	1009	79	–	–	PUNCT
ma-80	1009	80	11ey2	11ey2	NUM
ma-80	1009	81	2	2	NUM
ma-80	1009	82	36	36	NUM
ma-80	1009	83	-------------e	-------------e	NOUN
ma-80	1009	84	3	3	NUM
ma-80	1009	85	2	2	NUM
ma-80	1009	86	191	191	NUM
ma-80	1009	87	9	9	NUM
ma-80	1009	88	--------125	--------125	NOUN
ma-80	1009	89	3	3	NUM
ma-80	1009	90	2	2	NUM
ma-80	1009	91	----------	----------	PUNCT
ma-80	1009	92	–	–	PUNCT
ma-80	1009	93	25	25	NUM
ma-80	1009	94	e	e	SYM
ma-80	1009	95	2	2	NUM
ma-80	1009	96	------------8	------------8	NOUN
ma-80	1009	97	2	2	NUM
ma-80	1009	98	e	e	NOUN
ma-80	1009	99	---------6	---------6	NOUN
ma-80	1009	100	2	2	NUM
ma-80	1009	101	e	e	NOUN
ma-80	1009	102	3	3	NUM
ma-80	1009	103	2	2	NUM
ma-80	1009	104	----------+	----------+	PUNCT
ma-80	1010	1	+	+	PUNCT
ma-80	1011	1	+	+	CCONJ
ma-80	1011	2	y2	y2	NOUN
ma-80	1011	3	3	3	NUM
ma-80	1011	4	+	+	NOUN
ma-80	1011	5	–	–	PUNCT
ma-80	1011	6	+	+	NUM
ma-80	1011	7	e	e	X
ma-80	1011	8	2	2	NUM
ma-80	1011	9	281	281	NUM
ma-80	1011	10	6	6	NUM
ma-80	1011	11	--------146	--------146	NOUN
ma-80	1011	12	2	2	NUM
ma-80	1011	13	3	3	NUM
ma-80	1011	14	----------------	----------------	PUNCT
ma-80	1011	15	–	–	PUNCT
ma-80	1011	16	32	32	NUM
ma-80	1011	17	2e	2e	NOUN
ma-80	1011	18	22	22	NUM
ma-80	1011	19	2	2	NUM
ma-80	1011	20	18	18	NUM
ma-80	1011	21	2	2	NUM
ma-80	1011	22	e	e	NOUN
ma-80	1011	23	-------------+	-------------+	NOUN
ma-80	1011	24	+	+	CCONJ
ma-80	1011	25	+	+	CCONJ
ma-80	1011	26	y2	y2	PROPN
ma-80	1011	27	4	4	NUM
ma-80	1011	28	–	–	PUNCT
ma-80	1011	29	e	e	NOUN
ma-80	1011	30	5	5	NUM
ma-80	1011	31	2	2	NUM
ma-80	1011	32	335	335	NUM
ma-80	1011	33	9	9	NUM
ma-80	1011	34	--------40	--------40	PROPN
ma-80	1011	35	2	2	NUM
ma-80	1011	36	–	–	PUNCT
ma-80	1011	37	55e	55e	NUM
ma-80	1011	38	3	3	NUM
ma-80	1011	39	2	2	NUM
ma-80	1011	40	2	2	NUM
ma-80	1011	41	----------------20	----------------20	NUM
ma-80	1011	42	2	2	NUM
ma-80	1011	43	e	e	NOUN
ma-80	1011	44	18	18	NUM
ma-80	1011	45	2	2	NUM
ma-80	1011	46	e	e	NOUN
ma-80	1011	47	-------------+	-------------+	NOUN
ma-80	1011	48	+	+	CCONJ
ma-80	1012	1	+	+	CCONJ
ma-80	1012	2	y2	y2	NOUN
ma-80	1012	3	5	5	NUM
ma-80	1013	1	+	+	CCONJ
ma-80	1013	2	e	e	X
ma-80	1013	3	3	3	NUM
ma-80	1013	4	371	371	NUM
ma-80	1013	5	36	36	NUM
ma-80	1013	6	--------34	--------34	PROPN
ma-80	1013	7	2	2	NUM
ma-80	1013	8	3	3	NUM
ma-80	1013	9	-------------	-------------	PUNCT
ma-80	1013	10	–	–	PUNCT
ma-80	1013	11	8	8	NUM
ma-80	1013	12	2e	2e	NOUN
ma-80	1013	13	2	2	NUM
ma-80	1013	14	6	6	NUM
ma-80	1013	15	2e	2e	NUM
ma-80	1013	16	6	6	NUM
ma-80	1013	17	2	2	NUM
ma-80	1013	18	+	+	NUM
ma-80	1013	19	+	+	CCONJ
ma-80	1013	20	+	+	CCONJ
ma-80	1013	21	y2	y2	PROPN
ma-80	1013	22	6	6	NUM
ma-80	1013	23	=	=	NOUN
ma-80	1013	24	g4	g4	NOUN
ma-80	1013	25	1	1	NUM
ma-80	1013	26	–	–	PUNCT
ma-80	1013	27	y2	y2	ADJ
ma-80	1013	28			PROPN
ma-80	1013	29	2ey2	2ey2	NUM
ma-80	1013	30	1	1	NUM
ma-80	1013	31	2ey2	2ey2	NUM
ma-80	1013	32	3	3	NUM
ma-80	1013	33	---------------	---------------	PUNCT
ma-80	1013	34	–	–	PUNCT
ma-80	1013	35	11ey2	11ey2	NUM
ma-80	1013	36	2	2	NUM
ma-80	1013	37	36	36	NUM
ma-80	1013	38	-------------43e	-------------43e	NUM
ma-80	1013	39	3	3	NUM
ma-80	1013	40	2	2	NUM
ma-80	1013	41	y2	y2	NOUN
ma-80	1013	42	3	3	NUM
ma-80	1013	43	135	135	NUM
ma-80	1013	44	2	2	NUM
ma-80	1013	45	----------------------–+	----------------------–+	NOUN
ma-80	1013	46	+	+	CCONJ
ma-80	1013	47	e	e	X
ma-80	1013	48	2	2	NUM
ma-80	1013	49	4075	4075	NUM
ma-80	1013	50	27	27	NUM
ma-80	1013	51	2	2	NUM
ma-80	1013	52	------------895	------------895	NOUN
ma-80	1013	53	12	12	NUM
ma-80	1013	54	---------	---------	NUM
ma-80	1013	55	–	–	PUNCT
ma-80	1013	56	91e	91e	NOUN
ma-80	1013	57	2	2	NUM
ma-80	1013	58	---------	---------	PUNCT
ma-80	1013	59	–	–	PUNCT
ma-80	1013	60	61	61	NUM
ma-80	1013	61	2	2	NUM
ma-80	1013	62	-------	-------	PUNCT
ma-80	1013	63	–	–	PUNCT
ma-80	1013	64	27	27	NUM
ma-80	1013	65	2	2	NUM
ma-80	1013	66	e	e	X
ma-80	1013	67	-------------	-------------	PUNCT
ma-80	1013	68	–	–	PUNCT
ma-80	1013	69	64	64	NUM
ma-80	1013	70	2	2	NUM
ma-80	1013	71	3e	3e	NOUN
ma-80	1013	72	2	2	NUM
