id	sid	tid	token	lemma	pos
ap-4740	1	1	acta	acta	PROPN
ap-4740	1	2	polytechnica	polytechnica	PROPN
ap-4740	1	3	doi:10.14311	doi:10.14311	PROPN
ap-4740	1	4	/	/	SYM
ap-4740	1	5	ap.2018.58.0118	ap.2018.58.0118	PROPN
ap-4740	1	6	acta	acta	PROPN
ap-4740	1	7	polytechnica	polytechnica	PROPN
ap-4740	1	8	58(2):118–127	58(2):118–127	PROPN
ap-4740	1	9	,	,	PUNCT
ap-4740	1	10	2018	2018	NUM
ap-4740	1	11	©	©	PROPN
ap-4740	1	12	czech	czech	PROPN
ap-4740	1	13	technical	technical	PROPN
ap-4740	1	14	university	university	PROPN
ap-4740	1	15	in	in	ADP
ap-4740	1	16	prague	prague	PROPN
ap-4740	1	17	,	,	PUNCT
ap-4740	1	18	2018	2018	NUM
ap-4740	1	19	available	available	ADJ
ap-4740	1	20	online	online	ADV
ap-4740	1	21	at	at	ADP
ap-4740	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-4740	1	23	quasi	quasi	ADJ
ap-4740	1	24	-	-	ADJ
ap-4740	1	25	exactly	exactly	ADV
ap-4740	1	26	solvable	solvable	ADJ
ap-4740	1	27	schrödinger	schrödinger	ADJ
ap-4740	1	28	equations	equation	NOUN
ap-4740	1	29	,	,	PUNCT
ap-4740	1	30	symmetric	symmetric	ADJ
ap-4740	1	31	polynomials	polynomial	NOUN
ap-4740	1	32	and	and	CCONJ
ap-4740	1	33	functional	functional	ADJ
ap-4740	1	34	bethe	bethe	ADJ
ap-4740	1	35	ansatz	ansatz	ADJ
ap-4740	1	36	method	method	NOUN
ap-4740	1	37	christiane	christiane	NOUN
ap-4740	1	38	quesne	quesne	NOUN
ap-4740	1	39	physique	physique	NOUN
ap-4740	1	40	nucléaire	nucléaire	NOUN
ap-4740	1	41	théorique	théorique	PROPN
ap-4740	1	42	et	et	PROPN
ap-4740	1	43	physique	physique	PROPN
ap-4740	1	44	mathématique	mathématique	PROPN
ap-4740	1	45	,	,	PUNCT
ap-4740	1	46	université	université	PROPN
ap-4740	1	47	libre	libre	PROPN
ap-4740	1	48	de	de	X
ap-4740	1	49	bruxelles	bruxelles	PROPN
ap-4740	1	50	,	,	PUNCT
ap-4740	1	51	campus	campus	PROPN
ap-4740	1	52	de	de	X
ap-4740	1	53	la	la	X
ap-4740	1	54	plaine	plaine	PROPN
ap-4740	1	55	cp229	cp229	PROPN
ap-4740	1	56	,	,	PUNCT
ap-4740	1	57	boulevard	boulevard	PROPN
ap-4740	1	58	du	du	PROPN
ap-4740	1	59	triomphe	triomphe	PROPN
ap-4740	1	60	,	,	PUNCT
ap-4740	1	61	b-1050	b-1050	PROPN
ap-4740	1	62	brussels	brussels	PROPN
ap-4740	1	63	,	,	PUNCT
ap-4740	1	64	belgium	belgium	NOUN
ap-4740	1	65	correspondence	correspondence	NOUN
ap-4740	1	66	:	:	PUNCT
ap-4740	1	67	cquesne@ulb.ac.be	cquesne@ulb.ac.be	PROPN
ap-4740	1	68	abstract	abstract	NOUN
ap-4740	1	69	.	.	PUNCT
ap-4740	2	1	for	for	SCONJ
ap-4740	2	2	applications	application	NOUN
ap-4740	2	3	to	to	PART
ap-4740	2	4	quasi	quasi	VERB
ap-4740	2	5	-	-	ADJ
ap-4740	2	6	exactly	exactly	ADV
ap-4740	2	7	solvable	solvable	ADJ
ap-4740	2	8	schrödinger	schrödinger	ADJ
ap-4740	2	9	equations	equation	NOUN
ap-4740	2	10	in	in	ADP
ap-4740	2	11	quantum	quantum	ADJ
ap-4740	2	12	mechanics	mechanic	NOUN
ap-4740	2	13	,	,	PUNCT
ap-4740	2	14	we	we	PRON
ap-4740	2	15	consider	consider	VERB
ap-4740	2	16	the	the	DET
ap-4740	2	17	general	general	ADJ
ap-4740	2	18	conditions	condition	NOUN
ap-4740	2	19	that	that	PRON
ap-4740	2	20	have	have	VERB
ap-4740	2	21	to	to	PART
ap-4740	2	22	be	be	AUX
ap-4740	2	23	satisfied	satisfy	VERB
ap-4740	2	24	by	by	ADP
ap-4740	2	25	the	the	DET
ap-4740	2	26	coefficients	coefficient	NOUN
ap-4740	2	27	of	of	ADP
ap-4740	2	28	a	a	DET
ap-4740	2	29	second	second	ADJ
ap-4740	2	30	-	-	PUNCT
ap-4740	2	31	order	order	NOUN
ap-4740	2	32	differential	differential	ADJ
ap-4740	2	33	equation	equation	NOUN
ap-4740	2	34	with	with	ADP
ap-4740	2	35	at	at	ADP
ap-4740	2	36	most	most	ADJ
ap-4740	2	37	k+	k+	NOUN
ap-4740	2	38	1	1	NUM
ap-4740	2	39	singular	singular	ADJ
ap-4740	2	40	points	point	NOUN
ap-4740	2	41	in	in	ADP
ap-4740	2	42	order	order	NOUN
ap-4740	2	43	that	that	SCONJ
ap-4740	2	44	this	this	DET
ap-4740	2	45	equation	equation	NOUN
ap-4740	2	46	has	have	AUX
ap-4740	2	47	particular	particular	ADJ
ap-4740	2	48	solutions	solution	NOUN
ap-4740	2	49	that	that	PRON
ap-4740	2	50	are	be	AUX
ap-4740	2	51	nth	nth	ADJ
ap-4740	2	52	-	-	PUNCT
ap-4740	2	53	degree	degree	NOUN
ap-4740	2	54	polynomials	polynomial	NOUN
ap-4740	2	55	.	.	PUNCT
ap-4740	3	1	in	in	ADP
ap-4740	3	2	a	a	DET
ap-4740	3	3	first	first	ADJ
ap-4740	3	4	approach	approach	NOUN
ap-4740	3	5	,	,	PUNCT
ap-4740	3	6	we	we	PRON
ap-4740	3	7	show	show	VERB
ap-4740	3	8	that	that	SCONJ
ap-4740	3	9	such	such	ADJ
ap-4740	3	10	conditions	condition	NOUN
ap-4740	3	11	involve	involve	VERB
ap-4740	3	12	k	k	X
ap-4740	3	13	−	−	NUM
ap-4740	3	14	2	2	NUM
ap-4740	3	15	integration	integration	NOUN
ap-4740	3	16	constants	constant	NOUN
ap-4740	3	17	,	,	PUNCT
ap-4740	3	18	which	which	PRON
ap-4740	3	19	satisfy	satisfy	VERB
ap-4740	3	20	a	a	DET
ap-4740	3	21	system	system	NOUN
ap-4740	3	22	of	of	ADP
ap-4740	3	23	linear	linear	ADJ
ap-4740	3	24	equations	equation	NOUN
ap-4740	3	25	whose	whose	DET
ap-4740	3	26	coefficients	coefficient	NOUN
ap-4740	3	27	can	can	AUX
ap-4740	3	28	be	be	AUX
ap-4740	3	29	written	write	VERB
ap-4740	3	30	in	in	ADP
ap-4740	3	31	terms	term	NOUN
ap-4740	3	32	of	of	ADP
ap-4740	3	33	elementary	elementary	ADJ
ap-4740	3	34	symmetric	symmetric	ADJ
ap-4740	3	35	polynomials	polynomial	NOUN
ap-4740	3	36	in	in	ADP
ap-4740	3	37	the	the	DET
ap-4740	3	38	polynomial	polynomial	ADJ
ap-4740	3	39	solution	solution	NOUN
ap-4740	3	40	roots	root	NOUN
ap-4740	3	41	whenver	whenver	VERB
ap-4740	3	42	such	such	ADJ
ap-4740	3	43	roots	root	NOUN
ap-4740	3	44	are	be	AUX
ap-4740	3	45	all	all	ADV
ap-4740	3	46	real	real	ADJ
ap-4740	3	47	and	and	CCONJ
ap-4740	3	48	distinct	distinct	ADJ
ap-4740	3	49	.	.	PUNCT
ap-4740	4	1	in	in	ADP
ap-4740	4	2	a	a	DET
ap-4740	4	3	second	second	ADJ
ap-4740	4	4	approach	approach	NOUN
ap-4740	4	5	,	,	PUNCT
ap-4740	4	6	we	we	PRON
ap-4740	4	7	consider	consider	VERB
ap-4740	4	8	the	the	DET
ap-4740	4	9	functional	functional	ADJ
ap-4740	4	10	bethe	bethe	ADJ
ap-4740	4	11	ansatz	ansatz	ADJ
ap-4740	4	12	method	method	NOUN
ap-4740	4	13	in	in	ADP
ap-4740	4	14	its	its	PRON
ap-4740	4	15	most	most	ADV
