id	sid	tid	token	lemma	pos
cbi-60	1	1	v2i1	v2i1	ADP
cbi-60	1	2	volume	volume	NOUN
cbi-60	1	3	2	2	NUM
cbi-60	1	4	,	,	PUNCT
cbi-60	1	5	issue	issue	NOUN
cbi-60	1	6	1	1	NUM
cbi-60	1	7	letters	letter	NOUN
cbi-60	1	8	and	and	CCONJ
cbi-60	1	9	notes	note	VERB
cbi-60	1	10	divergent	divergent	ADJ
cbi-60	1	11	series	series	NOUN
cbi-60	1	12	and	and	CCONJ
cbi-60	1	13	its	its	PRON
cbi-60	1	14	assigned	assign	VERB
cbi-60	1	15	value	value	NOUN
cbi-60	1	16	in	in	ADP
cbi-60	1	17	a	a	DET
cbi-60	1	18	hyperreal	hyperreal	ADJ
cbi-60	1	19	context	context	NOUN
cbi-60	1	20	bas	bas	PROPN
cbi-60	1	21	van	van	PROPN
cbi-60	1	22	der	der	PROPN
cbi-60	1	23	reijden	reijden	VERB
cbi-60	1	24	doi	doi	NOUN
cbi-60	1	25	:	:	PUNCT
cbi-60	1	26	10.33014	10.33014	NUM
cbi-60	1	27	/	/	SYM
cbi-60	1	28	issn.2640	issn.2640	ADJ
cbi-60	1	29	-	-	PUNCT
cbi-60	1	30	5652.2.1.reijden.1	5652.2.1.reijden.1	NUM
cbi-60	1	31	abstract	abstract	NOUN
cbi-60	1	32	this	this	DET
cbi-60	1	33	letter	letter	NOUN
cbi-60	1	34	discusses	discuss	VERB
cbi-60	1	35	the	the	DET
cbi-60	1	36	deep	deep	ADJ
cbi-60	1	37	connection	connection	NOUN
cbi-60	1	38	between	between	ADP
cbi-60	1	39	the	the	DET
cbi-60	1	40	infinite	infinite	ADJ
cbi-60	1	41	sum	sum	NOUN
cbi-60	1	42	of	of	ADP
cbi-60	1	43	natural	natural	ADJ
cbi-60	1	44	numbers	number	NOUN
cbi-60	1	45	and	and	CCONJ
cbi-60	1	46	the	the	DET
cbi-60	1	47	value	value	NOUN
cbi-60	1	48	!	!	PUNCT
cbi-60	2	1	1	1	NUM
cbi-60	2	2	12	12	NUM
cbi-60	2	3	.	.	PUNCT
cbi-60	3	1	aside	aside	ADV
cbi-60	3	2	of	of	ADP
cbi-60	3	3	more	more	ADV
cbi-60	3	4	widely	widely	ADV
cbi-60	3	5	known	know	VERB
cbi-60	3	6	facts	fact	NOUN
cbi-60	3	7	,	,	PUNCT
cbi-60	3	8	we	we	PRON
cbi-60	3	9	consider	consider	VERB
cbi-60	3	10	a	a	DET
cbi-60	3	11	nontrivial	nontrivial	ADJ
cbi-60	3	12	way	way	NOUN
cbi-60	3	13	in	in	ADP
cbi-60	3	14	which	which	PRON
cbi-60	3	15	we	we	PRON
cbi-60	3	16	show	show	VERB
cbi-60	3	17	the	the	DET
cbi-60	3	18	veracity	veracity	NOUN
cbi-60	3	19	of	of	ADP
cbi-60	3	20	this	this	DET
cbi-60	3	21	connection	connection	NOUN
cbi-60	3	22	;	;	PUNCT
cbi-60	3	23	more	more	ADV
cbi-60	3	24	precisely	precisely	ADV
cbi-60	3	25	this	this	DET
cbi-60	3	26	concerns	concern	NOUN
cbi-60	3	27	the	the	DET
cbi-60	3	28	bgn	bgn	NOUN
cbi-60	3	29	method	method	NOUN
cbi-60	3	30	(	(	PUNCT
cbi-60	3	31	bartlett	bartlett	PROPN
cbi-60	3	32	,	,	PUNCT
cbi-60	3	33	gaastra	gaastra	PROPN
cbi-60	3	34	,	,	PUNCT
cbi-60	3	35	and	and	CCONJ
cbi-60	3	36	nemati	nemati	PROPN
cbi-60	3	37	,	,	PUNCT
cbi-60	3	38	2020	2020	NUM
cbi-60	3	39	)	)	PUNCT
cbi-60	3	40	applied	apply	VERB
cbi-60	3	41	on	on	ADP
cbi-60	3	42	the	the	DET
cbi-60	3	43	so	so	ADV
cbi-60	3	44	-	-	PUNCT
cbi-60	3	45	called	call	VERB
cbi-60	3	46	damped	damped	ADJ
cbi-60	3	47	oscillated	oscillate	VERB
cbi-60	3	48	abel	abel	PROPN
cbi-60	3	49	summed	sum	VERB
cbi-60	3	50	variant	variant	NOUN
cbi-60	3	51	of	of	ADP
cbi-60	3	52	the	the	DET
cbi-60	3	53	series	series	NOUN
cbi-60	3	54	.	.	PUNCT
cbi-60	4	1	moreover	moreover	ADV
cbi-60	4	2	,	,	PUNCT
cbi-60	4	3	we	we	PRON
cbi-60	4	4	have	have	AUX
cbi-60	4	5	found	find	VERB
cbi-60	4	6	a	a	DET
cbi-60	4	7	generalization	generalization	NOUN
cbi-60	4	8	of	of	ADP
cbi-60	4	9	this	this	DET
cbi-60	4	10	method	method	NOUN
cbi-60	4	11	which	which	PRON
cbi-60	4	12	‘	'	PUNCT
cbi-60	4	13	correctly	correctly	ADV
cbi-60	4	14	’	'	PUNCT
cbi-60	4	15	assigns	assign	NOUN
cbi-60	4	16	finite	finite	ADJ
cbi-60	4	17	values	value	NOUN
cbi-60	4	18	to	to	ADP
cbi-60	4	19	other	other	ADJ
cbi-60	4	20	divergent	divergent	ADJ
cbi-60	4	21	series	series	NOUN
cbi-60	4	22	.	.	PUNCT
cbi-60	5	1	we	we	PRON
cbi-60	5	2	conclude	conclude	VERB
cbi-60	5	3	with	with	ADP
cbi-60	5	4	some	some	DET
cbi-60	5	5	questions	question	NOUN
cbi-60	5	6	concerning	concern	VERB
cbi-60	5	7	whether	whether	SCONJ
cbi-60	5	8	and	and	CCONJ
cbi-60	5	9	how	how	SCONJ
cbi-60	5	10	we	we	PRON
cbi-60	5	11	can	can	AUX
cbi-60	5	12	analytically	analytically	ADV
cbi-60	5	13	relate	relate	VERB
cbi-60	5	14	our	our	PRON
cbi-60	5	15	hyperreal	hyperreal	ADJ
cbi-60	5	16	terms	term	NOUN
cbi-60	5	17	to	to	PART
cbi-60	5	18	frame	frame	VERB
cbi-60	5	19	the	the	DET
cbi-60	5	20	method	method	NOUN
cbi-60	5	21	in	in	ADP
cbi-60	5	22	a	a	DET
cbi-60	5	23	more	more	ADV
cbi-60	5	24	justifiable	justifiable	ADJ
cbi-60	5	25	and	and	CCONJ
cbi-60	5	26	applicable	applicable	ADJ
cbi-60	5	27	context	context	NOUN
cbi-60	5	28	.	.	PUNCT
cbi-60	6	1	background	background	NOUN
cbi-60	6	2	it	it	PRON
cbi-60	6	3	is	be	AUX
cbi-60	6	4	obvious	obvious	ADJ
cbi-60	6	5	that	that	SCONJ
cbi-60	6	6	the	the	DET
cbi-60	6	7	sum	sum	NOUN
cbi-60	6	8	of	of	ADP
cbi-60	6	9	natural	natural	ADJ
cbi-60	6	10	numbers	number	NOUN
cbi-60	6	11	1	1	NUM
cbi-60	6	12	+	+	SYM
cbi-60	6	13	2	2	NUM
cbi-60	6	14	+	+	SYM
cbi-60	6	15	3	3	NUM
cbi-60	6	16	+	+	NUM
cbi-60	6	17	·	·	PUNCT
cbi-60	6	18	·	·	PUNCT
cbi-60	6	19	·	·	PUNCT
cbi-60	6	20	tends	tend	VERB
cbi-60	6	21	to	to	PART
cbi-60	6	22	infinity	infinity	VERB
cbi-60	6	23	and	and	CCONJ
cbi-60	6	24	can	can	AUX
cbi-60	6	25	thus	thus	ADV
cbi-60	6	26	not	not	PART
cbi-60	6	27	be	be	AUX
cbi-60	6	28	equal	equal	ADJ
cbi-60	6	29	to	to	ADP
cbi-60	6	30	!	!	PUNCT
cbi-60	7	1	1	1	NUM
cbi-60	7	2	12	12	NUM
cbi-60	7	3	.	.	PUNCT