ma-80	1013	73	-------------	-------------	PUNCT
ma-80	1013	74	–	–	PUNCT
ma-80	1013	75	y2	y2	NOUN
ma-80	1013	76	4	4	NUM
ma-80	1013	77	–	–	PUNCT
ma-80	1013	78	e	e	X
ma-80	1013	79	5	5	NUM
ma-80	1013	80	2	2	NUM
ma-80	1013	81	6658	6658	NUM
ma-80	1013	82	2	2	NUM
ma-80	1013	83	27	27	NUM
ma-80	1013	84	------------------2126	------------------2126	NOUN
ma-80	1013	85	9	9	NUM
ma-80	1013	86	------------	------------	SYM
ma-80	1013	87	–	–	PUNCT
ma-80	1013	88	315e	315e	NUM
ma-80	1013	89	3	3	NUM
ma-80	1013	90	2	2	NUM
ma-80	1013	91	2	2	NUM
ma-80	1013	92	--------------------	--------------------	PUNCT
ma-80	1013	93	–	–	PUNCT
ma-80	1013	94	110	110	NUM
ma-80	1013	95	2e	2e	NUM
ma-80	1013	96	–	–	PUNCT
ma-80	1013	97	102	102	NUM
ma-80	1013	98	2	2	NUM
ma-80	1013	99	e	e	X
ma-80	1013	100	----------------	----------------	PROPN
ma-80	1013	101	–	–	PUNCT
ma-80	1013	102	256	256	NUM
ma-80	1013	103	2	2	NUM
ma-80	1013	104	3e	3e	NOUN
ma-80	1013	105	3	3	NUM
ma-80	1013	106	2	2	NUM
ma-80	1013	107	----------------	----------------	PUNCT
ma-80	1013	108	–	–	PUNCT
ma-80	1013	109	y2	y2	NOUN
ma-80	1013	110	5	5	NUM
ma-80	1014	1	+	+	CCONJ
ma-80	1014	2	e	e	X
ma-80	1014	3	3	3	NUM
ma-80	1014	4	8467	8467	NUM
ma-80	1014	5	2	2	NUM
ma-80	1014	6	27	27	NUM
ma-80	1014	7	------------------1175	------------------1175	NUM
ma-80	1014	8	4	4	NUM
ma-80	1014	9	------------	------------	PUNCT
ma-80	1014	10	–	–	PUNCT
ma-80	1014	11	207	207	NUM
ma-80	1014	12	2e	2e	NUM
ma-80	1014	13	2	2	NUM
ma-80	1014	14	–	–	PUNCT
ma-80	1014	15	149	149	NUM
ma-80	1014	16	2e	2e	NUM
ma-80	1014	17	–	–	PUNCT
ma-80	1014	18	144	144	NUM
ma-80	1014	19	2	2	NUM
ma-80	1014	20	–	–	PUNCT
ma-80	1014	21	128	128	NUM
ma-80	1014	22	2	2	NUM
ma-80	1014	23	e	e	X
ma-80	1014	24	----------------	----------------	PUNCT
ma-80	1014	25	–	–	PUNCT
ma-80	1014	26	y2	y2	NOUN
ma-80	1014	27	6	6	NUM
ma-80	1014	28	–	–	PUNCT
ma-80	1014	29	e	e	NOUN
ma-80	1014	30	7	7	NUM
ma-80	1014	31	2	2	NUM
ma-80	1014	32	4904	4904	NUM
ma-80	1014	33	2	2	NUM
ma-80	1014	34	27	27	NUM
ma-80	1014	35	------------------502	------------------502	NOUN
ma-80	1014	36	3	3	NUM
ma-80	1014	37	---------	---------	NOUN
ma-80	1014	38	–	–	PUNCT
ma-80	1014	39	245e	245e	NOUN
ma-80	1014	40	5	5	NUM
ma-80	1014	41	2	2	NUM
ma-80	1014	42	2	2	NUM
ma-80	1014	43	--------------------	--------------------	PUNCT
ma-80	1014	44	–	–	PUNCT
ma-80	1014	45	90	90	NUM
ma-80	1014	46	2e	2e	NOUN
ma-80	1014	47	3	3	NUM
ma-80	1014	48	2	2	NUM
ma-80	1014	49	–	–	PUNCT
ma-80	1014	50	90	90	NUM
ma-80	1014	51	2e	2e	NUM
ma-80	1014	52	–	–	PUNCT
ma-80	1014	53	256	256	NUM
ma-80	1014	54	2	2	NUM
ma-80	1014	55	3	3	NUM
ma-80	1014	56	e	e	X
ma-80	1014	57	----------------	----------------	PUNCT
ma-80	1014	58	–	–	PUNCT
ma-80	1014	59	y2	y2	NOUN
ma-80	1014	60	7	7	NUM
ma-80	1014	61	+	+	CCONJ
ma-80	1014	62	e	e	X
ma-80	1014	63	4	4	NUM
ma-80	1014	64	10843	10843	NUM
ma-80	1014	65	135	135	NUM
ma-80	1014	66	2	2	NUM
ma-80	1014	67	---------------1315	---------------1315	PROPN
ma-80	1014	68	36	36	NUM
ma-80	1014	69	------------	------------	PUNCT
ma-80	1014	70	–	–	PUNCT
ma-80	1014	71	55e	55e	NUM
ma-80	1014	72	3	3	NUM
ma-80	1014	73	2	2	NUM
ma-80	1014	74	-----------	-----------	NUM
ma-80	1014	75	–	–	PUNCT
ma-80	1014	76	41e	41e	X
ma-80	1014	77	2	2	NUM
ma-80	1014	78	2	2	NUM
ma-80	1014	79	-----------	-----------	PUNCT
ma-80	1014	80	–	–	PUNCT
ma-80	1014	81	21	21	NUM
ma-80	1014	82	2e	2e	NUM
ma-80	1014	83	–	–	PUNCT
ma-80	1014	84	64	64	NUM
ma-80	1014	85	2	2	NUM
ma-80	1014	86	3	3	NUM
ma-80	1014	87	-------------	-------------	PUNCT
ma-80	1014	88	–	–	PUNCT
ma-80	1014	89	y2	y2	NOUN
ma-80	1014	90	8	8	NUM
ma-80	1014	91	=	=	SYM
ma-80	1014	92	gk	gk	PROPN
ma-80	1014	93	1	1	NUM
ma-80	1014	94	–	–	PUNCT
ma-80	1014	95	y2	y2	ADJ
ma-80	1014	96			PROPN
ma-80	1014	97	2ey2	2ey2	NUM
ma-80	1014	98	1	1	NUM
ma-80	1014	99	1y2	1y2	ADJ
ma-80	1014	100	2y2	2y2	ADJ
ma-80	1014	101	2	2	NUM
ma-80	1014	102	3y2	3y2	NOUN
ma-80	1014	103	3	3	NUM
ma-80	1014	104	4y2	4y2	VERB
ma-80	1014	105	4	4	NUM
ma-80	1014	106			PROPN
ma-80	1014	107	2ky2	2ky2	PROPN
ma-80	1014	108	2k	2k	PROPN
ma-80	1014	109	+	+	CCONJ