ap-4740	4	16	general	general	ADJ
ap-4740	4	17	form	form	NOUN
ap-4740	4	18	under	under	ADP
ap-4740	4	19	the	the	DET
ap-4740	4	20	same	same	ADJ
ap-4740	4	21	assumption	assumption	NOUN
ap-4740	4	22	.	.	PUNCT
ap-4740	5	1	comparing	compare	VERB
ap-4740	5	2	the	the	DET
ap-4740	5	3	two	two	NUM
ap-4740	5	4	approaches	approach	NOUN
ap-4740	5	5	,	,	PUNCT
ap-4740	5	6	we	we	PRON
ap-4740	5	7	prove	prove	VERB
ap-4740	5	8	that	that	SCONJ
ap-4740	5	9	the	the	DET
ap-4740	5	10	above	above	ADV
ap-4740	5	11	-	-	PUNCT
ap-4740	5	12	mentioned	mention	VERB
ap-4740	5	13	k	k	NOUN
ap-4740	5	14	−	−	PROPN
ap-4740	5	15	2	2	NUM
ap-4740	5	16	integration	integration	NOUN
ap-4740	5	17	constants	constant	NOUN
ap-4740	5	18	can	can	AUX
ap-4740	5	19	be	be	AUX
ap-4740	5	20	expressed	express	VERB
ap-4740	5	21	as	as	ADP
ap-4740	5	22	linear	linear	ADJ
ap-4740	5	23	combinations	combination	NOUN
ap-4740	5	24	of	of	ADP
ap-4740	5	25	monomial	monomial	ADJ
ap-4740	5	26	symmetric	symmetric	ADJ
ap-4740	5	27	polynomials	polynomial	NOUN
ap-4740	5	28	in	in	ADP
ap-4740	5	29	the	the	DET
ap-4740	5	30	roots	root	NOUN
ap-4740	5	31	,	,	PUNCT
ap-4740	5	32	associated	associate	VERB
ap-4740	5	33	with	with	ADP
ap-4740	5	34	partitions	partition	NOUN
ap-4740	5	35	into	into	ADP
ap-4740	5	36	no	no	DET
ap-4740	5	37	more	more	ADJ
ap-4740	5	38	than	than	ADP
ap-4740	5	39	two	two	NUM
ap-4740	5	40	parts	part	NOUN
ap-4740	5	41	.	.	PUNCT
ap-4740	6	1	we	we	PRON
ap-4740	6	2	illustrate	illustrate	VERB
ap-4740	6	3	these	these	DET
ap-4740	6	4	results	result	NOUN
ap-4740	6	5	by	by	ADP
ap-4740	6	6	considering	consider	VERB
ap-4740	6	7	a	a	DET
ap-4740	6	8	quasi	quasi	ADJ
ap-4740	6	9	-	-	ADJ
ap-4740	6	10	exactly	exactly	ADV
ap-4740	6	11	solvable	solvable	ADJ
ap-4740	6	12	extension	extension	NOUN
ap-4740	6	13	of	of	ADP
ap-4740	6	14	the	the	DET
ap-4740	6	15	mathews	mathews	NOUN
ap-4740	6	16	-	-	PUNCT
ap-4740	6	17	lakshmanan	lakshmanan	PROPN
ap-4740	6	18	nonlinear	nonlinear	ADJ
ap-4740	6	19	oscillator	oscillator	NOUN
ap-4740	6	20	corresponding	correspond	VERB
ap-4740	6	21	to	to	ADP
ap-4740	6	22	k	k	PROPN
ap-4740	6	23	=	=	PUNCT
ap-4740	6	24	4	4	X
ap-4740	6	25	.	.	PUNCT
ap-4740	7	1	keywords	keyword	NOUN
ap-4740	7	2	:	:	PUNCT
ap-4740	7	3	schrödinger	schrödinger	ADJ
ap-4740	7	4	equation	equation	NOUN
ap-4740	7	5	;	;	PUNCT
ap-4740	7	6	quasi	quasi	ADJ
ap-4740	7	7	-	-	ADJ
ap-4740	7	8	exactly	exactly	ADV
ap-4740	7	9	solvable	solvable	ADJ
ap-4740	7	10	potentials	potential	NOUN
ap-4740	7	11	;	;	PUNCT
ap-4740	7	12	symmetric	symmetric	ADJ
ap-4740	7	13	polynomials	polynomial	NOUN
ap-4740	7	14	.	.	PUNCT
ap-4740	8	1	1	1	X
ap-4740	8	2	.	.	X
ap-4740	8	3	introduction	introduction	NOUN
ap-4740	8	4	in	in	ADP
ap-4740	8	5	quantum	quantum	ADJ
ap-4740	8	6	mechanics	mechanic	NOUN
ap-4740	8	7	,	,	PUNCT
ap-4740	8	8	solving	solve	VERB
ap-4740	8	9	the	the	DET
ap-4740	8	10	schrödinger	schrödinger	ADJ
ap-4740	8	11	equation	equation	NOUN
ap-4740	8	12	is	be	AUX
ap-4740	8	13	a	a	DET
ap-4740	8	14	fundamental	fundamental	ADJ
ap-4740	8	15	problem	problem	NOUN
ap-4740	8	16	for	for	ADP
ap-4740	8	17	understanding	understand	VERB
ap-4740	8	18	physical	physical	ADJ
ap-4740	8	19	systems	system	NOUN
ap-4740	8	20	.	.	PUNCT
ap-4740	9	1	exact	exact	ADJ
ap-4740	9	2	solutions	solution	NOUN
ap-4740	9	3	may	may	AUX
ap-4740	9	4	be	be	AUX
ap-4740	9	5	very	very	ADV
ap-4740	9	6	useful	useful	ADJ
ap-4740	9	7	for	for	ADP
ap-4740	9	8	developing	develop	VERB
ap-4740	9	9	a	a	DET
ap-4740	9	10	constructive	constructive	ADJ
ap-4740	9	11	perturbation	perturbation	NOUN
ap-4740	9	12	theory	theory	NOUN
ap-4740	9	13	or	or	CCONJ
ap-4740	9	14	for	for	ADP
ap-4740	9	15	suggesting	suggest	VERB
ap-4740	9	16	trial	trial	NOUN
ap-4740	9	17	functions	function	NOUN
ap-4740	9	18	in	in	ADP
ap-4740	9	19	variational	variational	ADJ
ap-4740	9	20	calculus	calculus	NOUN
ap-4740	9	21	for	for	ADP
ap-4740	9	22	more	more	ADV
ap-4740	9	23	complicated	complicated	ADJ
ap-4740	9	24	cases	case	NOUN
ap-4740	9	25	.	.	PUNCT
ap-4740	10	1	however	however	ADV
ap-4740	10	2	,	,	PUNCT
ap-4740	10	3	very	very	ADV
ap-4740	10	4	few	few	ADJ
ap-4740	10	5	potentials	potential	NOUN
ap-4740	10	6	can	can	AUX
ap-4740	10	7	actually	actually	ADV
ap-4740	10	8	be	be	AUX
ap-4740	10	9	exactly	exactly	ADV
ap-4740	10	10	solved	solve	VERB
ap-4740	10	11	(	(	PUNCT
ap-4740	10	12	see	see	VERB
ap-4740	10	13	,	,	PUNCT
ap-4740	10	14	e.g.	e.g.	ADV
ap-4740	10	15	,	,	PUNCT
ap-4740	10	16	one	one	NUM
ap-4740	10	17	of	of	ADP
ap-4740	10	18	their	their	PRON
ap-4740	10	19	lists	list	NOUN
ap-4740	10	20	in	in	ADP
ap-4740	10	21	[	[	X
ap-4740	10	22	1]).1	1]).1	NUM
ap-4740	10	23	these	these	DET
ap-4740	10	24	potentials	potential	NOUN
ap-4740	10	25	are	be	AUX
ap-4740	10	26	connected	connect	VERB
ap-4740	10	27	with	with	ADP
ap-4740	10	28	second	second	ADJ
ap-4740	10	29	-	-	PUNCT
ap-4740	10	30	order	order	NOUN
ap-4740	10	31	differential	differential	ADJ
ap-4740	10	32	equations	equation	NOUN
ap-4740	10	33	of	of	ADP
ap-4740	10	34	hypergeometric	hypergeometric	ADJ
ap-4740	10	35	type	type	NOUN
ap-4740	10	36	and	and	CCONJ
ap-4740	10	37	their	their	PRON
ap-4740	10	38	wavefunctions	wavefunction	NOUN
ap-4740	10	39	can	can	AUX
ap-4740	10	40	be	be	AUX
ap-4740	10	41	constructed	construct	VERB
ap-4740	10	42	by	by	ADP
ap-4740	10	43	using	use	VERB
ap-4740	10	44	the	the	DET
ap-4740	10	45	theory	theory	NOUN
ap-4740	10	46	of	of	ADP
ap-4740	10	47	corresponding	correspond	VERB
ap-4740	10	48	orthogonal	orthogonal	ADJ
ap-4740	10	49	polynomials	polynomial	NOUN
ap-4740	10	50	[	[	X
ap-4740	10	51	3	3	NUM
ap-4740	10	52	]	]	PUNCT
ap-4740	10	53	.	.	PUNCT
ap-4740	11	1	a	a	DET
ap-4740	11	2	second	second	ADJ
ap-4740	11	3	category	category	NOUN
ap-4740	11	4	of	of	ADP
ap-4740	11	5	exact	exact	ADJ
ap-4740	11	6	solutions	solution	NOUN
ap-4740	11	7	belongs	belong	VERB
ap-4740	11	8	to	to	ADP
ap-4740	11	9	the	the	DET