cbi-60	8	1	there	there	PRON
cbi-60	8	2	does	do	AUX
cbi-60	8	3	however	however	ADV
cbi-60	8	4	exist	exist	VERB
cbi-60	8	5	some	some	DET
cbi-60	8	6	connection	connection	NOUN
cbi-60	8	7	between	between	ADP
cbi-60	8	8	this	this	DET
cbi-60	8	9	series	series	NOUN
cbi-60	8	10	and	and	CCONJ
cbi-60	8	11	value	value	NOUN
cbi-60	8	12	and	and	CCONJ
cbi-60	8	13	it	it	PRON
cbi-60	8	14	is	be	AUX
cbi-60	8	15	highly	highly	ADV
cbi-60	8	16	probable	probable	ADJ
cbi-60	8	17	that	that	SCONJ
cbi-60	8	18	this	this	DET
cbi-60	8	19	connection	connection	NOUN
cbi-60	8	20	is	be	AUX
cbi-60	8	21	implicitely	implicitely	ADV
cbi-60	8	22	used	use	VERB
cbi-60	8	23	(	(	PUNCT
cbi-60	8	24	i.e.	i.e.	X
cbi-60	8	25	‘	'	PUNCT
cbi-60	8	26	under	under	ADP
cbi-60	8	27	the	the	DET
cbi-60	8	28	hood	hood	NOUN
cbi-60	8	29	’	'	PUNCT
cbi-60	8	30	)	)	PUNCT
cbi-60	8	31	in	in	ADP
cbi-60	8	32	e.g.	e.g.	ADJ
cbi-60	8	33	physics	physics	NOUN
cbi-60	8	34	(	(	PUNCT
cbi-60	8	35	which	which	PRON
cbi-60	8	36	often	often	ADV
cbi-60	8	37	turns	turn	VERB
cbi-60	8	38	out	out	ADP
cbi-60	8	39	to	to	PART
cbi-60	8	40	be	be	AUX
cbi-60	8	41	perfectly	perfectly	ADV
cbi-60	8	42	justifiable	justifiable	ADJ
cbi-60	8	43	,	,	PUNCT
cbi-60	8	44	as	as	SCONJ
cbi-60	8	45	can	can	AUX
cbi-60	8	46	be	be	AUX
cbi-60	8	47	shown	show	VERB
cbi-60	8	48	by	by	ADP
cbi-60	8	49	various	various	ADJ
cbi-60	8	50	experiments	experiment	NOUN
cbi-60	8	51	)	)	PUNCT
cbi-60	8	52	.	.	PUNCT
cbi-60	9	1	the	the	DET
cbi-60	9	2	first	first	ADJ
cbi-60	9	3	evidence	evidence	NOUN
cbi-60	9	4	of	of	ADP
cbi-60	9	5	this	this	DET
cbi-60	9	6	connection	connection	NOUN
cbi-60	9	7	is	be	AUX
cbi-60	9	8	retrieved	retrieve	VERB
cbi-60	9	9	when	when	SCONJ
cbi-60	9	10	one	one	PRON
cbi-60	9	11	considers	consider	VERB
cbi-60	9	12	the	the	DET
cbi-60	9	13	riemann	riemann	PROPN
cbi-60	9	14	zeta	zeta	PROPN
cbi-60	9	15	function	function	VERB
cbi-60	9	16	!	!	PUNCT
cbi-60	10	1	(	(	PUNCT
cbi-60	10	2	s	s	NOUN
cbi-60	10	3	)	)	PUNCT
cbi-60	10	4	.	.	PUNCT
cbi-60	11	1	it	it	PRON
cbi-60	11	2	is	be	AUX
cbi-60	11	3	known	know	VERB
cbi-60	11	4	that	that	PRON
cbi-60	11	5	!	!	PUNCT
cbi-60	12	1	(	(	PUNCT
cbi-60	12	2	s	s	X
cbi-60	12	3	)	)	PUNCT
cbi-60	12	4	is	be	AUX
cbi-60	12	5	equal	equal	ADJ
cbi-60	12	6	to	to	ADP
cbi-60	12	7	!	!	PUNCT
cbi-60	13	1	1	1	NUM
cbi-60	13	2	12	12	NUM
cbi-60	13	3	when	when	SCONJ
cbi-60	13	4	s	s	VERB
cbi-60	13	5	=	=	PUNCT
cbi-60	13	6	!	!	NOUN
cbi-60	13	7	1	1	NUM
cbi-60	14	1	and	and	CCONJ
cbi-60	14	2	it	it	PRON
cbi-60	14	3	is	be	AUX
cbi-60	14	4	interesting	interesting	ADJ
cbi-60	14	5	that	that	SCONJ
cbi-60	14	6	one	one	PRON
cbi-60	14	7	retrieves	retrieve	VERB
cbi-60	14	8	the	the	DET
cbi-60	14	9	sum	sum	NOUN
cbi-60	14	10	of	of	ADP
cbi-60	14	11	natural	natural	ADJ
cbi-60	14	12	numbers	number	NOUN
cbi-60	14	13	when	when	SCONJ
cbi-60	14	14	one	one	NUM
cbi-60	14	15	‘	'	PUNCT
cbi-60	14	16	plugs	plug	NOUN
cbi-60	14	17	in	in	ADP
cbi-60	14	18	’	'	PUNCT
cbi-60	14	19	s	s	PART
cbi-60	14	20	=	=	PUNCT
cbi-60	14	21	!	!	NOUN
cbi-60	14	22	1	1	NUM
cbi-60	14	23	at	at	ADP
cbi-60	14	24	the	the	DET
cbi-60	14	25	defining	define	VERB
cbi-60	14	26	series	series	NOUN
cbi-60	14	27	of	of	ADP
cbi-60	14	28	the	the	DET
cbi-60	14	29	riemann	riemann	PROPN
cbi-60	14	30	zeta	zeta	PROPN
cbi-60	14	31	function	function	VERB
cbi-60	14	32	!	!	PUNCT
cbi-60	14	33	"	"	PUNCT
cbi-60	15	1	k=1	k=1	PRON
cbi-60	15	2	1	1	NUM
cbi-60	15	3	k	k	NOUN
cbi-60	15	4	s	s	X
cbi-60	15	5	.	.	PUNCT
cbi-60	16	1	plugging	plug	VERB
cbi-60	16	2	s	s	NOUN
cbi-60	16	3	=	=	X
cbi-60	16	4	!	!	NOUN
cbi-60	16	5	1	1	NUM
cbi-60	16	6	in	in	ADP
cbi-60	16	7	the	the	DET
cbi-60	16	8	above	above	ADJ
cbi-60	16	9	series	series	NOUN
cbi-60	16	10	is	be	AUX
cbi-60	16	11	unfortunately	unfortunately	ADV
cbi-60	16	12	not	not	PART
cbi-60	16	13	justifiable	justifiable	ADJ
cbi-60	16	14	(	(	PUNCT
cbi-60	16	15	given	give	VERB
cbi-60	16	16	that	that	PRON
cbi-60	16	17	!	!	PUNCT
cbi-60	17	1	(	(	PUNCT
cbi-60	17	2	s	s	X
cbi-60	17	3	)	)	PUNCT
cbi-60	17	4	is	be	AUX
cbi-60	17	5	only	only	ADV
cbi-60	17	6	equal	equal	ADJ
cbi-60	17	7	to	to	ADP
cbi-60	17	8	this	this	DET
cbi-60	17	9	series	series	NOUN
cbi-60	17	10	when	when	SCONJ
cbi-60	17	11	#	#	SYM
cbi-60	17	12	(	(	PUNCT
cbi-60	17	13	s	s	NOUN
cbi-60	17	14	)	)	PUNCT
cbi-60	17	15	>	>	X
cbi-60	17	16	1	1	NUM
cbi-60	17	17	)	)	PUNCT
cbi-60	17	18	but	but	CCONJ
cbi-60	17	19	it	it	PRON
cbi-60	17	20	remains	remain	VERB
cbi-60	17	21	an	an	DET
cbi-60	17	22	interesting	interesting	ADJ
cbi-60	17	23	thing	thing	NOUN
cbi-60	17	24	to	to	PART
cbi-60	17	25	mention	mention	VERB
cbi-60	17	26	.	.	PUNCT
cbi-60	18	1	another	another	DET
cbi-60	18	2	evidence	evidence	NOUN
cbi-60	18	3	of	of	ADP
cbi-60	18	4	the	the	DET
cbi-60	18	5	connection	connection	NOUN
cbi-60	18	6	can	can	AUX
cbi-60	18	7	be	be	AUX
cbi-60	18	8	revealed	reveal	VERB
cbi-60	18	9	when	when	SCONJ
cbi-60	18	10	figure	figure	NOUN
cbi-60	18	11	1	1	NUM
cbi-60	18	12	:	:	PUNCT
cbi-60	18	13	smoothed	smooth	VERB
cbi-60	18	14	partial	partial	ADJ
cbi-60	18	15	sums	sum	NOUN
cbi-60	18	16	!	!	PUNCT
cbi-60	19	1	n	n	CCONJ
cbi-60	19	2	k=1	k=1	PUNCT
cbi-60	19	3	k	k	X
cbi-60	19	4	with	with	ADP
cbi-60	19	5	a	a	DET
cbi-60	19	6	yintercept	yintercept	NOUN
cbi-60	19	7	of	of	ADP
cbi-60	19	8	!	!	PUNCT