ma-80	1015	1	+	+	PUNCT
ma-80	1015	2	+	+	PUNCT
ma-80	1015	3	+	+	PUNCT
ma-80	1015	4	+	+	CCONJ
ma-80	1015	5	+	+	ADJ
ma-80	1015	6			ADJ
ma-80	1015	7			NUM
ma-80	1015	8	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	NOUN
ma-80	1015	9	by	by	ADP
ma-80	1015	10	equation	equation	NOUN
ma-80	1015	11	70	70	NUM
ma-80	1015	12	with	with	ADP
ma-80	1015	13	,	,	PUNCT
ma-80	1015	14	based	base	VERB
ma-80	1015	15	on	on	ADP
ma-80	1015	16	the	the	DET
ma-80	1015	17	points	point	NOUN
ma-80	1015	18	and	and	CCONJ
ma-80	1015	19	for	for	ADP
ma-80	1015	20	appropriately	appropriately	ADV
ma-80	1015	21	defined	define	VERB
ma-80	1015	22	constants	constant	NOUN
ma-80	1015	23	and	and	CCONJ
ma-80	1015	24	,	,	PUNCT
ma-80	1015	25	thus	thus	ADV
ma-80	1015	26	:	:	PUNCT
ma-80	1015	27	(	(	PUNCT
ma-80	1015	28	156	156	NUM
ma-80	1015	29	)	)	PUNCT
ma-80	1015	30	appendix	appendix	VERB
ma-80	1015	31	h.	h.	NOUN
ma-80	1015	32	proof	proof	NOUN
ma-80	1015	33	of	of	ADP
ma-80	1015	34	theorem	theorem	ADJ
ma-80	1015	35	7.1	7.1	NUM
ma-80	1015	36	a	a	DET
ma-80	1015	37	zero	zero	NUM
ma-80	1015	38	order	order	NOUN
ma-80	1015	39	spline	spline	NOUN
ma-80	1015	40	approximation	approximation	NOUN
ma-80	1015	41	is	be	AUX
ma-80	1015	42	simply	simply	ADV
ma-80	1015	43	an	an	DET
ma-80	1015	44	affine	affine	NOUN
ma-80	1015	45	approximation	approximation	NOUN
ma-80	1015	46	between	between	ADP
ma-80	1015	47	the	the	DET
ma-80	1015	48	two	two	NUM
ma-80	1015	49	specified	specify	VERB
ma-80	1015	50	points	point	NOUN
ma-80	1015	51	.	.	PUNCT
ma-80	1016	1	consistent	consistent	ADJ
ma-80	1016	2	with	with	ADP
ma-80	1016	3	figure	figure	NOUN
ma-80	1016	4	23	23	NUM
ma-80	1016	5	,	,	PUNCT
ma-80	1016	6	the	the	DET
ma-80	1016	7	zero	zero	NUM
ma-80	1016	8	order	order	NOUN
ma-80	1016	9	spline	spline	NOUN
ma-80	1016	10	approximation	approximation	NOUN
ma-80	1016	11	to	to	ADP
ma-80	1016	12	,	,	PUNCT
ma-80	1016	13	denoted	denote	VERB
ma-80	1016	14	,	,	PUNCT
ma-80	1016	15	is	be	AUX
ma-80	1016	16	an	an	DET
ma-80	1016	17	affine	affine	NOUN
ma-80	1016	18	approximation	approximation	NOUN
ma-80	1016	19	between	between	ADP
ma-80	1016	20	the	the	DET
ma-80	1016	21	points	point	NOUN
ma-80	1016	22	and	and	CCONJ
ma-80	1016	23	.	.	PUNCT
ma-80	1017	1	thus	thus	ADV
ma-80	1017	2	:	:	PUNCT
ma-80	1017	3	(	(	PUNCT
ma-80	1017	4	157	157	NUM
ma-80	1017	5	)	)	PUNCT
ma-80	1017	6	with	with	ADP
ma-80	1017	7	the	the	DET
ma-80	1017	8	approximation	approximation	NOUN
ma-80	1017	9	it	it	PRON
ma-80	1017	10	follows	follow	VERB
ma-80	1017	11	that	that	SCONJ
ma-80	1017	12	(	(	PUNCT
ma-80	1017	13	158	158	NUM
ma-80	1017	14	)	)	PUNCT
ma-80	1017	15	simplification	simplification	NOUN
ma-80	1017	16	yields	yield	NOUN
ma-80	1017	17	(	(	PUNCT
ma-80	1017	18	159	159	NUM
ma-80	1017	19	)	)	PUNCT
ma-80	1017	20	substitution	substitution	NOUN
ma-80	1017	21	of	of	ADP
ma-80	1017	22	and	and	CCONJ
ma-80	1017	23	yields	yield	VERB
ma-80	1017	24	the	the	DET
ma-80	1017	25	required	require	VERB
ma-80	1017	26	result	result	NOUN
ma-80	1017	27	.	.	PUNCT
ma-80	1018	1	h.1	h.1	X
ma-80	1018	2	.	.	PUNCT
ma-80	1018	3	general	general	ADJ
ma-80	1018	4	result	result	NOUN
ma-80	1018	5	.	.	PUNCT
ma-80	1019	1	the	the	DET
ma-80	1019	2	general	general	ADJ
ma-80	1019	3	result	result	NOUN
ma-80	1019	4	arises	arise	VERB
ma-80	1019	5	from	from	ADP
ma-80	1019	6	the	the	DET
ma-80	1019	7	spline	spline	NOUN
ma-80	1019	8	approximation	approximation	NOUN
ma-80	1019	9	,	,	PUNCT
ma-80	1019	10	specified	specify	VERB
ma-80	1019	11	where	where	SCONJ
ma-80	1019	12	,	,	PUNCT
ma-80	1019	13	,	,	PUNCT
ma-80	1019	14	and	and	CCONJ
ma-80	1019	15	with	with	ADP
ma-80	1019	16	(	(	PUNCT
ma-80	1019	17	160	160	NUM
ma-80	1019	18	)	)	PUNCT
ma-80	1019	19	here	here	ADV
ma-80	1019	20	is	be	AUX
ma-80	1019	21	defined	define	VERB
ma-80	1019	22	by	by	ADP
ma-80	1019	23	equation	equation	NOUN
ma-80	1019	24	120	120	NUM
ma-80	1019	25	.	.	PUNCT
ma-80	1020	1	the	the	DET
ma-80	1020	2	order	order	NOUN
ma-80	1020	3	spline	spline	NOUN
ma-80	1020	4	approximation	approximation	NOUN
ma-80	1020	5	,	,	PUNCT
ma-80	1020	6	for	for	ADP
ma-80	1020	7	,	,	PUNCT