ap-4740	11	10	so	so	ADV
ap-4740	11	11	-	-	PUNCT
ap-4740	11	12	called	call	VERB
ap-4740	11	13	quasi	quasi	ADJ
ap-4740	11	14	-	-	ADJ
ap-4740	11	15	exactly	exactly	ADV
ap-4740	11	16	solvable	solvable	ADJ
ap-4740	11	17	(	(	PUNCT
ap-4740	11	18	qes	qes	NOUN
ap-4740	11	19	)	)	PUNCT
ap-4740	11	20	schrödinger	schrödinger	ADJ
ap-4740	11	21	equations	equation	NOUN
ap-4740	11	22	.	.	PUNCT
ap-4740	12	1	these	these	PRON
ap-4740	12	2	occupy	occupy	VERB
ap-4740	12	3	an	an	DET
ap-4740	12	4	intermediate	intermediate	ADJ
ap-4740	12	5	place	place	NOUN
ap-4740	12	6	between	between	ADP
ap-4740	12	7	exactly	exactly	ADV
ap-4740	12	8	solvable	solvable	ADJ
ap-4740	12	9	(	(	PUNCT
ap-4740	12	10	es	es	NOUN
ap-4740	12	11	)	)	PUNCT
ap-4740	12	12	and	and	CCONJ
ap-4740	12	13	non	non	ADJ
ap-4740	12	14	-	-	ADJ
ap-4740	12	15	solvable	solvable	ADJ
ap-4740	12	16	ones	one	NOUN
ap-4740	12	17	in	in	ADP
ap-4740	12	18	the	the	DET
ap-4740	12	19	sense	sense	NOUN
ap-4740	12	20	that	that	SCONJ
ap-4740	12	21	only	only	ADV
ap-4740	12	22	a	a	DET
ap-4740	12	23	finite	finite	ADJ
ap-4740	12	24	number	number	NOUN
ap-4740	12	25	of	of	ADP
ap-4740	12	26	eigenstates	eigenstate	NOUN
ap-4740	12	27	can	can	AUX
ap-4740	12	28	be	be	AUX
ap-4740	12	29	found	find	VERB
ap-4740	12	30	explicitly	explicitly	ADV
ap-4740	12	31	by	by	ADP
ap-4740	12	32	algebraic	algebraic	ADJ
ap-4740	12	33	means	mean	NOUN
ap-4740	12	34	,	,	PUNCT
ap-4740	12	35	while	while	SCONJ
ap-4740	12	36	the	the	DET
ap-4740	12	37	remaining	remain	VERB
ap-4740	12	38	ones	one	NOUN
ap-4740	12	39	remain	remain	VERB
ap-4740	12	40	unknown	unknown	ADJ
ap-4740	12	41	.	.	PUNCT
ap-4740	13	1	the	the	DET
ap-4740	13	2	simplest	simple	ADJ
ap-4740	13	3	qes	qes	NOUN
ap-4740	13	4	problems	problem	NOUN
ap-4740	13	5	,	,	PUNCT
ap-4740	13	6	discovered	discover	VERB
ap-4740	13	7	in	in	ADP
ap-4740	13	8	the	the	DET
ap-4740	13	9	1980s	1980	NOUN
ap-4740	13	10	,	,	PUNCT
ap-4740	13	11	are	be	AUX
ap-4740	13	12	characterized	characterize	VERB
ap-4740	13	13	by	by	ADP
ap-4740	13	14	a	a	DET
ap-4740	13	15	hidden	hide	VERB
ap-4740	13	16	sl(2,r	sl(2,r	NOUN
ap-4740	13	17	)	)	PUNCT
ap-4740	13	18	algebraic	algebraic	ADJ
ap-4740	13	19	structure	structure	NOUN
ap-4740	14	1	[	[	X
ap-4740	14	2	4–8	4–8	X
ap-4740	14	3	]	]	PUNCT
ap-4740	14	4	and	and	CCONJ
ap-4740	14	5	are	be	AUX
ap-4740	14	6	connected	connect	VERB
ap-4740	14	7	with	with	ADP
ap-4740	14	8	polynomial	polynomial	ADJ
ap-4740	14	9	solutions	solution	NOUN
ap-4740	14	10	of	of	ADP
ap-4740	14	11	the	the	DET
ap-4740	14	12	heun	heun	NOUN
ap-4740	14	13	equation	equation	NOUN
ap-4740	14	14	[	[	X
ap-4740	14	15	9	9	NUM
ap-4740	14	16	]	]	PUNCT
ap-4740	14	17	.	.	PUNCT
ap-4740	15	1	generalizations	generalization	NOUN
ap-4740	15	2	of	of	ADP
ap-4740	15	3	this	this	DET
ap-4740	15	4	equation	equation	NOUN
ap-4740	15	5	are	be	AUX
ap-4740	15	6	related	relate	VERB
ap-4740	15	7	through	through	ADP
ap-4740	15	8	their	their	PRON
ap-4740	15	9	polynomial	polynomial	ADJ
ap-4740	15	10	solutions	solution	NOUN
ap-4740	15	11	to	to	ADP
ap-4740	15	12	more	more	ADV
ap-4740	15	13	complicated	complicated	ADJ
ap-4740	15	14	qes	qes	NOUN
ap-4740	15	15	problems	problem	NOUN
ap-4740	15	16	.	.	PUNCT
ap-4740	16	1	several	several	ADJ
ap-4740	16	2	procedures	procedure	NOUN
ap-4740	16	3	are	be	AUX
ap-4740	16	4	employed	employ	VERB
ap-4740	16	5	in	in	ADP
ap-4740	16	6	this	this	DET
ap-4740	16	7	context	context	NOUN
ap-4740	16	8	,	,	PUNCT
ap-4740	16	9	such	such	ADJ
ap-4740	16	10	as	as	ADP
ap-4740	16	11	the	the	DET
ap-4740	16	12	use	use	NOUN
ap-4740	16	13	of	of	ADP
ap-4740	16	14	high	high	ADJ
ap-4740	16	15	-	-	PUNCT
ap-4740	16	16	order	order	NOUN
ap-4740	16	17	recursion	recursion	NOUN
ap-4740	16	18	relations	relation	NOUN
ap-4740	16	19	(	(	PUNCT
ap-4740	16	20	see	see	VERB
ap-4740	16	21	,	,	PUNCT
ap-4740	16	22	e.g.	e.g.	ADV
ap-4740	16	23	,	,	PUNCT
ap-4740	16	24	[	[	X
ap-4740	16	25	10	10	NUM
ap-4740	16	26	]	]	PUNCT
ap-4740	16	27	)	)	PUNCT
ap-4740	16	28	or	or	CCONJ
ap-4740	16	29	the	the	DET
ap-4740	16	30	functional	functional	ADJ
ap-4740	16	31	bethe	bethe	PROPN
ap-4740	16	32	ansatz	ansatz	ADJ
ap-4740	16	33	(	(	PUNCT
ap-4740	16	34	fba	fba	ADJ
ap-4740	16	35	)	)	PUNCT
ap-4740	16	36	method	method	NOUN
ap-4740	16	37	[	[	X
ap-4740	16	38	11–13	11–13	NUM
ap-4740	16	39	]	]	X
ap-4740	16	40	,	,	PUNCT
ap-4740	16	41	which	which	PRON
ap-4740	16	42	has	have	AUX
ap-4740	16	43	proven	prove	VERB
ap-4740	16	44	very	very	ADV
ap-4740	16	45	effective	effective	ADJ
ap-4740	16	46	[	[	X
ap-4740	16	47	14–17	14–17	NUM
ap-4740	16	48	]	]	PUNCT
ap-4740	16	49	.	.	PUNCT
ap-4740	17	1	the	the	DET
ap-4740	17	2	purpose	purpose	NOUN
ap-4740	17	3	of	of	ADP
ap-4740	17	4	the	the	DET
ap-4740	17	5	present	present	ADJ
ap-4740	17	6	paper	paper	NOUN
ap-4740	17	7	is	be	AUX
ap-4740	17	8	to	to	PART
ap-4740	17	9	reconsider	reconsider	VERB
ap-4740	17	10	the	the	DET
ap-4740	17	11	general	general	ADJ
ap-4740	17	12	conditions	condition	NOUN
ap-4740	17	13	under	under	ADP
ap-4740	17	14	which	which	PRON
ap-4740	17	15	a	a	DET
ap-4740	17	16	second	second	ADJ
ap-4740	17	17	-	-	PUNCT
ap-4740	17	18	order	order	NOUN
ap-4740	17	19	differential	differential	ADJ
ap-4740	17	20	equation	equation	NOUN
ap-4740	17	21	x(z)y′′(z	x(z)y′′(z	PROPN
ap-4740	17	22	)	)	PUNCT
ap-4740	18	1	+	+	CCONJ
ap-4740	18	2	y	y	PROPN
ap-4740	18	3	(	(	PUNCT
ap-4740	18	4	z)y′(z	z)y′(z	PROPN
ap-4740	18	5	)	)	PUNCT
ap-4740	18	6	+	+	NOUN
ap-4740	18	7	z(z)y(z	z(z)y(z	NUM
ap-4740	18	8	)	)	PUNCT
ap-4740	18	9	=	=	SYM
ap-4740	18	10	0	0	NUM
ap-4740	18	11	with	with	ADP
ap-4740	18	12	polynomial	polynomial	ADJ
ap-4740	18	13	coefficients	coefficient	NOUN
ap-4740	18	14	x(z	x(z	PROPN
ap-4740	18	15	)	)	PUNCT
ap-4740	18	16	,	,	PUNCT
ap-4740	18	17	y	y	PROPN
ap-4740	18	18	(	(	PUNCT
ap-4740	18	19	z	z	NOUN
ap-4740	18	20	)	)	PUNCT
ap-4740	18	21	,	,	PUNCT
ap-4740	18	22	and	and	CCONJ
ap-4740	18	23	z(z	z(z	NOUN