cbi-60	20	1	1	1	NUM
cbi-60	20	2	12	12	NUM
cbi-60	20	3	.	.	PUNCT
cbi-60	21	1	one	one	NUM
cbi-60	21	2	considers	consider	VERB
cbi-60	21	3	the	the	DET
cbi-60	21	4	‘	'	PUNCT
cbi-60	21	5	smoothed	smoothed	ADJ
cbi-60	21	6	version	version	NOUN
cbi-60	21	7	’	'	PUNCT
cbi-60	21	8	of	of	ADP
cbi-60	21	9	the	the	DET
cbi-60	21	10	partial	partial	NOUN
cbi-60	21	11	sums!n	sums!n	PROPN
cbi-60	21	12	k=1	k=1	PROPN
cbi-60	21	13	k	k	NOUN
cbi-60	21	14	,	,	PUNCT
cbi-60	21	15	see	see	VERB
cbi-60	21	16	also	also	ADV
cbi-60	21	17	tao	tao	PROPN
cbi-60	21	18	,	,	PUNCT
cbi-60	21	19	2010	2010	NUM
cbi-60	21	20	.	.	PUNCT
cbi-60	22	1	it	it	PRON
cbi-60	22	2	turns	turn	VERB
cbi-60	22	3	out	out	ADP
cbi-60	22	4	that	that	SCONJ
cbi-60	22	5	these	these	DET
cbi-60	22	6	smoothed	smooth	VERB
cbi-60	22	7	partial	partial	ADJ
cbi-60	22	8	sums	sum	NOUN
cbi-60	22	9	have	have	VERB
cbi-60	22	10	the	the	DET
cbi-60	22	11	same	same	ADJ
cbi-60	22	12	behaviour	behaviour	NOUN
cbi-60	22	13	as	as	ADP
cbi-60	22	14	the	the	DET
cbi-60	22	15	regular	regular	ADJ
cbi-60	22	16	partial	partial	ADJ
cbi-60	22	17	sums	sum	NOUN
cbi-60	22	18	(	(	PUNCT
cbi-60	22	19	i.e.	i.e.	X
cbi-60	22	20	they	they	PRON
cbi-60	22	21	have	have	AUX
cbi-60	22	22	the	the	DET
cbi-60	22	23	same	same	ADJ
cbi-60	22	24	asymptotic	asymptotic	ADJ
cbi-60	22	25	expansion	expansion	NOUN
cbi-60	22	26	)	)	PUNCT
cbi-60	22	27	and	and	CCONJ
cbi-60	22	28	thus	thus	ADV
cbi-60	22	29	tend	tend	VERB
cbi-60	22	30	to	to	PART
cbi-60	22	31	infinity	infinity	VERB
cbi-60	22	32	when	when	SCONJ
cbi-60	22	33	n	n	ADP
cbi-60	22	34	$	$	SYM
cbi-60	22	35	"	"	PUNCT
cbi-60	22	36	.	.	PUNCT
cbi-60	23	1	however	however	ADV
cbi-60	23	2	,	,	PUNCT
cbi-60	23	3	one	one	PRON
cbi-60	23	4	probably	probably	ADV
cbi-60	23	5	recognizes	recognize	VERB
cbi-60	23	6	the	the	DET
cbi-60	23	7	constant	constant	ADJ
cbi-60	23	8	value	value	NOUN
cbi-60	23	9	in	in	ADP
cbi-60	23	10	its	its	PRON
cbi-60	23	11	asymptotic	asymptotic	ADJ
cbi-60	23	12	expansion	expansion	NOUN
cbi-60	23	13	,	,	PUNCT
cbi-60	23	14	which	which	PRON
cbi-60	23	15	is	be	AUX
cbi-60	23	16	(	(	PUNCT
cbi-60	23	17	according	accord	VERB
cbi-60	23	18	to	to	ADP
cbi-60	23	19	tao	tao	PROPN
cbi-60	23	20	(	(	PUNCT
cbi-60	23	21	2010	2010	NUM
cbi-60	23	22	)	)	PUNCT
cbi-60	23	23	)	)	PUNCT
cbi-60	23	24	given	give	VERB
cbi-60	23	25	by	by	ADP
cbi-60	23	26	cn2	cn2	PROPN
cbi-60	23	27	!	!	PROPN
cbi-60	23	28	1	1	NUM
cbi-60	23	29	12+o	12+o	NUM
cbi-60	23	30	(	(	PUNCT
cbi-60	23	31	1	1	NUM
cbi-60	23	32	n	n	NOUN
cbi-60	23	33	)	)	PUNCT
cbi-60	23	34	(	(	PUNCT
cbi-60	23	35	with	with	ADP
cbi-60	23	36	c	c	PROPN
cbi-60	23	37	some	some	DET
cbi-60	23	38	coe!cient	coe!cient	NOUN
cbi-60	23	39	of	of	ADP
cbi-60	23	40	little	little	ADJ
cbi-60	23	41	importance	importance	NOUN
cbi-60	23	42	in	in	ADP
cbi-60	23	43	this	this	DET
cbi-60	23	44	case	case	NOUN
cbi-60	23	45	)	)	PUNCT
cbi-60	23	46	.	.	PUNCT
cbi-60	24	1	moreover	moreover	ADV
cbi-60	24	2	,	,	PUNCT
cbi-60	24	3	it	it	PRON
cbi-60	24	4	is	be	AUX
cbi-60	24	5	given	give	VERB
cbi-60	24	6	that	that	PRON
cbi-60	24	7	!	!	PUNCT
cbi-60	25	1	1	1	NUM
cbi-60	25	2	12	12	NUM
cbi-60	25	3	is	be	AUX
cbi-60	25	4	attained	attain	VERB
cbi-60	25	5	when	when	SCONJ
cbi-60	25	6	one	one	PRON
cbi-60	25	7	looks	look	VERB
cbi-60	25	8	at	at	ADP
cbi-60	25	9	the	the	DET
cbi-60	25	10	intersection	intersection	NOUN
cbi-60	25	11	with	with	ADP
cbi-60	25	12	the	the	DET
cbi-60	25	13	y	y	NOUN
cbi-60	25	14	-	-	PUNCT
cbi-60	25	15	axis	axis	NOUN
cbi-60	25	16	in	in	ADP
cbi-60	25	17	figure	figure	NOUN
cbi-60	25	18	1	1	NUM
cbi-60	25	19	.	.	PUNCT
cbi-60	26	1	damped	damped	NOUN
cbi-60	26	2	oscillations	oscillation	NOUN
cbi-60	26	3	the	the	DET
cbi-60	26	4	first	first	ADJ
cbi-60	26	5	two	two	NUM
cbi-60	26	6	evidences	evidence	NOUN
cbi-60	26	7	we	we	PRON
cbi-60	26	8	mentioned	mention	VERB
cbi-60	26	9	are	be	AUX
cbi-60	26	10	quite	quite	ADV
cbi-60	26	11	widely	widely	ADV
cbi-60	26	12	known	know	VERB
cbi-60	26	13	but	but	CCONJ
cbi-60	26	14	a	a	DET
cbi-60	26	15	more	more	ADV
cbi-60	26	16	unknown	unknown	ADJ
cbi-60	26	17	fact	fact	NOUN
cbi-60	26	18	can	can	AUX
cbi-60	26	19	be	be	AUX
cbi-60	26	20	observed	observe	VERB
cbi-60	26	21	when	when	SCONJ
cbi-60	26	22	one	one	PRON
cbi-60	26	23	considers	consider	VERB
cbi-60	26	24	a	a	DET
cbi-60	26	25	damped	damped	ADJ
cbi-60	26	26	oscillating	oscillate	VERB
cbi-60	26	27	variant	variant	NOUN
cbi-60	26	28	of	of	ADP
cbi-60	26	29	the	the	DET
cbi-60	26	30	series	series	NOUN
cbi-60	26	31	1	1	NUM
cbi-60	27	1	+	+	SYM
cbi-60	27	2	2	2	NUM
cbi-60	27	3	+	+	NUM
cbi-60	27	4	3	3	NUM
cbi-60	27	5	+	+	NUM
cbi-60	27	6	·	·	PUNCT
cbi-60	27	7	·	·	PUNCT
cbi-60	27	8	·	·	PUNCT
cbi-60	27	9	,	,	PUNCT
cbi-60	27	10	namely	namely	ADV
cbi-60	27	11	"	"	PUNCT
cbi-60	27	12	"	"	PUNCT
cbi-60	27	13	k=1	k=1	PROPN
cbi-60	27	14	ke!k	ke!k	PROPN
cbi-60	27	15	!	!	PUNCT
cbi-60	27	16	cos(k	cos(k	X
cbi-60	27	17	"	"	PUNCT
cbi-60	27	18	)	)	PUNCT
cbi-60	27	19	.	.	PUNCT
cbi-60	28	1	(	(	PUNCT
cbi-60	28	2	1	1	X
cbi-60	28	3	)	)	PUNCT
cbi-60	28	4	30	30	NUM
cbi-60	28	5	letters	letter	NOUN
cbi-60	28	6	and	and	CCONJ
cbi-60	28	7	notes	note	NOUN
cbi-60	28	8	this	this	DET
cbi-60	28	9	variant	variant	NOUN
cbi-60	28	10	was	be	AUX
cbi-60	28	11	also	also	ADV