ma-80	1020	8	is	be	AUX
ma-80	1020	9	w	w	ADP
ma-80	1020	10	y	y	NOUN
ma-80	1020	11			PROPN
ma-80	1020	12	g	g	PROPN
ma-80	1020	13	1	1	NUM
ma-80	1020	14	–	–	PUNCT
ma-80	1020	15	y	y	NOUN
ma-80	1020	16	1	1	NUM
ma-80	1020	17	e	e	NOUN
ma-80	1020	18	---+	---+	NUM
ma-80	1020	19	1–=	1–=	NUM
ma-80	1020	20	2e	2e	NOUN
ma-80	1020	21	y	y	PROPN
ma-80	1020	22	1	1	NUM
ma-80	1020	23	e	e	NOUN
ma-80	1020	24	---+	---+	PROPN
ma-80	1020	25	1	1	NUM
ma-80	1020	26	1	1	SYM
ma-80	1020	27	y	y	PROPN
ma-80	1020	28	1	1	NUM
ma-80	1020	29	e	e	PROPN
ma-80	1020	30	---+	---+	PROPN
ma-80	1020	31	2	2	ADJ
ma-80	1020	32	y	y	NOUN
ma-80	1020	33	1	1	NUM
ma-80	1020	34	e	e	NOUN
ma-80	1020	35	---+	---+	NUM
ma-80	1020	36	3	3	NUM
ma-80	1020	37	y	y	NOUN
ma-80	1020	38	1	1	NUM
ma-80	1020	39	e	e	NOUN
ma-80	1020	40	---+	---+	NUM
ma-80	1020	41	3	3	NUM
ma-80	1020	42	2	2	NUM
ma-80	1020	43			NOUN
ma-80	1020	44	2k	2k	VERB
ma-80	1020	45	y	y	PROPN
ma-80	1020	46	1	1	NUM
ma-80	1020	47	e	e	NOUN
ma-80	1020	48	---+	---+	NUM
ma-80	1020	49	k	k	X
ma-80	1021	1	+	+	PUNCT
ma-80	1021	2	+	+	PUNCT
ma-80	1021	3	+	+	PUNCT
ma-80	1021	4	+	+	CCONJ
ma-80	1021	5	+	+	NUM
ma-80	1021	6	1.–	1.–	NUM
ma-80	1021	7	w	w	ADP
ma-80	1021	8	y	y	NOUN
ma-80	1021	9			PROPN
ma-80	1021	10	f0	f0	PROPN
ma-80	1021	11	uo	uo	X
ma-80	1021	12	uo	uo	NOUN
ma-80	1022	1	exp	exp	PROPN
ma-80	1023	1	uo	uo	PROPN
ma-80	1023	2			PROPN
ma-80	1023	3	vo	vo	NOUN
ma-80	1023	4	vo	vo	PROPN
ma-80	1023	5	exp	exp	PROPN
ma-80	1024	1	vo	vo	PROPN
ma-80	1024	2			PUNCT
ma-80	1024	3	f0	f0	ADJ
ma-80	1024	4	y	y	NOUN
ma-80	1024	5			PROPN
ma-80	1025	1	uo	uo	NOUN
ma-80	1025	2	y	y	PROPN
ma-80	1025	3	uo	uo	PROPN
ma-80	1025	4	uo	uo	PROPN
ma-80	1025	5	exp–	exp–	PROPN
ma-80	1025	6			PROPN
ma-80	1025	7	vo	vo	PROPN
ma-80	1025	8	uo	uo	PROPN
ma-80	1025	9	–	–	PUNCT
ma-80	1025	10	vo	vo	NOUN
ma-80	1025	11	vo	vo	NOUN
ma-80	1025	12	exp	exp	PROPN
ma-80	1025	13	uo	uo	PROPN
ma-80	1025	14	uo	uo	PROPN
ma-80	1025	15	exp	exp	PROPN
ma-80	1025	16	–	–	PUNCT
ma-80	1025	17	--------------------------------------------------------y	--------------------------------------------------------y	PUNCT
ma-80	1025	18	uo	uo	NUM
ma-80	1025	19	uo	uo	NOUN
ma-80	1025	20	exp	exp	PROPN
ma-80	1025	21	vo	vo	PROPN
ma-80	1025	22	vo	vo	PROPN
ma-80	1025	23	exp	exp	PUNCT
ma-80	1025	24	.+=	.+=	PROPN
ma-80	1025	25	xo	xo	PROPN
ma-80	1025	26	w	w	PROPN
ma-80	1025	27	yo	yo	PROPN
ma-80	1025	28	=	=	PROPN
ma-80	1025	29	f0	f0	PROPN
ma-80	1025	30	yo	yo	NOUN
ma-80	1025	31			NOUN
ma-80	1026	1	xo	xo	PROPN
ma-80	1027	1	uo	uo	INTJ
ma-80	1028	1	yo	yo	INTJ
ma-80	1028	2	uo	uo	X
ma-80	1028	3	uo	uo	PROPN
ma-80	1029	1	exp–	exp–	PROPN
ma-80	1029	2			PROPN
ma-80	1029	3	vo	vo	PROPN
ma-80	1029	4	uo	uo	PROPN
ma-80	1029	5	–	–	PUNCT
ma-80	1029	6	vo	vo	NOUN
ma-80	1029	7	vo	vo	NOUN
ma-80	1029	8	exp	exp	PROPN
ma-80	1029	9	uo	uo	PROPN
ma-80	1029	10	uo	uo	PROPN
ma-80	1029	11	exp	exp	PROPN
ma-80	1029	12	–	–	PUNCT
ma-80	1029	13	---------------------------------------------------------.+	---------------------------------------------------------.+	PROPN
ma-80	1029	14	xo	xo	PROPN
ma-80	1029	15	uovo	uovo	PROPN
ma-80	1029	16	vo	vo	VERB
ma-80	1029	17	exp	exp	PROPN
ma-80	1029	18	uo	uo	PROPN
ma-80	1029	19	exp–	exp–	PROPN
ma-80	1029	20			PROPN
ma-80	1029	21	yo	yo	PROPN
ma-80	1029	22	vo	vo	PROPN
ma-80	1029	23	uo–	uo–	PROPN
ma-80	1029	24	+	+	PROPN
ma-80	1029	25	vo	vo	PROPN
ma-80	1029	26	vo	vo	PROPN
ma-80	1029	27	exp	exp	PROPN
ma-80	1029	28	uo	uo	PROPN
ma-80	1029	29	uo	uo	PROPN
ma-80	1029	30	exp	exp	PROPN
ma-80	1029	31	–	–	PUNCT
ma-80	1029	32	------------------------------------------------------------------------------------------------.	------------------------------------------------------------------------------------------------.	PROPN
ma-80	1029	33	uo	uo	PROPN
ma-80	1029	34	wli	wli	PROPN
ma-80	1029	35	yo	yo	PROPN
ma-80	1029	36	=	=	PROPN
ma-80	1029	37	vo	vo	X
ma-80	1029	38	wui	wui	PROPN
ma-80	1030	1	yo	yo	PROPN
ma-80	1030	2	=	=	X
ma-80	1030	3	f	f	X
ma-80	1030	4	y	y	X
ma-80	1030	5			PROPN
ma-80	1030	6	w	w	PROPN
ma-80	1030	7	y	y	NOUN
ma-80	1030	8	=	=	NOUN