ap-4740	18	24	)	)	PUNCT
ap-4740	18	25	of	of	ADP
ap-4740	18	26	respective	respective	ADJ
ap-4740	18	27	degrees	degree	NOUN
ap-4740	18	28	k	k	PROPN
ap-4740	18	29	,	,	PUNCT
ap-4740	18	30	k	k	PROPN
ap-4740	18	31	−	−	PROPN
ap-4740	18	32	1	1	NUM
ap-4740	18	33	,	,	PUNCT
ap-4740	18	34	and	and	CCONJ
ap-4740	18	35	k	k	PROPN
ap-4740	18	36	−	−	PROPN
ap-4740	18	37	2	2	NUM
ap-4740	18	38	,	,	PUNCT
ap-4740	18	39	has	have	VERB
ap-4740	18	40	nth	nth	NOUN
ap-4740	18	41	-	-	PUNCT
ap-4740	18	42	degree	degree	NOUN
ap-4740	18	43	polynomial	polynomial	ADJ
ap-4740	18	44	solutions	solution	NOUN
ap-4740	18	45	yn(z	yn(z	NOUN
ap-4740	18	46	)	)	PUNCT
ap-4740	18	47	.	.	PUNCT
ap-4740	19	1	choosing	choose	VERB
ap-4740	19	2	appropriately	appropriately	ADV
ap-4740	19	3	the	the	DET
ap-4740	19	4	polynomial	polynomial	ADJ
ap-4740	19	5	z(z	z(z	NOUN
ap-4740	19	6	)	)	PUNCT
ap-4740	19	7	for	for	ADP
ap-4740	19	8	such	such	DET
ap-4740	19	9	a	a	DET
ap-4740	19	10	purpose	purpose	NOUN
ap-4740	19	11	is	be	AUX
ap-4740	19	12	known	know	VERB
ap-4740	19	13	as	as	ADP
ap-4740	19	14	the	the	DET
ap-4740	19	15	classical	classical	ADJ
ap-4740	19	16	heine	heine	PROPN
ap-4740	19	17	-	-	PUNCT
ap-4740	19	18	stieltjes	stieltjes	PROPN
ap-4740	19	19	problem	problem	NOUN
ap-4740	19	20	[	[	X
ap-4740	19	21	18	18	NUM
ap-4740	19	22	,	,	PUNCT
ap-4740	19	23	19	19	NUM
ap-4740	19	24	]	]	PUNCT
ap-4740	19	25	.	.	PUNCT
ap-4740	20	1	such	such	DET
ap-4740	20	2	a	a	DET
ap-4740	20	3	differential	differential	ADJ
ap-4740	20	4	equation	equation	NOUN
ap-4740	20	5	with	with	ADP
ap-4740	20	6	at	at	ADP
ap-4740	20	7	most	most	ADJ
ap-4740	20	8	k+1	k+1	DET
ap-4740	20	9	singular	singular	PROPN
ap-4740	20	10	points	point	NOUN
ap-4740	20	11	covers	cover	VERB
ap-4740	20	12	the	the	DET
ap-4740	20	13	cases	case	NOUN
ap-4740	20	14	of	of	ADP
ap-4740	20	15	the	the	DET
ap-4740	20	16	hypergeometric	hypergeometric	ADJ
ap-4740	20	17	equation	equation	NOUN
ap-4740	20	18	(	(	PUNCT
ap-4740	20	19	for	for	ADP
ap-4740	20	20	k	k	PROPN
ap-4740	20	21	=	=	SYM
ap-4740	20	22	2	2	NUM
ap-4740	20	23	)	)	PUNCT
ap-4740	20	24	,	,	PUNCT
ap-4740	20	25	the	the	DET
ap-4740	20	26	heun	heun	NOUN
ap-4740	20	27	equation	equation	NOUN
ap-4740	20	28	(	(	PUNCT
ap-4740	20	29	for	for	ADP
ap-4740	20	30	k	k	PROPN
ap-4740	20	31	=	=	SYM
ap-4740	20	32	3	3	NUM
ap-4740	20	33	)	)	PUNCT
ap-4740	20	34	,	,	PUNCT
ap-4740	20	35	and	and	CCONJ
ap-4740	20	36	generalized	generalized	ADJ
ap-4740	20	37	heun	heun	NOUN
ap-4740	20	38	equations	equation	NOUN
ap-4740	20	39	(	(	PUNCT
ap-4740	20	40	for	for	ADP
ap-4740	20	41	k	k	PROPN
ap-4740	20	42	≥	≥	NUM
ap-4740	20	43	4	4	NUM
ap-4740	20	44	)	)	PUNCT
ap-4740	20	45	,	,	PUNCT
ap-4740	20	46	and	and	CCONJ
ap-4740	20	47	plays	play	VERB
ap-4740	20	48	therefore	therefore	ADV
ap-4740	20	49	a	a	DET
ap-4740	20	50	crucial	crucial	ADJ
ap-4740	20	51	part	part	NOUN
ap-4740	20	52	in	in	ADP
ap-4740	20	53	es	es	X
ap-4740	20	54	and	and	CCONJ
ap-4740	20	55	qes	qes	NOUN
ap-4740	20	56	quantum	quantum	NOUN
ap-4740	20	57	problems	problem	NOUN
ap-4740	20	58	.	.	PUNCT
ap-4740	21	1	here	here	ADV
ap-4740	21	2	we	we	PRON
ap-4740	21	3	plan	plan	VERB
ap-4740	21	4	to	to	PART
ap-4740	21	5	emphasize	emphasize	VERB
ap-4740	21	6	the	the	DET
ap-4740	21	7	key	key	ADJ
ap-4740	21	8	role	role	NOUN
ap-4740	21	9	played	play	VERB
ap-4740	21	10	by	by	ADP
ap-4740	21	11	symmetric	symmetric	ADJ
ap-4740	21	12	polynomials	polynomial	NOUN
ap-4740	21	13	in	in	ADP
ap-4740	21	14	the	the	DET
ap-4740	21	15	polynomial	polynomial	ADJ
ap-4740	21	16	solution	solution	NOUN
ap-4740	21	17	roots	root	NOUN
ap-4740	21	18	whenever	whenever	SCONJ
ap-4740	21	19	such	such	ADJ
ap-4740	21	20	roots	root	NOUN
ap-4740	21	21	are	be	AUX
ap-4740	21	22	all	all	ADV
ap-4740	21	23	real	real	ADJ
ap-4740	21	24	and	and	CCONJ
ap-4740	21	25	distinct	distinct	ADJ
ap-4740	21	26	.	.	PUNCT
ap-4740	22	1	this	this	PRON
ap-4740	22	2	will	will	AUX
ap-4740	22	3	be	be	AUX
ap-4740	22	4	done	do	VERB
ap-4740	22	5	by	by	ADP
ap-4740	22	6	comparing	compare	VERB
ap-4740	22	7	two	two	NUM
ap-4740	22	8	different	different	ADJ
ap-4740	22	9	approaches	approach	NOUN
ap-4740	22	10	:	:	PUNCT
ap-4740	22	11	a	a	DET
ap-4740	22	12	first	first	ADJ
ap-4740	22	13	one	one	NUM
ap-4740	22	14	expressing	express	VERB
ap-4740	22	15	the	the	DET
ap-4740	22	16	polynomial	polynomial	ADJ
ap-4740	22	17	z(z	z(z	NOUN
ap-4740	22	18	)	)	PUNCT
ap-4740	22	19	in	in	ADP
ap-4740	22	20	terms	term	NOUN
ap-4740	22	21	of	of	ADP
ap-4740	22	22	k	k	NOUN
ap-4740	22	23	−	−	PROPN
ap-4740	22	24	2	2	NUM
ap-4740	22	25	integration	integration	NOUN
ap-4740	22	26	constants	constant	NOUN
ap-4740	22	27	,	,	PUNCT
ap-4740	22	28	and	and	CCONJ
ap-4740	22	29	a	a	DET
ap-4740	22	30	second	second	ADJ
ap-4740	22	31	one	one	NUM
ap-4740	22	32	based	base	VERB
ap-4740	22	33	on	on	ADP
ap-4740	22	34	the	the	DET
ap-4740	22	35	fba	fba	PROPN
ap-4740	22	36	method	method	NOUN
ap-4740	22	37	.	.	PUNCT
ap-4740	23	1	in	in	ADP
ap-4740	23	2	section	section	NOUN
ap-4740	23	3	2	2	NUM
ap-4740	23	4	,	,	PUNCT
ap-4740	23	5	the	the	DET
ap-4740	23	6	problem	problem	NOUN
ap-4740	23	7	of	of	ADP
ap-4740	23	8	second	second	ADJ
ap-4740	23	9	-	-	PUNCT
ap-4740	23	10	order	order	NOUN
ap-4740	23	11	differential	differential	ADJ
ap-4740	23	12	equations	equation	NOUN
ap-4740	23	13	with	with	ADP
ap-4740	23	14	polynomial	polynomial	ADJ
ap-4740	23	15	solutions	solution	NOUN
ap-4740	23	16	is	be	AUX
ap-4740	23	17	discussed	discuss	VERB
ap-4740	23	18	and	and	CCONJ
ap-4740	23	19	k−	k−	NOUN
ap-4740	23	20	2	2	NUM
ap-4740	23	21	integration	integration	NOUN
ap-4740	23	22	constants	constant	NOUN
ap-4740	23	23	are	be	AUX
ap-4740	23	24	introduced	introduce	VERB
ap-4740	23	25	.	.	PUNCT
ap-4740	24	1	in	in	ADP
ap-4740	24	2	section	section	NOUN
ap-4740	24	3	3	3	NUM
ap-4740	24	4	,	,	PUNCT
ap-4740	24	5	the	the	DET
ap-4740	24	6	fba	fba	PROPN
ap-4740	24	7	method	method	NOUN