cbi-60	28	12	discussed	discuss	VERB
cbi-60	28	13	in	in	ADP
cbi-60	28	14	a	a	DET
cbi-60	28	15	previous	previous	ADJ
cbi-60	28	16	letter	letter	NOUN
cbi-60	28	17	(	(	PUNCT
cbi-60	28	18	bartlett	bartlett	PROPN
cbi-60	28	19	and	and	CCONJ
cbi-60	28	20	khurshudyan	khurshudyan	PROPN
cbi-60	28	21	,	,	PUNCT
cbi-60	28	22	2019	2019	NUM
cbi-60	28	23	)	)	PUNCT
cbi-60	28	24	.	.	PUNCT
cbi-60	29	1	in	in	ADP
cbi-60	29	2	this	this	DET
cbi-60	29	3	letter	letter	NOUN
cbi-60	29	4	it	it	PRON
cbi-60	29	5	was	be	AUX
cbi-60	29	6	also	also	ADV
cbi-60	29	7	mentioned	mention	VERB
cbi-60	29	8	that	that	SCONJ
cbi-60	29	9	,	,	PUNCT
cbi-60	29	10	in	in	ADP
cbi-60	29	11	the	the	DET
cbi-60	29	12	context	context	NOUN
cbi-60	29	13	of	of	ADP
cbi-60	29	14	hyperreal	hyperreal	ADJ
cbi-60	29	15	numbers	number	NOUN
cbi-60	29	16	by	by	ADP
cbi-60	29	17	introducing	introduce	VERB
cbi-60	29	18	#	#	NOUN
cbi-60	29	19	:	:	PUNCT
cbi-60	29	20	=	=	PUNCT
cbi-60	29	21	"	"	PUNCT
cbi-60	29	22	(	(	PUNCT
cbi-60	29	23	i.e.	i.e.	X
cbi-60	29	24	by	by	ADP
cbi-60	29	25	appying	appye	VERB
cbi-60	29	26	the	the	DET
cbi-60	29	27	bgn	bgn	NOUN
cbi-60	29	28	method	method	NOUN
cbi-60	29	29	on	on	ADP
cbi-60	29	30	it	it	PRON
cbi-60	29	31	)	)	PUNCT
cbi-60	29	32	,	,	PUNCT
cbi-60	29	33	(	(	PUNCT
cbi-60	29	34	1	1	X
cbi-60	29	35	)	)	PUNCT
cbi-60	29	36	can	can	AUX
cbi-60	29	37	be	be	AUX
cbi-60	29	38	written	write	VERB
cbi-60	29	39	in	in	ADP
cbi-60	29	40	a	a	DET
cbi-60	29	41	closed	closed	ADJ
cbi-60	29	42	-	-	PUNCT
cbi-60	29	43	form	form	NOUN
cbi-60	29	44	expression	expression	NOUN
cbi-60	29	45	(	(	PUNCT
cbi-60	29	46	or	or	CCONJ
cbi-60	29	47	at	at	ADV
cbi-60	29	48	least	least	ADJ
cbi-60	29	49	as	as	ADP
cbi-60	29	50	an	an	DET
cbi-60	29	51	approximation	approximation	NOUN
cbi-60	29	52	of	of	ADP
cbi-60	29	53	it	it	PRON
cbi-60	29	54	)	)	PUNCT
cbi-60	29	55	.	.	PUNCT
cbi-60	30	1	it	it	PRON
cbi-60	30	2	remained	remain	VERB
cbi-60	30	3	however	however	ADV
cbi-60	30	4	still	still	ADV
cbi-60	30	5	unclear	unclear	ADJ
cbi-60	30	6	which	which	DET
cbi-60	30	7	value	value	NOUN
cbi-60	30	8	/	/	SYM
cbi-60	30	9	magnitude	magnitude	NOUN
cbi-60	30	10	the	the	DET
cbi-60	30	11	infinitesemal	infinitesemal	ADJ
cbi-60	30	12	quantity	quantity	NOUN
cbi-60	30	13	"	"	PUNCT
cbi-60	30	14	must	must	AUX
cbi-60	30	15	be1	be1	VERB
cbi-60	30	16	in	in	ADP
cbi-60	30	17	order	order	NOUN
cbi-60	30	18	that	that	SCONJ
cbi-60	30	19	the	the	DET
cbi-60	30	20	bgn	bgn	NOUN
cbi-60	30	21	method	method	NOUN
cbi-60	30	22	applied	apply	VERB
cbi-60	30	23	on	on	ADP
cbi-60	30	24	(	(	PUNCT
cbi-60	30	25	1	1	X
cbi-60	30	26	)	)	PUNCT
cbi-60	30	27	equals	equal	VERB
cbi-60	30	28	the	the	DET
cbi-60	30	29	‘	'	PUNCT
cbi-60	30	30	appropriate	appropriate	ADJ
cbi-60	30	31	’	'	PUNCT
cbi-60	30	32	value	value	NOUN
cbi-60	30	33	!	!	PUNCT
cbi-60	31	1	1	1	NUM
cbi-60	31	2	12	12	NUM
cbi-60	31	3	;	;	PUNCT
cbi-60	31	4	only	only	ADV
cbi-60	31	5	numerical	numerical	ADJ
cbi-60	31	6	evidence	evidence	NOUN
cbi-60	31	7	was	be	AUX
cbi-60	31	8	given	give	VERB
cbi-60	31	9	.	.	PUNCT
cbi-60	32	1	in	in	ADP
cbi-60	32	2	particular	particular	ADJ
cbi-60	32	3	,	,	PUNCT
cbi-60	32	4	it	it	PRON
cbi-60	32	5	was	be	AUX
cbi-60	32	6	shown	show	VERB
cbi-60	32	7	that	that	SCONJ
cbi-60	32	8	if	if	SCONJ
cbi-60	32	9	"	"	PUNCT
cbi-60	32	10	=	=	SYM
cbi-60	32	11	1	1	NUM
cbi-60	32	12	"	"	PUNCT
cbi-60	32	13	,	,	PUNCT
cbi-60	32	14	the	the	DET
cbi-60	32	15	computing	computing	NOUN
cbi-60	32	16	software	software	NOUN
cbi-60	32	17	“	"	PUNCT
cbi-60	32	18	wolfram	wolfram	PROPN
cbi-60	32	19	mathematica	mathematica	PROPN
cbi-60	32	20	”	"	PUNCT
cbi-60	32	21	will	will	AUX
cbi-60	32	22	include	include	VERB
cbi-60	32	23	the	the	DET
cbi-60	32	24	constant	constant	ADJ
cbi-60	32	25	!	!	PUNCT
cbi-60	33	1	1	1	NUM
cbi-60	33	2	12	12	NUM
cbi-60	33	3	in	in	ADP
cbi-60	33	4	its	its	PRON
cbi-60	33	5	bgn	bgn	NOUN
cbi-60	33	6	expression	expression	NOUN
cbi-60	33	7	(	(	PUNCT
cbi-60	33	8	which	which	PRON
cbi-60	33	9	is	be	AUX
cbi-60	33	10	similar	similar	ADJ
cbi-60	33	11	to	to	ADP
cbi-60	33	12	the	the	DET
cbi-60	33	13	observation	observation	NOUN
cbi-60	33	14	of	of	ADP
cbi-60	33	15	the	the	DET
cbi-60	33	16	previous	previous	ADJ
cbi-60	33	17	paragraph	paragraph	NOUN
cbi-60	33	18	)	)	PUNCT
cbi-60	33	19	.	.	PUNCT
cbi-60	34	1	at	at	ADP
cbi-60	34	2	the	the	DET
cbi-60	34	3	time	time	NOUN
cbi-60	34	4	that	that	PRON
cbi-60	34	5	bartlett	bartlett	PROPN
cbi-60	34	6	and	and	CCONJ
cbi-60	34	7	khurshudyan	khurshudyan	PROPN
cbi-60	34	8	(	(	PUNCT
cbi-60	34	9	2019	2019	NUM
cbi-60	34	10	)	)	PUNCT
cbi-60	34	11	was	be	AUX
cbi-60	34	12	written	write	VERB
cbi-60	34	13	,	,	PUNCT
cbi-60	34	14	it	it	PRON
cbi-60	34	15	only	only	ADV
cbi-60	34	16	seemed	seem	VERB
cbi-60	34	17	clear	clear	ADJ
cbi-60	34	18	that	that	SCONJ
cbi-60	34	19	there	there	PRON
cbi-60	34	20	is	be	VERB
cbi-60	34	21	a	a	DET
cbi-60	34	22	numerical	numerical	ADJ
cbi-60	34	23	evidence	evidence	NOUN
cbi-60	34	24	that	that	SCONJ
cbi-60	34	25	(	(	PUNCT
cbi-60	34	26	1	1	X
cbi-60	34	27	)	)	PUNCT
cbi-60	34	28	equals	equal	VERB
cbi-60	34	29	!	!	PUNCT
cbi-60	35	1	1	1	NUM
cbi-60	35	2	12	12	NUM
cbi-60	35	3	when	when	SCONJ
cbi-60	35	4	we	we	PRON
cbi-60	35	5	take	take	VERB
cbi-60	35	6	"	"	PUNCT
cbi-60	35	7	in	in	ADP