ma-80	1030	9	uo	uo	NOUN
ma-80	1030	10	uo	uo	NOUN
ma-80	1031	1	exp	exp	PROPN
ma-80	1031	2	uo	uo	PROPN
ma-80	1031	3			PROPN
ma-80	1031	4	vo	vo	NOUN
ma-80	1031	5	vo	vo	PROPN
ma-80	1031	6	exp	exp	PROPN
ma-80	1031	7	vo	vo	PROPN
ma-80	1031	8			PROPN
ma-80	1031	9	uo	uo	NOUN
ma-80	1031	10	wli	wli	PROPN
ma-80	1031	11	yo	yo	PROPN
ma-80	1031	12	=	=	PROPN
ma-80	1031	13	vo	vo	X
ma-80	1031	14	wui	wui	PROPN
ma-80	1032	1	yo	yo	PROPN
ma-80	1032	2	=	=	PROPN
ma-80	1032	3	w	w	ADP
ma-80	1032	4	1	1	NUM
ma-80	1032	5			PROPN
ma-80	1032	6	y	y	NOUN
ma-80	1032	7			PUNCT
ma-80	1032	8	e	e	NOUN
ma-80	1032	9	w	w	NOUN
ma-80	1032	10	y	y	PROPN
ma-80	1032	11			PROPN
ma-80	1032	12	–	–	PUNCT
ma-80	1032	13	1	1	NUM
ma-80	1032	14	w	w	NOUN
ma-80	1032	15	y	y	NOUN
ma-80	1032	16	+	+	NUM
ma-80	1032	17	----------------------=	----------------------=	PUNCT
ma-80	1033	1	w	w	NOUN
ma-80	1033	2	k	k	NOUN
ma-80	1033	3			PROPN
ma-80	1033	4	y	y	NOUN
ma-80	1033	5			PROPN
ma-80	1033	6	pk	pk	NOUN
ma-80	1033	7	w	w	NOUN
ma-80	1033	8	y	y	NOUN
ma-80	1033	9			X
ma-80	1033	10	e	e	NOUN
ma-80	1033	11	kw	kw	PROPN
ma-80	1033	12	–	–	PUNCT
ma-80	1033	13	y	y	NOUN
ma-80	1033	14			PROPN
ma-80	1033	15	1	1	NUM
ma-80	1034	1	w	w	NOUN
ma-80	1034	2	y	y	NOUN
ma-80	1034	3	+	+	ADP
ma-80	1034	4	2k	2k	ADP
ma-80	1034	5	1	1	NUM
ma-80	1034	6	–	–	PUNCT
ma-80	1034	7	------------------------------------------=	------------------------------------------=	X
ma-80	1035	1	k	k	NOUN
ma-80	1035	2	1	1	NUM
ma-80	1035	3	2	2	NUM
ma-80	1035	4			NOUN
ma-80	1035	5			NOUN
ma-80	1035	6	.	.	X
ma-80	1035	7	pk	pk	NOUN
ma-80	1035	8	nth	nth	NOUN
ma-80	1035	9	y	y	PROPN
ma-80	1035	10	uo	uo	NOUN
ma-80	1035	11	uo	uo	VERB
ma-80	1035	12	exp	exp	PROPN
ma-80	1035	13	vo	vo	PROPN
ma-80	1035	14	vo	vo	PROPN
ma-80	1035	15	exp	exp	PUNCT
ma-80	1035	16			PROPN
ma-80	1035	17	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	NOUN
ma-80	1035	18	(	(	PUNCT
ma-80	1035	19	161	161	NUM
ma-80	1035	20	)	)	PUNCT
ma-80	1035	21	the	the	DET
ma-80	1035	22	results	result	NOUN
ma-80	1035	23	,	,	PUNCT
ma-80	1035	24	imply	imply	VERB
ma-80	1035	25	that	that	SCONJ
ma-80	1035	26	(	(	PUNCT
ma-80	1035	27	162	162	NUM
ma-80	1035	28	)	)	PUNCT
ma-80	1035	29	assuming	assume	VERB
ma-80	1035	30	.	.	PUNCT
ma-80	1036	1	hence	hence	ADV
ma-80	1036	2	:	:	PUNCT
ma-80	1036	3	(	(	PUNCT
ma-80	1036	4	163	163	NUM
ma-80	1036	5	)	)	PUNCT
ma-80	1036	6	the	the	DET
ma-80	1036	7	required	require	VERB
ma-80	1036	8	result	result	NOUN
ma-80	1036	9	follows	follow	VERB
ma-80	1036	10	:	:	PUNCT
ma-80	1036	11	the	the	DET
ma-80	1036	12	approximation	approximation	NOUN
ma-80	1036	13	for	for	ADP
ma-80	1036	14	,	,	PUNCT
ma-80	1036	15	denoted	denote	VERB
ma-80	1036	16	,	,	PUNCT
ma-80	1036	17	arises	arise	VERB
ma-80	1036	18	for	for	ADP
ma-80	1036	19	the	the	DET
ma-80	1036	20	case	case	NOUN
ma-80	1036	21	of	of	ADP
ma-80	1036	22	.	.	PUNCT
ma-80	1037	1	thus	thus	ADV
ma-80	1037	2	,	,	PUNCT
ma-80	1037	3	.	.	PUNCT
ma-80	1038	1	fn	fn	VERB
ma-80	1039	1	y	y	NOUN
ma-80	1040	1			PROPN
ma-80	1040	2	vo	vo	NOUN
ma-80	1040	3	vo	vo	PROPN
ma-80	1040	4	exp	exp	PROPN
ma-80	1040	5	y–	y–	PROPN
ma-80	1040	6	n	n	PROPN
ma-80	1040	7	1	1	NUM
ma-80	1040	8	+	+	NUM
ma-80	1040	9	vo	vo	NOUN
ma-80	1040	10	vo	vo	NOUN
ma-80	1040	11	exp	exp	PROPN
ma-80	1040	12	uo	uo	PROPN
ma-80	1040	13	uo	uo	PROPN
ma-80	1040	14	exp–	exp–	PROPN
ma-80	1040	15	n	n	PROPN
ma-80	1040	16	1	1	NUM
ma-80	1040	17	+	+	CCONJ
ma-80	1040	18	-----------------------------------------------------------------------=	-----------------------------------------------------------------------=	PROPN
ma-80	1040	19	y	y	PROPN
ma-80	1040	20	uo	uo	PROPN
ma-80	1040	21	uo	uo	PROPN
ma-80	1041	1	exp–	exp–	NUM
ma-80	1041	2	r	r	X
ma-80	1041	3	w	w	ADP
ma-80	1041	4	r	r	NOUN
ma-80	1041	5	u–	u–	NOUN
ma-80	1041	6			PUNCT
ma-80	1041	7	uo	uo	NOUN
ma-80	1041	8	uo	uo	NOUN
ma-80	1041	9	exp	exp	PRON
ma-80	1041	10			NOUN
ma-80	1042	1	r	r	NOUN
ma-80	1042	2	u–	u–	NOUN
ma-80	1042	3			PROPN
ma-80	1042	4	!	!	PUNCT
ma-80	1042	5	------------------------------------------------n	------------------------------------------------n	PUNCT