ap-4740	24	8	is	be	AUX
ap-4740	24	9	derived	derive	VERB
ap-4740	24	10	in	in	ADP
ap-4740	24	11	its	its	PRON
ap-4740	24	12	most	most	ADV
ap-4740	24	13	general	general	ADJ
ap-4740	24	14	form	form	NOUN
ap-4740	24	15	.	.	PUNCT
ap-4740	25	1	a	a	DET
ap-4740	25	2	comparison	comparison	NOUN
ap-4740	25	3	between	between	ADP
ap-4740	25	4	the	the	DET
ap-4740	25	5	two	two	NUM
ap-4740	25	6	approaches	approach	NOUN
ap-4740	25	7	is	be	AUX
ap-4740	25	8	carried	carry	VERB
ap-4740	25	9	out	out	ADP
ap-4740	25	10	in	in	ADP
ap-4740	25	11	section	section	NOUN
ap-4740	25	12	4	4	NUM
ap-4740	25	13	.	.	PUNCT
ap-4740	26	1	the	the	DET
ap-4740	26	2	results	result	NOUN
ap-4740	26	3	so	so	ADV
ap-4740	26	4	obtained	obtain	VERB
ap-4740	26	5	are	be	AUX
ap-4740	26	6	illustrated	illustrate	VERB
ap-4740	26	7	in	in	ADP
ap-4740	26	8	1here	1here	NUM
ap-4740	26	9	we	we	PRON
ap-4740	26	10	do	do	AUX
ap-4740	26	11	not	not	PART
ap-4740	26	12	plan	plan	VERB
ap-4740	26	13	to	to	PART
ap-4740	26	14	discuss	discuss	VERB
ap-4740	26	15	the	the	DET
ap-4740	26	16	recent	recent	ADJ
ap-4740	26	17	development	development	NOUN
ap-4740	26	18	of	of	ADP
ap-4740	26	19	the	the	DET
ap-4740	26	20	exceptional	exceptional	ADJ
ap-4740	26	21	orthogonal	orthogonal	ADJ
ap-4740	26	22	polynomials	polynomial	NOUN
ap-4740	26	23	and	and	CCONJ
ap-4740	26	24	the	the	DET
ap-4740	26	25	associated	associated	ADJ
ap-4740	26	26	polynomially	polynomially	ADV
ap-4740	26	27	solvable	solvable	ADJ
ap-4740	26	28	analytic	analytic	ADJ
ap-4740	26	29	potentials	potential	NOUN
ap-4740	26	30	(	(	PUNCT
ap-4740	26	31	see	see	VERB
ap-4740	26	32	,	,	PUNCT
ap-4740	26	33	e.g.	e.g.	ADV
ap-4740	26	34	,	,	PUNCT
ap-4740	26	35	[	[	X
ap-4740	26	36	2	2	NUM
ap-4740	26	37	]	]	PUNCT
ap-4740	26	38	and	and	CCONJ
ap-4740	26	39	references	reference	NOUN
ap-4740	26	40	quoted	quote	VERB
ap-4740	26	41	therein	therein	ADV
ap-4740	26	42	)	)	PUNCT
ap-4740	26	43	.	.	PUNCT
ap-4740	27	1	118	118	NUM
ap-4740	27	2	http://dx.doi.org/10.14311/ap.2018.58.0118	http://dx.doi.org/10.14311/ap.2018.58.0118	X
ap-4740	27	3	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-4740	27	4	vol	vol	NOUN
ap-4740	27	5	.	.	PUNCT
ap-4740	28	1	58	58	NUM
ap-4740	28	2	no	no	INTJ
ap-4740	28	3	.	.	PUNCT
ap-4740	29	1	2/2018	2/2018	NOUN
ap-4740	29	2	quasi	quasi	ADJ
ap-4740	29	3	-	-	ADJ
ap-4740	29	4	exactly	exactly	ADV
ap-4740	29	5	solvable	solvable	ADJ
ap-4740	29	6	schrödinger	schrödinger	ADJ
ap-4740	29	7	equations	equation	NOUN
ap-4740	29	8	section	section	NOUN
ap-4740	29	9	5	5	NUM
ap-4740	29	10	by	by	ADP
ap-4740	29	11	considering	consider	VERB
ap-4740	29	12	a	a	DET
ap-4740	29	13	qes	qes	NOUN
ap-4740	29	14	extension	extension	NOUN
ap-4740	29	15	of	of	ADP
ap-4740	29	16	the	the	DET
ap-4740	29	17	mathews	mathews	NOUN
ap-4740	29	18	-	-	PUNCT
ap-4740	29	19	lakshmanan	lakshmanan	PROPN
ap-4740	29	20	nonlinear	nonlinear	ADJ
ap-4740	29	21	oscillator	oscillator	NOUN
ap-4740	29	22	.	.	PUNCT
ap-4740	30	1	finally	finally	ADV
ap-4740	30	2	,	,	PUNCT
ap-4740	30	3	section	section	NOUN
ap-4740	30	4	6	6	NUM
ap-4740	30	5	contains	contain	VERB
ap-4740	30	6	the	the	DET
ap-4740	30	7	conclusion	conclusion	NOUN
ap-4740	30	8	.	.	PUNCT
ap-4740	31	1	2	2	X
ap-4740	31	2	.	.	X
ap-4740	31	3	second	second	ADJ
ap-4740	31	4	-	-	PUNCT
ap-4740	31	5	order	order	NOUN
ap-4740	31	6	differential	differential	ADJ
ap-4740	31	7	equations	equation	NOUN
ap-4740	31	8	with	with	ADP
ap-4740	31	9	polynomial	polynomial	ADJ
ap-4740	31	10	solutions	solution	NOUN
ap-4740	31	11	and	and	CCONJ
ap-4740	31	12	integration	integration	NOUN
ap-4740	31	13	constants	constant	NOUN
ap-4740	31	14	on	on	ADP
ap-4740	31	15	starting	start	VERB
ap-4740	31	16	from	from	ADP
ap-4740	31	17	a	a	DET
ap-4740	31	18	schrödinger	schrödinger	ADJ
ap-4740	31	19	equation	equation	NOUN
ap-4740	31	20	(	(	PUNCT
ap-4740	31	21	t	t	NOUN
ap-4740	31	22	+	+	CCONJ
ap-4740	31	23	v	v	NOUN
ap-4740	31	24	)	)	PUNCT
ap-4740	31	25	ψ(x	ψ(x	NOUN
ap-4740	31	26	)	)	PUNCT
ap-4740	31	27	=	=	SYM
ap-4740	31	28	eψ(x	eψ(x	NOUN
ap-4740	31	29	)	)	PUNCT
ap-4740	31	30	,	,	PUNCT
ap-4740	31	31	where	where	SCONJ
ap-4740	31	32	the	the	DET
ap-4740	31	33	real	real	ADJ
ap-4740	31	34	variable	variable	NOUN
ap-4740	31	35	x	x	PUNCT
ap-4740	31	36	varies	vary	VERB
ap-4740	31	37	in	in	ADP
ap-4740	31	38	a	a	DET
ap-4740	31	39	given	give	VERB
ap-4740	31	40	domain	domain	NOUN
ap-4740	31	41	,	,	PUNCT
ap-4740	31	42	the	the	DET
ap-4740	31	43	potential	potential	ADJ
ap-4740	31	44	energy	energy	NOUN
ap-4740	31	45	v	v	NOUN
ap-4740	31	46	is	be	AUX
ap-4740	31	47	a	a	DET
ap-4740	31	48	function	function	NOUN
ap-4740	31	49	of	of	ADP
ap-4740	31	50	x	x	NOUN
ap-4740	31	51	,	,	PUNCT
ap-4740	31	52	and	and	CCONJ
ap-4740	31	53	the	the	DET
ap-4740	31	54	kinetic	kinetic	ADJ
ap-4740	31	55	energy	energy	NOUN
ap-4740	31	56	t	t	PROPN
ap-4740	31	57	depends	depend	VERB
ap-4740	31	58	on	on	ADP
ap-4740	31	59	d	d	PROPN
ap-4740	31	60	/	/	SYM
ap-4740	31	61	dx	dx	PROPN
ap-4740	31	62	(	(	PUNCT
ap-4740	31	63	and	and	CCONJ
ap-4740	31	64	possibly	possibly	ADV
ap-4740	31	65	on	on	ADP
ap-4740	31	66	x	x	SYM
ap-4740	31	67	whenever	whenever	SCONJ
ap-4740	31	68	the	the	DET
ap-4740	31	69	space	space	NOUN
ap-4740	31	70	is	be	AUX
ap-4740	31	71	curved	curve	VERB
ap-4740	31	72	or	or	CCONJ
ap-4740	31	73	the	the	DET
ap-4740	31	74	mass	mass	NOUN
ap-4740	31	75	depends	depend	VERB
ap-4740	31	76	on	on	ADP
ap-4740	31	77	the	the	DET
ap-4740	31	78	position	position	NOUN
ap-4740	31	79	[	[	X
ap-4740	31	80	20	20	NUM
ap-4740	31	81	]	]	NUM
ap-4740	31	82	)	)	PUNCT
ap-4740	31	83	,	,	PUNCT
ap-4740	31	84	and	and	CCONJ
ap-4740	31	85	on	on	ADP
ap-4740	31	86	making	make	VERB
ap-4740	31	87	an	an	DET
ap-4740	31	88	appropriate	appropriate	ADJ
ap-4740	31	89	gauge	gauge	NOUN
ap-4740	31	90	transformation	transformation	NOUN
ap-4740	31	91	and	and	CCONJ
ap-4740	31	92	a	a	DET
ap-4740	31	93	change	change	NOUN