cbi-60	35	8	a	a	DET
cbi-60	35	9	su!ciently	su!ciently	ADV
cbi-60	35	10	small	small	ADJ
cbi-60	35	11	interval	interval	NOUN
cbi-60	35	12	.	.	PUNCT
cbi-60	36	1	recently	recently	ADV
cbi-60	36	2	,	,	PUNCT
cbi-60	36	3	we	we	PRON
cbi-60	36	4	have	have	AUX
cbi-60	36	5	found	find	VERB
cbi-60	36	6	that	that	DET
cbi-60	36	7	sugiyama	sugiyama	NOUN
cbi-60	36	8	(	(	PUNCT
cbi-60	36	9	2014	2014	NUM
cbi-60	36	10	)	)	PUNCT
cbi-60	36	11	(	(	PUNCT
cbi-60	36	12	section	section	NOUN
cbi-60	36	13	2.3	2.3	NUM
cbi-60	36	14	)	)	PUNCT
cbi-60	36	15	provides	provide	VERB
cbi-60	36	16	a	a	DET
cbi-60	36	17	more	more	ADV
cbi-60	36	18	theoretical	theoretical	ADJ
cbi-60	36	19	derivation	derivation	NOUN
cbi-60	36	20	of	of	ADP
cbi-60	36	21	this	this	DET
cbi-60	36	22	matter	matter	NOUN
cbi-60	36	23	.	.	PUNCT
cbi-60	37	1	although	although	SCONJ
cbi-60	37	2	the	the	DET
cbi-60	37	3	website	website	NOUN
cbi-60	37	4	and	and	CCONJ
cbi-60	37	5	its	its	PRON
cbi-60	37	6	choice	choice	NOUN
cbi-60	37	7	of	of	ADP
cbi-60	37	8	words	word	NOUN
cbi-60	37	9	are	be	AUX
cbi-60	37	10	somewhat	somewhat	ADV
cbi-60	37	11	vague	vague	ADJ
cbi-60	37	12	and	and	CCONJ
cbi-60	37	13	confusing	confusing	ADJ
cbi-60	37	14	,	,	PUNCT
cbi-60	37	15	the	the	DET
cbi-60	37	16	derivation	derivation	NOUN
cbi-60	37	17	seems	seem	VERB
cbi-60	37	18	correct	correct	ADJ
cbi-60	37	19	.	.	PUNCT
cbi-60	38	1	in	in	ADP
cbi-60	38	2	this	this	DET
cbi-60	38	3	derivation	derivation	NOUN
cbi-60	38	4	there	there	PRON
cbi-60	38	5	is	be	VERB
cbi-60	38	6	being	be	AUX
cbi-60	38	7	made	make	VERB
cbi-60	38	8	use	use	NOUN
cbi-60	38	9	of	of	ADP
cbi-60	38	10	a	a	DET
cbi-60	38	11	so	so	ADV
cbi-60	38	12	-	-	PUNCT
cbi-60	38	13	called	call	VERB
cbi-60	38	14	‘	'	PUNCT
cbi-60	38	15	damped	damp	VERB
cbi-60	38	16	oscillated	oscillated	ADJ
cbi-60	38	17	abel	abel	PROPN
cbi-60	38	18	summation	summation	NOUN
cbi-60	38	19	method	method	NOUN
cbi-60	38	20	’	'	PUNCT
cbi-60	38	21	,	,	PUNCT
cbi-60	38	22	which	which	PRON
cbi-60	38	23	is	be	AUX
cbi-60	38	24	a	a	DET
cbi-60	38	25	kind	kind	NOUN
cbi-60	38	26	of	of	ADP
cbi-60	38	27	generalization	generalization	NOUN
cbi-60	38	28	of	of	ADP
cbi-60	38	29	the	the	DET
cbi-60	38	30	more	more	ADV
cbi-60	38	31	common	common	ADJ
cbi-60	38	32	abel	abel	PROPN
cbi-60	38	33	summation	summation	NOUN
cbi-60	38	34	method	method	NOUN
cbi-60	38	35	used	use	VERB
cbi-60	38	36	to	to	PART
cbi-60	38	37	assign	assign	VERB
cbi-60	38	38	finite	finite	ADJ
cbi-60	38	39	values	value	NOUN
cbi-60	38	40	to	to	ADP
cbi-60	38	41	divergent	divergent	ADJ
cbi-60	38	42	series	series	NOUN
cbi-60	38	43	.	.	PUNCT
cbi-60	39	1	in	in	ADP
cbi-60	39	2	this	this	DET
cbi-60	39	3	article	article	NOUN
cbi-60	39	4	,	,	PUNCT
cbi-60	39	5	this	this	DET
cbi-60	39	6	method	method	NOUN
cbi-60	39	7	of	of	ADP
cbi-60	39	8	‘	'	PUNCT
cbi-60	39	9	damped	damp	VERB
cbi-60	39	10	oscillated	oscillated	ADJ
cbi-60	39	11	abel	abel	PROPN
cbi-60	39	12	summation	summation	NOUN
cbi-60	39	13	’	'	PUNCT
cbi-60	39	14	is	be	AUX
cbi-60	39	15	consequently	consequently	ADV
cbi-60	39	16	used	use	VERB
cbi-60	39	17	on	on	ADP
cbi-60	39	18	a	a	DET
cbi-60	39	19	larger	large	ADJ
cbi-60	39	20	class	class	NOUN
cbi-60	39	21	of	of	ADP
cbi-60	39	22	divergent	divergent	ADJ
cbi-60	39	23	series	series	NOUN
cbi-60	39	24	as	as	ADV
cbi-60	39	25	well	well	ADV
cbi-60	39	26	;	;	PUNCT
cbi-60	39	27	furthermore	furthermore	ADV
cbi-60	39	28	it	it	PRON
cbi-60	39	29	turns	turn	VERB
cbi-60	39	30	out	out	ADP
cbi-60	39	31	that	that	SCONJ
cbi-60	39	32	the	the	DET
cbi-60	39	33	‘	'	PUNCT
cbi-60	39	34	damping	damp	VERB
cbi-60	39	35	’	'	PUNCT
cbi-60	39	36	and	and	CCONJ
cbi-60	39	37	’	'	PUNCT
cbi-60	39	38	vibrating	vibrate	VERB
cbi-60	39	39	’	'	PUNCT
cbi-60	39	40	constant	constant	ADJ
cbi-60	39	41	should	should	AUX
cbi-60	39	42	not	not	PART
cbi-60	39	43	be	be	AUX
cbi-60	39	44	necessarily	necessarily	ADV
cbi-60	39	45	equal	equal	ADJ
cbi-60	39	46	to	to	ADP
cbi-60	39	47	each	each	DET
cbi-60	39	48	other	other	ADJ
cbi-60	39	49	.	.	PUNCT
cbi-60	40	1	we	we	PRON
cbi-60	40	2	thus	thus	ADV
cbi-60	40	3	in	in	ADP
cbi-60	40	4	fact	fact	NOUN
cbi-60	40	5	have	have	VERB
cbi-60	40	6	that	that	PRON
cbi-60	40	7	(	(	PUNCT
cbi-60	40	8	see	see	VERB
cbi-60	40	9	also	also	ADV
cbi-60	40	10	section	section	VERB
cbi-60	40	11	5.2	5.2	NUM
cbi-60	40	12	and	and	CCONJ
cbi-60	40	13	section	section	NOUN
cbi-60	40	14	6.1	6.1	NUM
cbi-60	40	15	of	of	ADP
cbi-60	40	16	sugiyama	sugiyama	NOUN
cbi-60	40	17	(	(	PUNCT
cbi-60	40	18	2014	2014	NUM
cbi-60	40	19	)	)	PUNCT
cbi-60	40	20	,	,	PUNCT
cbi-60	40	21	we	we	PRON
cbi-60	40	22	here	here	ADV
cbi-60	40	23	write	write	VERB
cbi-60	40	24	"	"	PUNCT
cbi-60	40	25	instead	instead	ADV
cbi-60	40	26	of	of	ADP
cbi-60	40	27	x	x	NOUN
cbi-60	40	28	)	)	PUNCT
cbi-60	40	29	!	!	PUNCT
cbi-60	40	30	"	"	PUNCT
cbi-60	41	1	k=1	k=1	X
cbi-60	42	1	k	k	X
cbi-60	42	2	i	i	PRON
cbi-60	42	3	can	can	AUX
cbi-60	42	4	be	be	AUX
cbi-60	42	5	transformed	transform	VERB
cbi-60	42	6	to	to	ADP
cbi-60	42	7	(	(	PUNCT
cbi-60	42	8	letting	let	VERB
cbi-60	42	9	i	i	PRON
cbi-60	42	10	%	%	VERB
cbi-60	42	11	1	1	NUM
cbi-60	42	12	be	be	AUX
cbi-60	42	13	an	an	DET
cbi-60	42	14	integer	integer	NOUN
cbi-60	42	15	)	)	PUNCT
cbi-60	42	16	"	"	PUNCT
cbi-60	42	17	"	"	PUNCT