ma-80	1043	1	u+	u+	PROPN
ma-80	1043	2			PROPN
ma-80	1043	3	!	!	PUNCT
ma-80	1044	1	u!n	u!n	PROPN
ma-80	1044	2	!	!	PUNCT
ma-80	1044	3	-------------------	-------------------	PROPN
ma-80	1044	4	u	u	NOUN
ma-80	1045	1	0=	0=	NOUN
ma-80	1045	2	r	r	NOUN
ma-80	1045	3			X
ma-80	1045	4	1	1	NUM
ma-80	1045	5	vo	vo	NOUN
ma-80	1045	6	vo	vo	PROPN
ma-80	1045	7	exp	exp	PROPN
ma-80	1045	8	uo	uo	PROPN
ma-80	1045	9	uo	uo	PROPN
ma-80	1045	10	exp–	exp–	PROPN
ma-80	1046	1	u	u	PROPN
ma-80	1046	2	-----------------------------------------------------------------	-----------------------------------------------------------------	PUNCT
ma-80	1046	3	r	r	NOUN
ma-80	1046	4	0=	0=	NOUN
ma-80	1047	1	n	n	NOUN
ma-80	1047	2			X
ma-80	1048	1	+	+	CCONJ
ma-80	1048	2	y	y	PROPN
ma-80	1048	3	uo	uo	PROPN
ma-80	1048	4	uo	uo	PROPN
ma-80	1048	5	exp–	exp–	PROPN
ma-80	1048	6	n	n	PROPN
ma-80	1048	7	1	1	NUM
ma-80	1048	8	+	+	NUM
ma-80	1048	9	vo	vo	NOUN
ma-80	1048	10	vo	vo	NOUN
ma-80	1048	11	exp	exp	PROPN
ma-80	1048	12	uo	uo	PROPN
ma-80	1048	13	uo	uo	PROPN
ma-80	1048	14	exp–	exp–	PROPN
ma-80	1048	15	n	n	PROPN
ma-80	1048	16	1	1	NUM
ma-80	1048	17	+	+	NUM
ma-80	1048	18	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PROPN
ma-80	1048	19	vo	vo	NOUN
ma-80	1048	20	vo	vo	PROPN
ma-80	1048	21	exp	exp	PROPN
ma-80	1048	22	y–	y–	NOUN
ma-80	1048	23	r	r	X
ma-80	1048	24	1–	1–	NUM
ma-80	1048	25	r	r	DET
ma-80	1048	26	u	u	NOUN
ma-80	1048	27	–	–	PUNCT
ma-80	1048	28	w	w	NOUN
ma-80	1048	29	r	r	NOUN
ma-80	1048	30	u–	u–	NOUN
ma-80	1048	31			PROPN
ma-80	1048	32	vo	vo	NOUN
ma-80	1048	33	vo	vo	PROPN
ma-80	1048	34	exp	exp	PRON
ma-80	1048	35			NOUN
ma-80	1049	1	r	r	NOUN
ma-80	1049	2	u–	u–	NOUN
ma-80	1049	3			PROPN
ma-80	1049	4	!	!	PUNCT
ma-80	1049	5	--------------------------------------------------------------------n	--------------------------------------------------------------------n	PUNCT
ma-80	1050	1	u+	u+	PROPN
ma-80	1050	2			PROPN
ma-80	1050	3	!	!	PUNCT
ma-80	1051	1	u!n	u!n	PROPN
ma-80	1051	2	!	!	PUNCT
ma-80	1051	3	-------------------	-------------------	PROPN
ma-80	1051	4	u	u	NOUN
ma-80	1052	1	0=	0=	NOUN
ma-80	1052	2	r	r	NOUN
ma-80	1052	3			X
ma-80	1052	4	1	1	NUM
ma-80	1052	5	vo	vo	NOUN
ma-80	1052	6	vo	vo	PROPN
ma-80	1052	7	exp	exp	PROPN
ma-80	1052	8	uo	uo	PROPN
ma-80	1052	9	uo	uo	PROPN
ma-80	1052	10	exp–	exp–	PROPN
ma-80	1053	1	u	u	PROPN
ma-80	1053	2	-----------------------------------------------------------------	-----------------------------------------------------------------	PUNCT
ma-80	1053	3	r	r	NOUN
ma-80	1053	4	0=	0=	NOUN
ma-80	1054	1	n	n	CCONJ
ma-80	1054	2			X
ma-80	1054	3	w	w	ADP
ma-80	1054	4	uo	uo	X
ma-80	1054	5	uo	uo	NOUN
ma-80	1054	6	exp	exp	PROPN
ma-80	1054	7			PROPN
ma-80	1054	8	uo=	uo=	PROPN
ma-80	1054	9	w	w	PROPN
ma-80	1054	10	vo	vo	PROPN
ma-80	1054	11	vo	vo	PROPN
ma-80	1054	12	exp	exp	PROPN
ma-80	1054	13			PROPN
ma-80	1054	14	vo=	vo=	NOUN
ma-80	1054	15	w	w	NOUN
ma-80	1054	16	r	r	NOUN
ma-80	1054	17	u–	u–	NOUN
ma-80	1054	18			PUNCT
ma-80	1054	19	uo	uo	NOUN
ma-80	1054	20	uo	uo	NOUN
ma-80	1054	21	exp	exp	PRON
ma-80	1054	22			NOUN
ma-80	1054	23	pr	pr	NOUN
ma-80	1054	24	u	u	NOUN
ma-80	1054	25	–	–	PUNCT
ma-80	1054	26	uo	uo	NOUN
ma-80	1054	27	e	e	X
ma-80	1055	1	r	r	NOUN
ma-80	1055	2	u–	u–	NOUN
ma-80	1055	3	uo	uo	PROPN
ma-80	1055	4	–	–	PUNCT
ma-80	1055	5	1	1	NUM
ma-80	1055	6	uo+	uo+	NOUN
ma-80	1055	7	2	2	NOUN
ma-80	1055	8	r	r	NOUN
ma-80	1055	9	u–	u–	NOUN
ma-80	1055	10			PROPN
ma-80	1055	11	1	1	NUM
ma-80	1055	12	–	–	PUNCT
ma-80	1055	13	----------------------------------------------=	----------------------------------------------=	X
ma-80	1055	14	w	w	NOUN
ma-80	1055	15	r	r	NOUN
ma-80	1055	16	u–	u–	NOUN
ma-80	1055	17			PROPN
ma-80	1055	18	vo	vo	NOUN
ma-80	1055	19	vo	vo	PROPN
ma-80	1055	20	exp	exp	PUNCT
ma-80	1055	21			NOUN
ma-80	1055	22	pr	pr	NOUN
ma-80	1055	23	u	u	NOUN
ma-80	1055	24	–	–	PUNCT
ma-80	1055	25	vo	vo	NOUN
ma-80	1055	26	e	e	PROPN
ma-80	1055	27	r	r	NOUN
ma-80	1055	28	u–	u–	NOUN
ma-80	1055	29	vo	vo	NUM
ma-80	1055	30	–	–	PUNCT
ma-80	1055	31	1	1	NUM
ma-80	1055	32	vo+	vo+	PROPN