ap-4740	31	94	of	of	ADP
ap-4740	31	95	variable	variable	NOUN
ap-4740	31	96	x	x	PUNCT
ap-4740	31	97	=	=	SYM
ap-4740	31	98	x(z	x(z	PROPN
ap-4740	31	99	)	)	PUNCT
ap-4740	31	100	,	,	PUNCT
ap-4740	31	101	one	one	PRON
ap-4740	31	102	may	may	AUX
ap-4740	31	103	arrive	arrive	VERB
ap-4740	31	104	at	at	ADP
ap-4740	31	105	a	a	DET
ap-4740	31	106	second	second	ADJ
ap-4740	31	107	-	-	PUNCT
ap-4740	31	108	order	order	NOUN
ap-4740	31	109	differential	differential	ADJ
ap-4740	31	110	equation	equation	NOUN
ap-4740	31	111	with	with	ADP
ap-4740	31	112	at	at	ADP
ap-4740	31	113	most	most	ADJ
ap-4740	31	114	k	k	NOUN
ap-4740	31	115	+	+	CCONJ
ap-4740	31	116	1	1	NUM
ap-4740	31	117	singular	singular	ADJ
ap-4740	31	118	points	point	NOUN
ap-4740	31	119	,	,	PUNCT
ap-4740	31	120	x(z)y′′(z	x(z)y′′(z	PROPN
ap-4740	31	121	)	)	PUNCT
ap-4740	32	1	+	+	CCONJ
ap-4740	32	2	y	y	PROPN
ap-4740	32	3	(	(	PUNCT
ap-4740	32	4	z)y′(z	z)y′(z	PROPN
ap-4740	32	5	)	)	PUNCT
ap-4740	32	6	+	+	NUM
ap-4740	32	7	z(z)y(z	z(z)y(z	NUM
ap-4740	32	8	)	)	PUNCT
ap-4740	32	9	=	=	SYM
ap-4740	32	10	0	0	NUM
ap-4740	32	11	,	,	PUNCT
ap-4740	32	12	(	(	PUNCT
ap-4740	32	13	2.1	2.1	NUM
ap-4740	32	14	)	)	PUNCT
ap-4740	32	15	where	where	SCONJ
ap-4740	32	16	x(z	x(z	PROPN
ap-4740	32	17	)	)	PUNCT
ap-4740	32	18	=	=	PRON
ap-4740	32	19	k∑	k∑	PROPN
ap-4740	32	20	l=0	l=0	PROPN
ap-4740	32	21	alz	alz	PROPN
ap-4740	32	22	l	l	PROPN
ap-4740	32	23	,	,	PUNCT
ap-4740	32	24	y	y	PROPN
ap-4740	32	25	(	(	PUNCT
ap-4740	32	26	z	z	NOUN
ap-4740	32	27	)	)	PUNCT
ap-4740	32	28	=	=	PRON
ap-4740	33	1	k−1∑	k−1∑	PROPN
ap-4740	33	2	l=0	l=0	PROPN
ap-4740	33	3	blz	blz	PROPN
ap-4740	33	4	l	l	PROPN
ap-4740	33	5	,	,	PUNCT
ap-4740	33	6	z(z	z(z	NOUN
ap-4740	33	7	)	)	PUNCT
ap-4740	33	8	=	=	PUNCT
ap-4740	33	9	k−2∑	k−2∑	PROPN
ap-4740	33	10	l=0	l=0	PROPN
ap-4740	33	11	clz	clz	NOUN
ap-4740	33	12	l	l	NOUN
ap-4740	33	13	,	,	PUNCT
ap-4740	33	14	(	(	PUNCT
ap-4740	33	15	2.2	2.2	NUM
ap-4740	33	16	)	)	PUNCT
ap-4740	33	17	and	and	CCONJ
ap-4740	33	18	al	al	PROPN
ap-4740	33	19	,	,	PUNCT
ap-4740	33	20	bl	bl	PROPN
ap-4740	33	21	,	,	PUNCT
ap-4740	33	22	cl	cl	NOUN
ap-4740	33	23	are	be	AUX
ap-4740	33	24	some	some	DET
ap-4740	33	25	(	(	PUNCT
ap-4740	33	26	real	real	ADJ
ap-4740	33	27	)	)	PUNCT
ap-4740	33	28	constants	constant	NOUN
ap-4740	33	29	.	.	PUNCT
ap-4740	34	1	polynomial	polynomial	ADJ
ap-4740	34	2	solutions	solution	NOUN
ap-4740	34	3	yn(z	yn(z	NOUN
ap-4740	34	4	)	)	PUNCT
ap-4740	34	5	of	of	ADP
ap-4740	34	6	this	this	DET
ap-4740	34	7	equation	equation	NOUN
ap-4740	34	8	will	will	AUX
ap-4740	34	9	yield	yield	VERB
ap-4740	34	10	exact	exact	ADJ
ap-4740	34	11	solutions	solution	NOUN
ap-4740	34	12	ψn(x	ψn(x	ADP
ap-4740	34	13	)	)	PUNCT
ap-4740	34	14	of	of	ADP
ap-4740	34	15	the	the	DET
ap-4740	34	16	starting	start	VERB
ap-4740	34	17	schrödinger	schrödinger	ADJ
ap-4740	34	18	equation	equation	NOUN
ap-4740	34	19	provided	provide	VERB
ap-4740	34	20	the	the	DET
ap-4740	34	21	latter	latter	ADJ
ap-4740	34	22	are	be	AUX
ap-4740	34	23	normalizable	normalizable	ADJ
ap-4740	34	24	.	.	PUNCT
ap-4740	35	1	on	on	ADP
ap-4740	35	2	deriving	derive	VERB
ap-4740	35	3	equation	equation	NOUN
ap-4740	35	4	(	(	PUNCT
ap-4740	35	5	2.1	2.1	NUM
ap-4740	35	6	)	)	PUNCT
ap-4740	35	7	k	k	NOUN
ap-4740	36	1	−	−	PROPN
ap-4740	36	2	2	2	NUM
ap-4740	36	3	times	time	NOUN
ap-4740	36	4	,	,	PUNCT
ap-4740	36	5	we	we	PRON
ap-4740	36	6	obtain	obtain	VERB
ap-4740	36	7	xy(k	xy(k	PUNCT
ap-4740	36	8	)	)	PUNCT
ap-4740	37	1	+	+	CCONJ
ap-4740	38	1	[	[	X
ap-4740	38	2	(	(	PUNCT
ap-4740	38	3	k	k	NOUN
ap-4740	38	4	−	−	PROPN
ap-4740	38	5	2	2	NUM
ap-4740	38	6	1	1	NUM
ap-4740	38	7	)	)	PUNCT
ap-4740	38	8	x	x	PUNCT
ap-4740	38	9	′	′	NUM
ap-4740	39	1	+	+	CCONJ
ap-4740	39	2	y	y	X
ap-4740	39	3	]	]	PUNCT
ap-4740	39	4	y(k−1	y(k−1	X
ap-4740	39	5	)	)	PUNCT
ap-4740	39	6	+	+	CCONJ
ap-4740	40	1	[	[	X
ap-4740	40	2	(	(	PUNCT
ap-4740	40	3	k	k	NOUN
ap-4740	40	4	−	−	PROPN
ap-4740	40	5	2	2	NUM
ap-4740	40	6	2	2	NUM
ap-4740	40	7	)	)	PUNCT
ap-4740	40	8	x	x	PUNCT
ap-4740	41	1	′′	′′	PROPN
ap-4740	41	2	+	+	CCONJ
ap-4740	41	3	(	(	PUNCT
ap-4740	41	4	k	k	NOUN
ap-4740	41	5	−	−	PROPN
ap-4740	41	6	2	2	NUM
ap-4740	41	7	1	1	NUM
ap-4740	41	8	)	)	PUNCT
ap-4740	41	9	y	y	NOUN
ap-4740	42	1	′	′	VERB
ap-4740	43	1	+	+	CCONJ
ap-4740	43	2	z	z	X
ap-4740	43	3	]	]	PUNCT
ap-4740	43	4	y(k−2	y(k−2	PROPN
ap-4740	43	5	)	)	PUNCT
ap-4740	44	1	+	+	CCONJ
ap-4740	44	2	·	·	PUNCT
ap-4740	44	3	·	·	PUNCT
ap-4740	44	4	·	·	PUNCT
ap-4740	45	1	+	+	PUNCT
ap-4740	45	2	[	[	PUNCT
ap-4740	45	3	x(k−2	x(k−2	PROPN
ap-4740	45	4	)	)	PUNCT
ap-4740	45	5	+	+	CCONJ
ap-4740	45	6	(	(	PUNCT
ap-4740	45	7	k	k	X
ap-4740	45	8	−	−	PROPN
ap-4740	45	9	2	2	NUM
ap-4740	45	10	1	1	NUM
ap-4740	45	11	)	)	PUNCT
ap-4740	45	12	y	y	PROPN
ap-4740	45	13	(	(	PUNCT
ap-4740	45	14	k−3	k−3	PROPN
ap-4740	45	15	)	)	PUNCT
ap-4740	46	1	+	+	CCONJ
ap-4740	46	2	(	(	PUNCT
ap-4740	46	3	k	k	X
ap-4740	46	4	−	−	PROPN
ap-4740	46	5	2	2	NUM
ap-4740	46	6	2	2	NUM
ap-4740	46	7	)	)	PUNCT
ap-4740	46	8	z(k−4	z(k−4	NOUN
ap-4740	46	9	)	)	PUNCT
ap-4740	46	10	]	]	PUNCT
ap-4740	47	1	y′′	y′′	PROPN
ap-4740	47	2	+	+	CCONJ
ap-4740	47	3	[	[	PUNCT
ap-4740	47	4	y	y	PROPN
ap-4740	47	5	(	(	PUNCT
ap-4740	47	6	k−2	k−2	PROPN
ap-4740	47	7	)	)	PUNCT
ap-4740	47	8	+	+	CCONJ
ap-4740	47	9	(	(	PUNCT
ap-4740	47	10	k	k	X
ap-4740	47	11	−	−	PROPN
ap-4740	47	12	2	2	NUM
ap-4740	47	13	1	1	NUM
ap-4740	47	14	)	)	PUNCT
ap-4740	47	15	z(k−3	z(k−3	PROPN
ap-4740	47	16	)	)	PUNCT
ap-4740	47	17	]	]	PUNCT
ap-4740	47	18	y′	y′	X
ap-4740	48	1	+	+	CCONJ
ap-4740	48	2	z(k−2)y	z(k−2)y	X
ap-4740	48	3	=	=	SYM
ap-4740	48	4	0	0	PROPN
ap-4740	48	5	,	,	PUNCT
ap-4740	48	6	(	(	PUNCT
ap-4740	48	7	2.3	2.3	NUM
ap-4740	48	8	)	)	PUNCT
ap-4740	48	9	which	which	PRON
ap-4740	48	10	is	be	AUX
ap-4740	48	11	a	a	DET
ap-4740	48	12	kth	kth	NOUN
ap-4740	48	13	-	-	PUNCT
ap-4740	48	14	order	order	NOUN
ap-4740	48	15	homogeneous	homogeneous	ADJ