cbi-60	42	18	k=1	k=1	PROPN
cbi-60	42	19	k	k	PROPN
cbi-60	42	20	ie!k	ie!k	PROPN
cbi-60	42	21	!	!	PROPN
cbi-60	42	22	cot	cot	NOUN
cbi-60	42	23	!	!	PUNCT
cbi-60	43	1	2i+2	2i+2	VERB
cbi-60	43	2	cos(k	cos(k	NOUN
cbi-60	43	3	"	"	PUNCT
cbi-60	43	4	)	)	PUNCT
cbi-60	43	5	and	and	CCONJ
cbi-60	43	6	"	"	PUNCT
cbi-60	43	7	"	"	PUNCT
cbi-60	43	8	k=1	k=1	PROPN
cbi-60	44	1	k	k	PROPN
cbi-60	44	2	ie!k	ie!k	PROPN
cbi-60	44	3	i+1	i+1	ADV
cbi-60	44	4	2	2	NUM
cbi-60	44	5	!	!	PUNCT
cbi-60	45	1	cos(k	cos(k	PRON
cbi-60	45	2	i+1	i+1	NUM
cbi-60	45	3	2	2	NUM
cbi-60	45	4	"	"	PUNCT
cbi-60	45	5	)	)	PUNCT
cbi-60	45	6	and	and	CCONJ
cbi-60	45	7	consequently	consequently	ADV
cbi-60	45	8	taking	take	VERB
cbi-60	45	9	the	the	DET
cbi-60	45	10	limit	limit	NOUN
cbi-60	45	11	"	"	PUNCT
cbi-60	45	12	$	$	SYM
cbi-60	45	13	0	0	NUM
cbi-60	45	14	yields	yield	VERB
cbi-60	45	15	the	the	DET
cbi-60	45	16	‘	'	PUNCT
cbi-60	45	17	appropriate	appropriate	ADJ
cbi-60	45	18	’	'	PUNCT
cbi-60	45	19	assigned	assign	VERB
cbi-60	45	20	value	value	NOUN
cbi-60	45	21	;	;	PUNCT
cbi-60	45	22	we	we	PRON
cbi-60	45	23	also	also	ADV
cbi-60	45	24	numerically	numerically	ADV
cbi-60	45	25	verified	verify	VERB
cbi-60	45	26	this2	this2	ADP
cbi-60	45	27	.	.	PUNCT
cbi-60	46	1	it	it	PRON
cbi-60	46	2	remains	remain	VERB
cbi-60	46	3	of	of	ADP
cbi-60	46	4	course	course	NOUN
cbi-60	46	5	interesting	interesting	ADJ
cbi-60	46	6	how	how	SCONJ
cbi-60	46	7	this	this	PRON
cbi-60	46	8	damped	damp	VERB
cbi-60	46	9	oscillated	oscillate	VERB
cbi-60	46	10	abel	abel	PROPN
cbi-60	46	11	summation	summation	NOUN
cbi-60	46	12	method	method	NOUN
cbi-60	46	13	can	can	AUX
cbi-60	46	14	be	be	AUX
cbi-60	46	15	stated	state	VERB
cbi-60	46	16	in	in	ADP
cbi-60	46	17	our	our	PRON
cbi-60	46	18	more	more	ADJ
cbi-60	46	19	‘	'	PUNCT
cbi-60	46	20	detailed	detailed	ADJ
cbi-60	46	21	’	'	PUNCT
cbi-60	46	22	hyperreal	hyperreal	ADJ
cbi-60	46	23	context	context	NOUN
cbi-60	46	24	;	;	PUNCT
cbi-60	46	25	i.e.	i.e.	X
cbi-60	46	26	in	in	ADP
cbi-60	46	27	which	which	PRON
cbi-60	46	28	we	we	PRON
cbi-60	46	29	know	know	VERB
cbi-60	46	30	the	the	DET
cbi-60	46	31	exact	exact	ADJ
cbi-60	46	32	values	value	NOUN
cbi-60	46	33	of	of	ADP
cbi-60	46	34	"	"	PUNCT
cbi-60	46	35	(	(	PUNCT
cbi-60	46	36	possibly	possibly	ADV
cbi-60	46	37	in	in	ADP
cbi-60	46	38	terms	term	NOUN
cbi-60	46	39	of	of	ADP
cbi-60	46	40	#	#	NOUN
cbi-60	46	41	)	)	PUNCT
cbi-60	46	42	in	in	ADP
cbi-60	46	43	order	order	NOUN
cbi-60	46	44	that	that	SCONJ
cbi-60	46	45	the	the	DET
cbi-60	46	46	bgn	bgn	NOUN
cbi-60	46	47	method	method	NOUN
cbi-60	46	48	assigns	assign	VERB
cbi-60	46	49	the	the	DET
cbi-60	46	50	‘	'	PUNCT
cbi-60	46	51	appropriate	appropriate	ADJ
cbi-60	46	52	’	'	PUNCT
cbi-60	46	53	value	value	NOUN
cbi-60	46	54	to	to	ADP
cbi-60	46	55	a	a	DET
cbi-60	46	56	divegent	divegent	NOUN
cbi-60	46	57	series	series	NOUN
cbi-60	46	58	.	.	PUNCT
cbi-60	47	1	unless	unless	SCONJ
cbi-60	47	2	it	it	PRON
cbi-60	47	3	is	be	AUX
cbi-60	47	4	still	still	ADV
cbi-60	47	5	untrivial	untrivial	ADJ
cbi-60	47	6	which	which	DET
cbi-60	47	7	values	value	NOUN
cbi-60	47	8	"	"	PUNCT
cbi-60	47	9	must	must	AUX
cbi-60	47	10	have	have	VERB
cbi-60	47	11	in	in	ADP
cbi-60	47	12	order	order	NOUN
cbi-60	47	13	that	that	SCONJ
cbi-60	47	14	the	the	DET
cbi-60	47	15	mentioned	mention	VERB
cbi-60	47	16	method	method	NOUN
cbi-60	47	17	assigns	assign	VERB
cbi-60	47	18	this	this	DET
cbi-60	47	19	value	value	NOUN
cbi-60	47	20	,	,	PUNCT
cbi-60	47	21	we	we	PRON
cbi-60	47	22	can	can	AUX
cbi-60	47	23	however	however	ADV
cbi-60	47	24	say	say	VERB
cbi-60	47	25	from	from	ADP
cbi-60	47	26	equation	equation	NOUN
cbi-60	47	27	(	(	PUNCT
cbi-60	47	28	5.57	5.57	NUM
cbi-60	47	29	)	)	PUNCT
cbi-60	47	30	in	in	ADP
cbi-60	47	31	sugiyama	sugiyama	NOUN
cbi-60	47	32	(	(	PUNCT
cbi-60	47	33	2014	2014	NUM
cbi-60	47	34	)	)	PUNCT
cbi-60	48	1	that	that	SCONJ
cbi-60	48	2	in	in	ADP
cbi-60	48	3	1	1	NUM
cbi-60	48	4	in	in	ADP
cbi-60	48	5	relation	relation	NOUN
cbi-60	48	6	to	to	ADP
cbi-60	48	7	"	"	PUNCT
cbi-60	48	8	2by	2by	ADJ
cbi-60	48	9	again	again	ADV
cbi-60	48	10	letting	let	VERB
cbi-60	48	11	!	!	PUNCT
cbi-60	49	1	be	be	AUX
cbi-60	49	2	in	in	ADP
cbi-60	49	3	a	a	DET
cbi-60	49	4	su!ciently	su!ciently	ADV
cbi-60	49	5	small	small	ADJ
cbi-60	49	6	interval	interval	NOUN
cbi-60	49	7	general	general	NOUN
cbi-60	49	8	1	1	NUM
cbi-60	49	9	!	!	PUNCT
cbi-60	49	10	must	must	AUX
cbi-60	49	11	be	be	AUX
cbi-60	49	12	a	a	DET
cbi-60	49	13	lot	lot	NOUN
cbi-60	49	14	smaller	small	ADJ
cbi-60	49	15	than	than	ADP
cbi-60	49	16	#	#	NOUN
cbi-60	49	17	(	(	PUNCT
cbi-60	49	18	this	this	PRON
cbi-60	49	19	was	be	AUX
cbi-60	49	20	also	also	ADV
cbi-60	49	21	shown	show	VERB
cbi-60	49	22	by	by	ADP
cbi-60	49	23	numerical	numerical	ADJ
cbi-60	49	24	experiments	experiment	NOUN
cbi-60	49	25	:	:	PUNCT
cbi-60	49	26	if	if	SCONJ
cbi-60	49	27	we	we	PRON
cbi-60	49	28	set	set	VERB
cbi-60	49	29	"	"	PUNCT
cbi-60	49	30	=	=	SYM
cbi-60	49	31	0.01	0.01	NUM
cbi-60	49	32	,	,	PUNCT
cbi-60	49	33	#	#	NOUN
cbi-60	49	34	must	must	AUX
cbi-60	49	35	be	be	AUX
cbi-60	49	36	a	a	DET
cbi-60	49	37	lot	lot	NOUN
cbi-60	49	38	larger	large	ADJ
cbi-60	49	39	than	than	ADP
cbi-60	49	40	100	100	NUM
cbi-60	49	41	)	)	PUNCT
cbi-60	49	42	.	.	PUNCT