ma-80	1055	33	2	2	VERB
ma-80	1055	34	r	r	NOUN
ma-80	1055	35	u–	u–	NOUN
ma-80	1055	36			PROPN
ma-80	1055	37	1	1	NUM
ma-80	1055	38	–	–	PUNCT
ma-80	1055	39	----------------------------------------------=	----------------------------------------------=	PUNCT
ma-80	1055	40	r	r	NOUN
ma-80	1055	41	u	u	NOUN
ma-80	1055	42	fn	fn	VERB
ma-80	1055	43	y	y	NOUN
ma-80	1056	1			PROPN
ma-80	1056	2	vo	vo	NOUN
ma-80	1056	3	vo	vo	PROPN
ma-80	1056	4	exp	exp	PROPN
ma-80	1056	5	y–	y–	PROPN
ma-80	1056	6	n	n	PROPN
ma-80	1056	7	1	1	NUM
ma-80	1056	8	+	+	NUM
ma-80	1056	9	vo	vo	NOUN
ma-80	1056	10	vo	vo	NOUN
ma-80	1056	11	exp	exp	PROPN
ma-80	1056	12	uo	uo	PROPN
ma-80	1056	13	uo	uo	PROPN
ma-80	1056	14	exp–	exp–	PROPN
ma-80	1056	15	n	n	PROPN
ma-80	1056	16	1	1	NUM
ma-80	1056	17	+	+	CCONJ
ma-80	1056	18	-----------------------------------------------------------------------=	-----------------------------------------------------------------------=	PROPN
ma-80	1056	19	y	y	PROPN
ma-80	1056	20	uo	uo	PROPN
ma-80	1056	21	uo	uo	PROPN
ma-80	1056	22	exp–	exp–	PROPN
ma-80	1056	23	r	r	PROPN
ma-80	1056	24	n	n	CCONJ
ma-80	1056	25	r+	r+	NOUN
ma-80	1056	26	!uo	!uo	PROPN
ma-80	1057	1	r!n	r!n	PROPN
ma-80	1057	2	!	!	PROPN
ma-80	1057	3	vo	vo	PROPN
ma-80	1057	4	vo	vo	PROPN
ma-80	1057	5	exp	exp	PROPN
ma-80	1057	6	uo	uo	PROPN
ma-80	1057	7	uo	uo	PROPN
ma-80	1057	8	exp–	exp–	PROPN
ma-80	1058	1	r	r	PROPN
ma-80	1058	2	-------------------------------------------------------------------------+	-------------------------------------------------------------------------+	PROPN
ma-80	1058	3	pr	pr	PROPN
ma-80	1058	4	u	u	PROPN
ma-80	1058	5	–	–	PUNCT
ma-80	1058	6	uo	uo	NOUN
ma-80	1058	7	e	e	X
ma-80	1059	1	r	r	NOUN
ma-80	1059	2	u–	u–	NOUN
ma-80	1059	3	uo	uo	PROPN
ma-80	1059	4	–	–	PUNCT
ma-80	1059	5	r	r	NOUN
ma-80	1059	6	u–	u–	NOUN
ma-80	1059	7			PROPN
ma-80	1059	8	!	!	NOUN
ma-80	1059	9	1	1	NUM
ma-80	1059	10	uo+	uo+	PROPN
ma-80	1059	11	2	2	NOUN
ma-80	1059	12	r	r	NOUN
ma-80	1059	13	u–	u–	NOUN
ma-80	1059	14			PROPN
ma-80	1059	15	1	1	NUM
ma-80	1059	16	–	–	PUNCT
ma-80	1059	17	------------------------------------------------------------n	------------------------------------------------------------n	X
ma-80	1060	1	u+	u+	ADJ
ma-80	1060	2			PROPN
ma-80	1060	3	!	!	PUNCT
ma-80	1061	1	u!n	u!n	PROPN
ma-80	1061	2	!	!	PUNCT
ma-80	1061	3	-------------------	-------------------	PROPN
ma-80	1061	4	u	u	NOUN
ma-80	1062	1	0=	0=	NOUN
ma-80	1062	2	r	r	NOUN
ma-80	1062	3	1	1	NUM
ma-80	1062	4	–	–	PUNCT
ma-80	1062	5			X
ma-80	1062	6	1	1	NUM
ma-80	1062	7	vo	vo	NOUN
ma-80	1062	8	vo	vo	PROPN
ma-80	1062	9	exp	exp	PROPN
ma-80	1062	10	uo	uo	PROPN
ma-80	1062	11	uo	uo	PROPN
ma-80	1062	12	exp–	exp–	PROPN
ma-80	1063	1	u	u	PROPN
ma-80	1063	2	-----------------------------------------------------------------	-----------------------------------------------------------------	PUNCT
ma-80	1063	3			ADJ
ma-80	1063	4	r	r	NOUN
ma-80	1063	5	0=	0=	NOUN
ma-80	1064	1	n	n	NOUN
ma-80	1064	2			X
ma-80	1065	1	+	+	CCONJ
ma-80	1065	2	y	y	PROPN
ma-80	1065	3	uo	uo	PROPN
ma-80	1065	4	uo	uo	PROPN
ma-80	1065	5	exp–	exp–	PROPN
ma-80	1065	6	n	n	PROPN
ma-80	1065	7	1	1	NUM
ma-80	1065	8	+	+	NUM
ma-80	1065	9	vo	vo	NOUN
ma-80	1065	10	vo	vo	NOUN
ma-80	1065	11	exp	exp	PROPN
ma-80	1065	12	uo	uo	PROPN
ma-80	1065	13	uo	uo	PROPN
ma-80	1065	14	exp–	exp–	PROPN
ma-80	1065	15	n	n	PROPN
ma-80	1065	16	1	1	NUM
ma-80	1065	17	+	+	NUM
ma-80	1065	18	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PROPN
ma-80	1065	19	vo	vo	NOUN
ma-80	1065	20	vo	vo	PROPN
ma-80	1065	21	exp	exp	PROPN
ma-80	1065	22	y–	y–	PROPN
ma-80	1065	23	r	r	PROPN
ma-80	1065	24	n	n	PROPN
ma-80	1065	25	r+	r+	VERB
ma-80	1065	26	!vo	!vo	PROPN
ma-80	1065	27	r!n	r!n	PROPN
ma-80	1065	28	!	!	PROPN
ma-80	1065	29	vo	vo	PROPN
ma-80	1065	30	vo	vo	PROPN
ma-80	1065	31	exp	exp	PROPN
ma-80	1065	32	uo	uo	PROPN
ma-80	1065	33	uo	uo	PROPN
ma-80	1065	34	exp–	exp–	PROPN
ma-80	1065	35	r	r	PROPN
ma-80	1065	36	-------------------------------------------------------------------------+	-------------------------------------------------------------------------+	NUM