ap-4740	48	16	differential	differential	ADJ
ap-4740	48	17	equation	equation	NOUN
ap-4740	48	18	with	with	ADP
ap-4740	48	19	polynomial	polynomial	ADJ
ap-4740	48	20	coefficients	coefficient	NOUN
ap-4740	48	21	of	of	ADP
ap-4740	48	22	degree	degree	NOUN
ap-4740	48	23	not	not	PART
ap-4740	48	24	exceeding	exceed	VERB
ap-4740	48	25	the	the	DET
ap-4740	48	26	corresponding	corresponding	ADJ
ap-4740	48	27	order	order	NOUN
ap-4740	48	28	of	of	ADP
ap-4740	48	29	differentiation	differentiation	NOUN
ap-4740	48	30	.	.	PUNCT
ap-4740	49	1	since	since	SCONJ
ap-4740	49	2	all	all	DET
ap-4740	49	3	its	its	PRON
ap-4740	49	4	derivatives	derivative	NOUN
ap-4740	49	5	will	will	AUX
ap-4740	49	6	have	have	VERB
ap-4740	49	7	the	the	DET
ap-4740	49	8	same	same	ADJ
ap-4740	49	9	property	property	NOUN
ap-4740	49	10	,	,	PUNCT
ap-4740	49	11	it	it	PRON
ap-4740	49	12	can	can	AUX
ap-4740	49	13	be	be	AUX
ap-4740	49	14	differentiated	differentiate	VERB
ap-4740	49	15	n	n	DET
ap-4740	49	16	times	time	NOUN
ap-4740	49	17	by	by	ADP
ap-4740	49	18	using	use	VERB
ap-4740	49	19	the	the	DET
ap-4740	49	20	new	new	ADJ
ap-4740	49	21	representation	representation	NOUN
ap-4740	49	22	y(n)(z	y(n)(z	NOUN
ap-4740	49	23	)	)	PUNCT
ap-4740	49	24	=	=	NOUN
ap-4740	49	25	vn(z	vn(z	NOUN
ap-4740	49	26	)	)	PUNCT
ap-4740	49	27	.	.	PUNCT
ap-4740	50	1	in	in	ADP
ap-4740	50	2	such	such	DET
ap-4740	50	3	a	a	DET
ap-4740	50	4	notation	notation	NOUN
ap-4740	50	5	,	,	PUNCT
ap-4740	50	6	equation	equation	NOUN
ap-4740	50	7	(	(	PUNCT
ap-4740	50	8	2.3	2.3	NUM
ap-4740	50	9	)	)	PUNCT
ap-4740	50	10	can	can	AUX
ap-4740	50	11	be	be	AUX
ap-4740	50	12	written	write	VERB
ap-4740	50	13	as	as	ADP
ap-4740	50	14	xv	xv	PROPN
ap-4740	50	15	(	(	PUNCT
ap-4740	50	16	k	k	NOUN
ap-4740	50	17	)	)	PUNCT
ap-4740	50	18	0	0	PUNCT
ap-4740	51	1	+	+	CCONJ
ap-4740	51	2	[	[	X
ap-4740	51	3	(	(	PUNCT
ap-4740	51	4	k	k	NOUN
ap-4740	51	5	−	−	PROPN
ap-4740	51	6	2	2	NUM
ap-4740	51	7	1	1	NUM
ap-4740	51	8	)	)	PUNCT
ap-4740	51	9	x	x	PUNCT
ap-4740	52	1	′	′	NUM
ap-4740	53	1	+	+	CCONJ
ap-4740	53	2	y	y	X
ap-4740	53	3	]	]	X
ap-4740	53	4	v	v	PROPN
ap-4740	53	5	(	(	PUNCT
ap-4740	53	6	k−1	k−1	PROPN
ap-4740	53	7	)	)	PUNCT
ap-4740	53	8	0	0	PUNCT
ap-4740	54	1	+	+	CCONJ
ap-4740	55	1	[	[	X
ap-4740	55	2	(	(	PUNCT
ap-4740	55	3	k	k	NOUN
ap-4740	55	4	−	−	PROPN
ap-4740	55	5	2	2	NUM
ap-4740	55	6	2	2	NUM
ap-4740	55	7	)	)	PUNCT
ap-4740	55	8	x	x	PUNCT
ap-4740	56	1	′′	′′	PROPN
ap-4740	56	2	+	+	CCONJ
ap-4740	56	3	(	(	PUNCT
ap-4740	56	4	k	k	NOUN
ap-4740	56	5	−	−	PROPN
ap-4740	56	6	2	2	NUM
ap-4740	56	7	1	1	NUM
ap-4740	56	8	)	)	PUNCT
ap-4740	56	9	y	y	NOUN
ap-4740	57	1	′	′	VERB
ap-4740	58	1	+	+	CCONJ
ap-4740	58	2	z	z	X
ap-4740	58	3	]	]	X
ap-4740	58	4	v	v	X
ap-4740	58	5	(	(	PUNCT
ap-4740	58	6	k−2	k−2	PROPN
ap-4740	58	7	)	)	PUNCT
ap-4740	58	8	0	0	PUNCT
ap-4740	59	1	+	+	CCONJ
ap-4740	59	2	·	·	PUNCT
ap-4740	59	3	·	·	PUNCT
ap-4740	59	4	·	·	PUNCT
ap-4740	60	1	+	+	PUNCT
ap-4740	60	2	[	[	PUNCT
ap-4740	60	3	x(k−2	x(k−2	PROPN
ap-4740	60	4	)	)	PUNCT
ap-4740	60	5	+	+	CCONJ
ap-4740	60	6	(	(	PUNCT
ap-4740	60	7	k	k	X
ap-4740	60	8	−	−	PROPN
ap-4740	60	9	2	2	NUM
ap-4740	60	10	1	1	NUM
ap-4740	60	11	)	)	PUNCT
ap-4740	60	12	y	y	PROPN
ap-4740	60	13	(	(	PUNCT
ap-4740	60	14	k−3	k−3	PROPN
ap-4740	60	15	)	)	PUNCT
ap-4740	61	1	+	+	CCONJ
ap-4740	61	2	(	(	PUNCT
ap-4740	61	3	k	k	X
ap-4740	61	4	−	−	PROPN
ap-4740	61	5	2	2	NUM
ap-4740	61	6	2	2	NUM
ap-4740	61	7	)	)	PUNCT
ap-4740	61	8	z(k−4	z(k−4	NOUN
ap-4740	61	9	)	)	PUNCT
ap-4740	61	10	]	]	PUNCT
ap-4740	62	1	v′′0	v′′0	PUNCT
ap-4740	63	1	+	+	PUNCT
ap-4740	63	2	[	[	PUNCT
ap-4740	63	3	y	y	PROPN
ap-4740	63	4	(	(	PUNCT
ap-4740	63	5	k−2	k−2	PROPN
ap-4740	63	6	)	)	PUNCT
ap-4740	64	1	+	+	CCONJ
ap-4740	64	2	(	(	PUNCT
ap-4740	64	3	k	k	X
ap-4740	64	4	−	−	PROPN
ap-4740	64	5	2	2	NUM
ap-4740	64	6	1	1	NUM
ap-4740	64	7	)	)	PUNCT
ap-4740	64	8	z(k−3	z(k−3	PROPN
ap-4740	64	9	)	)	PUNCT
ap-4740	64	10	]	]	PUNCT
ap-4740	65	1	v′0	v′0	NOUN
ap-4740	66	1	+	+	CCONJ
ap-4740	66	2	z(k−2)v0	z(k−2)v0	X
ap-4740	66	3	=	=	SYM
ap-4740	66	4	0	0	PROPN
ap-4740	66	5	.	.	PUNCT
ap-4740	67	1	(	(	PUNCT
ap-4740	67	2	2.4	2.4	NUM
ap-4740	67	3	)	)	PUNCT
ap-4740	67	4	its	its	PRON
ap-4740	67	5	nth	nth	NOUN
ap-4740	67	6	derivative	derivative	NOUN
ap-4740	67	7	can	can	AUX
ap-4740	67	8	be	be	AUX
ap-4740	67	9	easily	easily	ADV
ap-4740	67	10	shown	show	VERB
ap-4740	67	11	to	to	PART
ap-4740	67	12	be	be	AUX
ap-4740	67	13	given	give	VERB
ap-4740	67	14	by	by	ADP
ap-4740	67	15	k∑	k∑	ADJ
ap-4740	67	16	l=0	l=0	PROPN
ap-4740	67	17	(	(	PUNCT
ap-4740	67	18	n+	n+	NUM
ap-4740	67	19	k	k	NOUN
ap-4740	68	1	−	−	PROPN
ap-4740	68	2	2	2	NUM
ap-4740	68	3	k	k	NOUN
ap-4740	68	4	−	−	PROPN
ap-4740	68	5	l	l	NOUN
ap-4740	68	6	)	)	PUNCT
ap-4740	68	7	x(k−l)v(l	x(k−l)v(l	NOUN
ap-4740	68	8	)	)	PUNCT
ap-4740	68	9	n	n	PROPN
ap-4740	68	10	+	+	CCONJ
ap-4740	68	11	k−1∑	k−1∑	PROPN
ap-4740	68	12	l=0	l=0	PROPN
ap-4740	68	13	(	(	PUNCT
ap-4740	68	14	n+	n+	NUM
ap-4740	68	15	k	k	NOUN
ap-4740	68	16	−	−	PROPN
ap-4740	68	17	2	2	NUM
ap-4740	68	18	k	k	NOUN
ap-4740	68	19	−	−	PROPN
ap-4740	68	20	l	l	NOUN
ap-4740	68	21	−	−	NOUN
ap-4740	68	22	1	1	X
ap-4740	68	23	)	)	PUNCT
ap-4740	68	24	y	y	PROPN
ap-4740	68	25	(	(	PUNCT
ap-4740	68	26	k−l−1)v(l	k−l−1)v(l	PROPN
ap-4740	68	27	)	)	PUNCT
ap-4740	68	28	n	n	NOUN
ap-4740	68	29	+	+	CCONJ
ap-4740	68	30	k−2∑	k−2∑	PROPN
ap-4740	68	31	l=0	l=0	PROPN
ap-4740	68	32	(	(	PUNCT
ap-4740	68	33	n+	n+	NUM
ap-4740	68	34	k	k	NOUN
ap-4740	68	35	−	−	PROPN
ap-4740	68	36	2	2	NUM
ap-4740	68	37	k	k	NOUN
ap-4740	68	38	−	−	PROPN
ap-4740	68	39	l	l	NOUN
ap-4740	68	40	−	−	PROPN
ap-4740	68	41	2	2	NUM
ap-4740	68	42	)	)	PUNCT
ap-4740	68	43	z(k−l−2)v(l	z(k−l−2)v(l	NUM
ap-4740	68	44	)	)	PUNCT
ap-4740	68	45	n	n	NOUN
ap-4740	68	46	=	=	SYM
ap-4740	68	47	0	0	PROPN
ap-4740	68	48	.	.	PUNCT
ap-4740	68	49	(	(	PUNCT
ap-4740	68	50	2.5	2.5	NUM
ap-4740	68	51	)	)	PUNCT