cbi-60	50	1	conclusion	conclusion	NOUN
cbi-60	50	2	in	in	ADP
cbi-60	50	3	conclusion	conclusion	NOUN
cbi-60	50	4	,	,	PUNCT
cbi-60	50	5	we	we	PRON
cbi-60	50	6	can	can	AUX
cbi-60	50	7	thus	thus	ADV
cbi-60	50	8	say	say	VERB
cbi-60	50	9	that	that	SCONJ
cbi-60	50	10	the	the	DET
cbi-60	50	11	connection	connection	NOUN
cbi-60	50	12	between	between	ADP
cbi-60	50	13	the	the	DET
cbi-60	50	14	often	often	ADV
cbi-60	50	15	assigned	assign	VERB
cbi-60	50	16	value	value	NOUN
cbi-60	50	17	of	of	ADP
cbi-60	50	18	a	a	DET
cbi-60	50	19	divergent	divergent	ADJ
cbi-60	50	20	series	series	NOUN
cbi-60	50	21	is	be	AUX
cbi-60	50	22	hidden	hide	VERB
cbi-60	50	23	in	in	ADP
cbi-60	50	24	its	its	PRON
cbi-60	50	25	asymptotic	asymptotic	ADJ
cbi-60	50	26	expansion	expansion	NOUN
cbi-60	50	27	.	.	PUNCT
cbi-60	51	1	furthermore	furthermore	ADV
cbi-60	51	2	,	,	PUNCT
cbi-60	51	3	some	some	DET
cbi-60	51	4	slight	slight	ADJ
cbi-60	51	5	variations	variation	NOUN
cbi-60	51	6	(	(	PUNCT
cbi-60	51	7	performed	perform	VERB
cbi-60	51	8	in	in	ADP
cbi-60	51	9	the	the	DET
cbi-60	51	10	context	context	NOUN
cbi-60	51	11	of	of	ADP
cbi-60	51	12	hyperreals	hyperreal	NOUN
cbi-60	51	13	)	)	PUNCT
cbi-60	51	14	of	of	ADP
cbi-60	51	15	the	the	DET
cbi-60	51	16	terms	term	NOUN
cbi-60	51	17	in	in	ADP
cbi-60	51	18	the	the	DET
cbi-60	51	19	divergent	divergent	ADJ
cbi-60	51	20	series	series	NOUN
cbi-60	51	21	will	will	AUX
cbi-60	51	22	alterate	alterate	VERB
cbi-60	51	23	its	its	PRON
cbi-60	51	24	asymptotic	asymptotic	ADJ
cbi-60	51	25	expansion	expansion	NOUN
cbi-60	51	26	in	in	ADP
cbi-60	51	27	such	such	DET
cbi-60	51	28	a	a	DET
cbi-60	51	29	manner	manner	NOUN
cbi-60	51	30	that	that	SCONJ
cbi-60	51	31	that	that	SCONJ
cbi-60	51	32	the	the	DET
cbi-60	51	33	bgn	bgn	NOUN
cbi-60	51	34	method	method	NOUN
cbi-60	51	35	assigns	assign	VERB
cbi-60	51	36	the	the	DET
cbi-60	51	37	‘	'	PUNCT
cbi-60	51	38	desired	desire	VERB
cbi-60	51	39	value	value	NOUN
cbi-60	51	40	’	'	PUNCT
cbi-60	51	41	to	to	ADP
cbi-60	51	42	it	it	PRON
cbi-60	51	43	.	.	PUNCT
cbi-60	52	1	as	as	SCONJ
cbi-60	52	2	it	it	PRON
cbi-60	52	3	is	be	AUX
cbi-60	52	4	at	at	ADP
cbi-60	52	5	this	this	DET
cbi-60	52	6	point	point	NOUN
cbi-60	52	7	still	still	ADV
cbi-60	52	8	untrivial	untrivial	ADJ
cbi-60	52	9	when	when	SCONJ
cbi-60	52	10	equality	equality	NOUN
cbi-60	52	11	holds	hold	VERB
cbi-60	52	12	,	,	PUNCT
cbi-60	52	13	and	and	CCONJ
cbi-60	52	14	how	how	SCONJ
cbi-60	52	15	in	in	ADP
cbi-60	52	16	this	this	DET
cbi-60	52	17	case	case	NOUN
cbi-60	52	18	"	"	PUNCT
cbi-60	52	19	and	and	CCONJ
cbi-60	52	20	#	#	NOUN
cbi-60	52	21	thus	thus	ADV
cbi-60	52	22	must	must	AUX
cbi-60	52	23	be	be	AUX
cbi-60	52	24	related	relate	VERB
cbi-60	52	25	,	,	PUNCT
cbi-60	52	26	remains	remain	VERB
cbi-60	52	27	an	an	DET
cbi-60	52	28	interesting	interesting	ADJ
cbi-60	52	29	topic	topic	NOUN
cbi-60	52	30	for	for	ADP
cbi-60	52	31	further	further	ADJ
cbi-60	52	32	research	research	NOUN
cbi-60	52	33	.	.	PUNCT
cbi-60	53	1	to	to	PART
cbi-60	53	2	state	state	VERB
cbi-60	53	3	this	this	PRON
cbi-60	53	4	in	in	ADP
cbi-60	53	5	a	a	PRON
cbi-60	53	6	more	more	ADV
cbi-60	53	7	general	general	ADJ
cbi-60	53	8	and	and	CCONJ
cbi-60	53	9	mathematically	mathematically	ADV
cbi-60	53	10	way	way	NOUN
cbi-60	53	11	:	:	PUNCT
cbi-60	53	12	consider	consider	VERB
cbi-60	53	13	a	a	DET
cbi-60	53	14	divergent	divergent	ADJ
cbi-60	53	15	series	series	NOUN
cbi-60	53	16	with	with	ADP
cbi-60	53	17	bgn	bgn	NOUN
cbi-60	53	18	expansion	expansion	NOUN
cbi-60	53	19	a	a	PRON
cbi-60	53	20	(	(	PUNCT
cbi-60	53	21	"	"	PUNCT
cbi-60	53	22	(	(	PUNCT
cbi-60	53	23	#	#	NOUN
cbi-60	53	24	)	)	PUNCT
cbi-60	53	25	)	)	PUNCT
cbi-60	53	26	#	#	SYM
cbi-60	53	27	2	2	NUM
cbi-60	53	28	+	+	SYM
cbi-60	53	29	c	c	NOUN
cbi-60	53	30	+	+	CCONJ
cbi-60	53	31	o(1/	o(1/	NOUN
cbi-60	53	32	#	#	NOUN
cbi-60	53	33	)	)	PUNCT
cbi-60	53	34	(	(	PUNCT
cbi-60	53	35	here	here	ADV
cbi-60	53	36	a	a	PRON
cbi-60	53	37	is	be	AUX
cbi-60	53	38	a	a	DET
cbi-60	53	39	value	value	NOUN
cbi-60	53	40	dependent	dependent	ADJ
cbi-60	53	41	of	of	ADP
cbi-60	53	42	"	"	PUNCT
cbi-60	53	43	which	which	PRON
cbi-60	53	44	is	be	AUX
cbi-60	53	45	in	in	ADP
cbi-60	53	46	turn	turn	NOUN
cbi-60	53	47	dependent	dependent	ADJ
cbi-60	53	48	of	of	ADP
cbi-60	53	49	#	#	NOUN
cbi-60	53	50	and	and	CCONJ
cbi-60	53	51	c	c	NOUN
cbi-60	53	52	is	be	AUX
cbi-60	53	53	the	the	DET
cbi-60	53	54	‘	'	PUNCT
cbi-60	53	55	appropriate	appropriate	ADJ
cbi-60	53	56	’	'	PUNCT
cbi-60	53	57	value	value	NOUN
cbi-60	53	58	we	we	PRON
cbi-60	53	59	want	want	VERB
cbi-60	53	60	to	to	PART
cbi-60	53	61	have	have	VERB
cbi-60	53	62	)	)	PUNCT
cbi-60	53	63	,	,	PUNCT
cbi-60	53	64	the	the	DET
cbi-60	53	65	question	question	NOUN
cbi-60	53	66	is	be	AUX
cbi-60	53	67	now	now	ADV
cbi-60	53	68	which	which	DET
cbi-60	53	69	variations	variation	NOUN
cbi-60	53	70	(	(	PUNCT
cbi-60	53	71	in	in	ADP
cbi-60	53	72	terms	term	NOUN
cbi-60	53	73	of	of	ADP
cbi-60	53	74	"	"	PUNCT
cbi-60	53	75	(	(	PUNCT
cbi-60	53	76	#	#	NOUN
cbi-60	53	77	)	)	PUNCT
cbi-60	53	78	)	)	PUNCT
cbi-60	54	1	we	we	PRON
cbi-60	54	2	have	have	VERB
cbi-60	54	3	to	to	PART
cbi-60	54	4	make	make	VERB
cbi-60	54	5	in	in	ADP
cbi-60	54	6	order	order	NOUN
cbi-60	54	7	to	to	PART
cbi-60	54	8	make	make	VERB