ma-80	1065	37	1–	1–	NUM
ma-80	1065	38	r	r	DET
ma-80	1065	39	u	u	NOUN
ma-80	1065	40	–	–	PUNCT
ma-80	1065	41	pr	pr	NOUN
ma-80	1065	42	u	u	NOUN
ma-80	1065	43	–	–	PUNCT
ma-80	1065	44	vo	vo	NOUN
ma-80	1065	45	e	e	PROPN
ma-80	1065	46	r	r	NOUN
ma-80	1065	47	u–	u–	NOUN
ma-80	1065	48	vo	vo	PUNCT
ma-80	1065	49	–	–	PUNCT
ma-80	1065	50	r	r	NOUN
ma-80	1065	51	u–	u–	NOUN
ma-80	1065	52			PROPN
ma-80	1065	53	!	!	NOUN
ma-80	1065	54	1	1	NUM
ma-80	1065	55	vo+	vo+	PROPN
ma-80	1065	56	2	2	VERB
ma-80	1065	57	r	r	NOUN
ma-80	1065	58	u–	u–	NOUN
ma-80	1065	59			PROPN
ma-80	1065	60	1	1	NUM
ma-80	1065	61	–	–	PUNCT
ma-80	1065	62	-----------------------------------------------------------------n	-----------------------------------------------------------------n	PUNCT
ma-80	1065	63	u+	u+	PROPN
ma-80	1065	64			PROPN
ma-80	1065	65	!	!	PUNCT
ma-80	1066	1	u!n	u!n	PROPN
ma-80	1066	2	!	!	PUNCT
ma-80	1066	3	-------------------	-------------------	PROPN
ma-80	1066	4	u	u	NOUN
ma-80	1067	1	0=	0=	NOUN
ma-80	1067	2	r	r	NOUN
ma-80	1067	3	1	1	NUM
ma-80	1067	4	–	–	PUNCT
ma-80	1067	5			X
ma-80	1067	6	1	1	NUM
ma-80	1067	7	vo	vo	NOUN
ma-80	1067	8	vo	vo	PROPN
ma-80	1067	9	exp	exp	PROPN
ma-80	1067	10	uo	uo	PROPN
ma-80	1067	11	uo	uo	PROPN
ma-80	1067	12	exp–	exp–	PROPN
ma-80	1068	1	u	u	PROPN
ma-80	1068	2	-----------------------------------------------------------------	-----------------------------------------------------------------	PUNCT
ma-80	1068	3			ADJ
ma-80	1068	4	r	r	NOUN
ma-80	1068	5	0=	0=	NOUN
ma-80	1068	6	n	n	CCONJ
ma-80	1068	7			X
ma-80	1068	8	w	w	ADP
ma-80	1068	9	yo	yo	NOUN
ma-80	1068	10			PROPN
ma-80	1068	11	wn	wn	PROPN
ma-80	1068	12	i	i	NOUN
ma-80	1068	13	yo	yo	NOUN
ma-80	1068	14			PROPN
ma-80	1068	15	y	y	PROPN
ma-80	1068	16	yo=	yo=	PROPN
ma-80	1068	17	wn	wn	PROPN
ma-80	1068	18	i	i	PROPN
ma-80	1068	19	yo	yo	NOUN
ma-80	1068	20			PROPN
ma-80	1068	21	fn	fn	NOUN
ma-80	1068	22	yo	yo	NOUN
ma-80	1068	23	=	=	PROPN
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ma-80	1068	25	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	PROPN
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ma-80	1068	30	https://doi.org/10.1007/s10910-018-0932-3	https://doi.org/10.1007/s10910-018-0932-3	NUM
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ma-80	1068	32	https://doi.org/10.1007/bf02124750	https://doi.org/10.1007/bf02124750	X
ma-80	1068	33	https://doi.org/10.1155/2021/6695559	https://doi.org/10.1155/2021/6695559	PROPN
ma-80	1068	34	https://doi.org/10.1017/s0022377805003788	https://doi.org/10.1017/s0022377805003788	NUM
ma-80	1068	35	https://doi.org/10.30538/oms2021.0149	https://doi.org/10.30538/oms2021.0149	NOUN
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ma-80	1068	37	https://scholar.google.com/citations?user=invpkckaaaaj&hl=en&oi=sra	https://scholar.google.com/citations?user=invpkckaaaaj&hl=en&oi=sra	PROPN
ma-80	1068	38	https://doi.org/10.28924/ada/ma.2.14	https://doi.org/10.28924/ada/ma.2.14	PROPN
ma-80	1068	39	https://doi.org/10.1016/j.bej.2012.01.010	https://doi.org/10.1016/j.bej.2012.01.010	NOUN
ma-80	1068	40	https://doi.org/10.3390/mca24020035	https://doi.org/10.3390/mca24020035	NOUN
ma-80	1068	41	https://doi.org/10.1007/s10444-017-9530-3	https://doi.org/10.1007/s10444-017-9530-3	NUM
ma-80	1068	42	https://doi.org/10.1016/j.physleta.2015.12.004	https://doi.org/10.1016/j.physleta.2015.12.004	PROPN
ma-80	1068	43	https://doi.org/10.1111/2041-210x.12568	https://doi.org/10.1111/2041-210x.12568	PROPN
ma-80	1068	44	https://doi.org/10.1088/0143-0807/36/3/035030	https://doi.org/10.1088/0143-0807/36/3/035030	PROPN
ma-80	1068	45	http://arxiv.org/abs/1408.3999	http://arxiv.org/abs/1408.3999	PROPN
ma-80	1068	46	https://doi.org/10.1093/imamat/hxu057	https://doi.org/10.1093/imamat/hxu057	NOUN
ma-80	1068	47	https://doi.org/10.1139/p00-065	https://doi.org/10.1139/p00-065	PROPN
ma-80	1069	1	https://doi.org/10.1016/j.cpc.2012.07.008	https://doi.org/10.1016/j.cpc.2012.07.008	NOUN
ma-80	1069	2	https://doi.org/10.3390/math6040056	https://doi.org/10.3390/math6040056	NOUN