cbi-60	54	9	a	a	DET
cbi-60	54	10	(	(	PUNCT
cbi-60	54	11	"	"	PUNCT
cbi-60	54	12	(	(	PUNCT
cbi-60	54	13	#	#	NOUN
cbi-60	54	14	)	)	PUNCT
cbi-60	54	15	)	)	PUNCT
cbi-60	54	16	#	#	SYM
cbi-60	54	17	2	2	NUM
cbi-60	54	18	equal	equal	ADJ
cbi-60	54	19	to	to	ADP
cbi-60	54	20	zero	zero	NUM
cbi-60	54	21	.	.	PUNCT
cbi-60	55	1	bartlett	bartlett	PROPN
cbi-60	55	2	,	,	PUNCT
cbi-60	55	3	j	j	PROPN
cbi-60	55	4	,	,	PUNCT
cbi-60	55	5	l	l	PROPN
cbi-60	55	6	gaastra	gaastra	PROPN
cbi-60	55	7	,	,	PUNCT
cbi-60	55	8	and	and	CCONJ
cbi-60	55	9	d	d	X
cbi-60	55	10	nemati	nemati	NOUN
cbi-60	55	11	(	(	PUNCT
cbi-60	55	12	2020	2020	NUM
cbi-60	55	13	)	)	PUNCT
cbi-60	55	14	.	.	PUNCT
cbi-60	56	1	“	"	PUNCT
cbi-60	56	2	hyperreal	hyperreal	ADJ
cbi-60	56	3	numbers	number	NOUN
cbi-60	56	4	for	for	ADP
cbi-60	56	5	infinite	infinite	ADJ
cbi-60	56	6	divergent	divergent	ADJ
cbi-60	56	7	series	series	NOUN
cbi-60	56	8	”	"	PUNCT
cbi-60	56	9	.	.	PUNCT
cbi-60	57	1	in	in	ADP
cbi-60	57	2	:	:	PUNCT
cbi-60	57	3	communications	communication	NOUN
cbi-60	57	4	of	of	ADP
cbi-60	57	5	the	the	DET
cbi-60	57	6	blyth	blyth	PROPN
cbi-60	57	7	institute	institute	PROPN
cbi-60	57	8	2.1	2.1	NUM
cbi-60	57	9	,	,	PUNCT
cbi-60	57	10	pp	pp	ADJ
cbi-60	57	11	.	.	PUNCT
cbi-60	58	1	7–16	7–16	PROPN
cbi-60	58	2	.	.	PUNCT
cbi-60	59	1	bartlett	bartlett	PROPN
cbi-60	59	2	,	,	PUNCT
cbi-60	59	3	j	j	PROPN
cbi-60	59	4	and	and	CCONJ
cbi-60	59	5	a	a	DET
cbi-60	59	6	khurshudyan	khurshudyan	NOUN
cbi-60	59	7	(	(	PUNCT
cbi-60	59	8	2019	2019	NUM
cbi-60	59	9	)	)	PUNCT
cbi-60	59	10	.	.	PUNCT
cbi-60	60	1	“	"	PUNCT
cbi-60	60	2	numberphile	numberphile	ADJ
cbi-60	60	3	’s	’s	ADJ
cbi-60	60	4	proof	proof	NOUN
cbi-60	60	5	for	for	ADP
cbi-60	60	6	the	the	DET
cbi-60	60	7	sum	sum	NOUN
cbi-60	60	8	1	1	NUM
cbi-60	60	9	+	+	NOUN
cbi-60	60	10	2	2	NUM
cbi-60	60	11	+	+	NOUN
cbi-60	60	12	3	3	NUM
cbi-60	60	13	+	+	NOUN
cbi-60	60	14	...	...	PUNCT
cbi-60	60	15	”	"	PUNCT
cbi-60	60	16	in	in	ADP
cbi-60	60	17	:	:	PUNCT
cbi-60	60	18	communications	communication	NOUN
cbi-60	60	19	of	of	ADP
cbi-60	60	20	the	the	DET
cbi-60	60	21	blyth	blyth	PROPN
cbi-60	60	22	institute	institute	PROPN
cbi-60	60	23	1.1	1.1	NUM
cbi-60	60	24	,	,	PUNCT
cbi-60	60	25	pp	pp	ADJ
cbi-60	60	26	.	.	PUNCT
cbi-60	61	1	54–55	54–55	X
cbi-60	61	2	.	.	PUNCT
cbi-60	62	1	sugiyama	sugiyama	NOUN
cbi-60	62	2	,	,	PUNCT
cbi-60	62	3	k	k	PROPN
cbi-60	62	4	(	(	PUNCT
cbi-60	62	5	2014	2014	NUM
cbi-60	62	6	)	)	PUNCT
cbi-60	62	7	.	.	PUNCT
cbi-60	63	1	new	new	ADJ
cbi-60	63	2	proof	proof	NOUN
cbi-60	63	3	that	that	SCONJ
cbi-60	63	4	the	the	DET
cbi-60	63	5	sum	sum	NOUN
cbi-60	63	6	of	of	ADP
cbi-60	63	7	natural	natural	ADJ
cbi-60	63	8	numbers	number	NOUN
cbi-60	63	9	is	be	AUX
cbi-60	63	10	-1/12	-1/12	NOUN
cbi-60	63	11	of	of	ADP
cbi-60	63	12	the	the	DET
cbi-60	63	13	zeta	zeta	PROPN
cbi-60	63	14	function	function	NOUN
cbi-60	63	15	.	.	PUNCT
cbi-60	64	1	url	url	PROPN
cbi-60	64	2	:	:	PUNCT
cbi-60	64	3	https	https	NOUN
cbi-60	64	4	:	:	PUNCT
cbi-60	64	5	/	/	SYM
cbi-60	64	6	/	/	SYM
cbi-60	64	7	xseek	xseek	PROPN
cbi-60	64	8	qm	qm	PROPN
cbi-60	64	9	.	.	PUNCT
cbi-60	65	1	net	net	ADJ
cbi-60	65	2	/	/	SYM
cbi-60	65	3	regularization	regularization	NOUN
cbi-60	65	4	_	_	PUNCT
cbi-60	66	1	e	e	X
cbi-60	66	2	.	.	PUNCT
cbi-60	67	1	htm	htm	PROPN
cbi-60	67	2	#	#	NOUN
cbi-60	67	3	_	_	PROPN
cbi-60	67	4	toc524947400	toc524947400	NOUN
cbi-60	67	5	(	(	PUNCT
cbi-60	67	6	visited	visit	VERB
cbi-60	67	7	on	on	ADP
cbi-60	67	8	11/16/2019	11/16/2019	NUM
cbi-60	67	9	)	)	PUNCT
cbi-60	67	10	.	.	PUNCT
cbi-60	68	1	tao	tao	PROPN
cbi-60	68	2	,	,	PUNCT
cbi-60	68	3	t	t	PROPN
cbi-60	68	4	(	(	PUNCT
cbi-60	68	5	2010	2010	NUM
cbi-60	68	6	)	)	PUNCT
cbi-60	68	7	.	.	PUNCT
cbi-60	69	1	the	the	DET
cbi-60	69	2	euler	euler	NOUN
cbi-60	69	3	-	-	PUNCT
cbi-60	69	4	maclaurin	maclaurin	NOUN
cbi-60	69	5	formula	formula	NOUN
cbi-60	69	6	,	,	PUNCT
cbi-60	69	7	bernoulli	bernoulli	NOUN
cbi-60	69	8	numbers	number	NOUN
cbi-60	69	9	,	,	PUNCT
cbi-60	69	10	the	the	DET
cbi-60	69	11	zeta	zeta	NOUN
cbi-60	69	12	function	function	NOUN
cbi-60	69	13	,	,	PUNCT
cbi-60	69	14	and	and	CCONJ
cbi-60	69	15	real	real	ADJ
cbi-60	69	16	-	-	PUNCT
cbi-60	69	17	variable	variable	ADJ
cbi-60	69	18	analytic	analytic	ADJ
cbi-60	69	19	continuation	continuation	NOUN
cbi-60	69	20	.	.	PUNCT
cbi-60	70	1	url	url	PROPN
cbi-60	70	2	:	:	PUNCT
cbi-60	70	3	https://terrytao.wordpress	https://terrytao.wordpress	NOUN
cbi-60	70	4	.	.	PUNCT
cbi-60	71	1	com/2010/04/10	com/2010/04/10	PUNCT
cbi-60	71	2	/	/	SYM
cbi-60	71	3	the	the	DET
cbi-60	71	4	-	-	PUNCT
cbi-60	71	5	euler	euler	NOUN
cbi-60	71	6	-	-	PUNCT
cbi-60	71	7	maclaurin	maclaurin	NOUN
cbi-60	71	8	-	-	PUNCT
cbi-60	71	9	formulabernoulli	formulabernoulli	NOUN
cbi-60	71	10	numbers	number	NOUN
cbi-60	71	11	the	the	DET
cbi-60	71	12	zeta	zeta	NOUN
cbi-60	71	13	function	function	NOUN
cbi-60	71	14	and	and	CCONJ
cbi-60	71	15	real	real	ADJ
cbi-60	71	16	-	-	PUNCT
cbi-60	71	17	variable	variable	ADJ
cbi-60	71	18	-	-	PUNCT
cbi-60	71	19	analytic	analytic	NOUN
cbi-60	71	20	-	-	PUNCT
cbi-60	71	21	continuation/	continuation/	NOUN
cbi-60	71	22	(	(	PUNCT
cbi-60	71	23	visited	visit	VERB
cbi-60	71	24	on	on	ADP
cbi-60	71	25	01/07/2019	01/07/2019	NUM
cbi-60	71	26	)	)	PUNCT
cbi-60	71	27	.	.	PUNCT