ap-4740	68	52	when	when	SCONJ
ap-4740	68	53	the	the	DET
ap-4740	68	54	coefficient	coefficient	NOUN
ap-4740	68	55	of	of	ADP
ap-4740	68	56	vn	vn	PROPN
ap-4740	68	57	in	in	ADP
ap-4740	68	58	(	(	PUNCT
ap-4740	68	59	2.5	2.5	NUM
ap-4740	68	60	)	)	PUNCT
ap-4740	68	61	is	be	AUX
ap-4740	68	62	equal	equal	ADJ
ap-4740	68	63	to	to	ADP
ap-4740	68	64	zero	zero	NUM
ap-4740	68	65	,	,	PUNCT
ap-4740	68	66	i.e.	i.e.	X
ap-4740	68	67	,	,	PUNCT
ap-4740	68	68	(	(	PUNCT
ap-4740	68	69	n+	n+	X
ap-4740	68	70	k	k	NOUN
ap-4740	69	1	−	−	PROPN
ap-4740	69	2	2	2	NUM
ap-4740	69	3	k	k	NOUN
ap-4740	69	4	)	)	PUNCT
ap-4740	69	5	x(k	x(k	PROPN
ap-4740	69	6	)	)	PUNCT
ap-4740	70	1	+	+	CCONJ
ap-4740	70	2	(	(	PUNCT
ap-4740	70	3	n+	n+	NUM
ap-4740	70	4	k	k	NOUN
ap-4740	71	1	−	−	PROPN
ap-4740	72	1	2	2	NUM
ap-4740	73	1	k	k	NOUN
ap-4740	73	2	−	−	PROPN
ap-4740	73	3	1	1	X
ap-4740	73	4	)	)	PUNCT
ap-4740	73	5	y	y	PROPN
ap-4740	73	6	(	(	PUNCT
ap-4740	73	7	k−1	k−1	PROPN
ap-4740	73	8	)	)	PUNCT
ap-4740	74	1	+	+	CCONJ
ap-4740	74	2	(	(	PUNCT
ap-4740	74	3	n+	n+	NUM
ap-4740	74	4	k	k	NOUN
ap-4740	75	1	−	−	PROPN
ap-4740	76	1	2	2	NUM
ap-4740	77	1	k	k	NOUN
ap-4740	77	2	−	−	PROPN
ap-4740	77	3	2	2	X
ap-4740	77	4	)	)	PUNCT
ap-4740	77	5	z(k−2	z(k−2	NOUN
ap-4740	77	6	)	)	PUNCT
ap-4740	77	7	=	=	SYM
ap-4740	77	8	0	0	NUM
ap-4740	77	9	,	,	PUNCT
ap-4740	77	10	(	(	PUNCT
ap-4740	77	11	2.6	2.6	NUM
ap-4740	77	12	)	)	PUNCT
ap-4740	77	13	there	there	ADV
ap-4740	77	14	only	only	ADV
ap-4740	77	15	remains	remain	VERB
ap-4740	77	16	derivatives	derivative	NOUN
ap-4740	77	17	of	of	ADP
ap-4740	77	18	vn	vn	NOUN
ap-4740	77	19	in	in	ADP
ap-4740	77	20	the	the	DET
ap-4740	77	21	equation	equation	NOUN
ap-4740	77	22	.	.	PUNCT
ap-4740	78	1	it	it	PRON
ap-4740	78	2	is	be	AUX
ap-4740	78	3	then	then	ADV
ap-4740	78	4	obvious	obvious	ADJ
ap-4740	78	5	that	that	SCONJ
ap-4740	78	6	the	the	DET
ap-4740	78	7	latter	latter	NOUN
ap-4740	78	8	has	have	VERB
ap-4740	78	9	a	a	DET
ap-4740	78	10	particular	particular	ADJ
ap-4740	78	11	solution	solution	NOUN
ap-4740	78	12	for	for	ADP
ap-4740	78	13	which	which	PRON
ap-4740	78	14	vn	vn	PROPN
ap-4740	78	15	=	=	SYM
ap-4740	78	16	y(n	y(n	PROPN
ap-4740	78	17	)	)	PUNCT
ap-4740	78	18	is	be	AUX
ap-4740	78	19	a	a	DET
ap-4740	78	20	constant	constant	ADJ
ap-4740	78	21	or	or	CCONJ
ap-4740	78	22	,	,	PUNCT
ap-4740	78	23	in	in	ADP
ap-4740	78	24	other	other	ADJ
ap-4740	78	25	words	word	NOUN
ap-4740	78	26	,	,	PUNCT
ap-4740	78	27	there	there	PRON
ap-4740	78	28	exists	exist	VERB
ap-4740	78	29	a	a	DET
ap-4740	78	30	particular	particular	ADJ
ap-4740	78	31	solution	solution	NOUN
ap-4740	78	32	y(z	y(z	NOUN
ap-4740	78	33	)	)	PUNCT
ap-4740	78	34	=	=	SYM
ap-4740	79	1	yn(z	yn(z	NOUN
ap-4740	79	2	)	)	PUNCT
ap-4740	79	3	of	of	ADP
ap-4740	79	4	equation	equation	NOUN
ap-4740	79	5	(	(	PUNCT
ap-4740	79	6	2.1	2.1	NUM
ap-4740	79	7	)	)	PUNCT
ap-4740	79	8	that	that	PRON
ap-4740	79	9	is	be	AUX
ap-4740	79	10	a	a	DET
ap-4740	79	11	polynomial	polynomial	ADJ
ap-4740	79	12	of	of	ADP
ap-4740	79	13	degree	degree	NOUN
ap-4740	79	14	n.	n.	NOUN
ap-4740	79	15	on	on	ADP
ap-4740	79	16	integrating	integrate	VERB
ap-4740	79	17	equation	equation	NOUN
ap-4740	79	18	(	(	PUNCT
ap-4740	79	19	2.6	2.6	NUM
ap-4740	79	20	)	)	PUNCT
ap-4740	80	1	k	k	NOUN
ap-4740	80	2	−	−	PROPN
ap-4740	80	3	2	2	NUM
ap-4740	80	4	times	time	NOUN
ap-4740	80	5	,	,	PUNCT
ap-4740	80	6	we	we	PRON
ap-4740	80	7	find	find	VERB
ap-4740	80	8	that	that	SCONJ
ap-4740	80	9	this	this	PRON
ap-4740	80	10	occurs	occur	VERB
ap-4740	80	11	whenever	whenever	SCONJ
ap-4740	80	12	z(z	z(z	VERB
ap-4740	80	13	)	)	PUNCT
ap-4740	80	14	=	=	SYM
ap-4740	81	1	zn(z	zn(z	NOUN
ap-4740	81	2	)	)	PUNCT
ap-4740	81	3	is	be	AUX
ap-4740	81	4	given	give	VERB
ap-4740	81	5	by	by	ADP
ap-4740	81	6	zn(z	zn(z	NOUN
ap-4740	81	7	)	)	PUNCT
ap-4740	81	8	=	=	PUNCT
ap-4740	81	9	−n(n−	−n(n−	VERB
ap-4740	81	10	1	1	X
ap-4740	81	11	)	)	PUNCT
ap-4740	81	12	k(k	k(k	ADV
ap-4740	81	13	−	−	PROPN
ap-4740	81	14	1)x	1)x	NUM
ap-4740	81	15	′′(z)−	′′(z)−	PROPN
ap-4740	81	16	n	n	CCONJ
ap-4740	81	17	k	k	PROPN
ap-4740	81	18	−	−	PROPN
ap-4740	81	19	1y	1y	NUM
ap-4740	81	20	′(z	′(z	NOUN
ap-4740	81	21	)	)	PUNCT
ap-4740	82	1	+	+	NUM
ap-4740	82	2	k−3∑	k−3∑	X
ap-4740	82	3	l=0	l=0	PROPN
ap-4740	82	4	ck−l−2,n	ck−l−2,n	VERB
ap-4740	83	1	zl	zl	X
ap-4740	83	2	l	l	NOUN
ap-4740	83	3	!	!	PUNCT
ap-4740	84	1	,	,	PUNCT
ap-4740	84	2	(	(	PUNCT
ap-4740	84	3	2.7	2.7	NUM
ap-4740	84	4	)	)	PUNCT
ap-4740	84	5	where	where	SCONJ
ap-4740	84	6	c1,n	c1,n	PROPN
ap-4740	84	7	,	,	PUNCT
ap-4740	84	8	c2,n	c2,n	PROPN
ap-4740	84	9	,	,	PUNCT
ap-4740	84	10	.	.	PUNCT
ap-4740	84	11	.	.	PUNCT
ap-4740	84	12	.	.	PUNCT
ap-4740	85	1	,	,	PUNCT
ap-4740	85	2	ck−2,n	ck−2,n	X
ap-4740	85	3	are	be	AUX
ap-4740	85	4	k	k	NOUN
ap-4740	85	5	−	−	NUM
ap-4740	85	6	2	2	NUM
ap-4740	85	7	integration	integration	NOUN
ap-4740	85	8	constants	constant	NOUN
ap-4740	85	9	.	.	PUNCT
ap-4740	86	1	this	this	PRON
ap-4740	86	2	is	be	AUX
ap-4740	86	3	the	the	DET
ap-4740	86	4	first	first	ADJ
ap-4740	86	5	main	main	ADJ
ap-4740	86	6	result	result	NOUN
ap-4740	86	7	of	of	ADP
ap-4740	86	8	this	this	DET
ap-4740	86	9	paper	paper	NOUN
ap-4740	86	10	.	.	PUNCT
ap-4740	87	1	it	it	PRON
ap-4740	87	2	is	be	AUX
ap-4740	87	3	worth	worth	ADJ
ap-4740	87	4	observing	observe	VERB
ap-4740	87	5	that	that	SCONJ
ap-4740	87	6	in	in	ADP
ap-4740	87	7	the	the	DET
ap-4740	87	8	hypergeometric	hypergeometric	ADJ
ap-4740	87	9	case	case	NOUN
ap-4740	87	10	,	,	PUNCT
ap-4740	87	11	we	we	PRON
ap-4740	87	12	have	have	VERB
ap-4740	87	13	k	k	NOUN
ap-4740	87	14	=	=	SYM
ap-4740	87	15	2	2	NUM
ap-4740	87	16	so	so	SCONJ
ap-4740	87	17	that	that	SCONJ
ap-4740	87	18	the	the	DET
ap-4740	87	19	polynomial	polynomial	ADJ
ap-4740	87	20	z(z	z(z	NOUN
ap-4740	87	21	)	)	PUNCT
ap-4740	87	22	reduces	reduce	VERB
ap-4740	87	23	to	to	ADP
ap-4740	87	24	a	a	DET
ap-4740	87	25	constant	constant	ADJ
ap-4740	87	26	λ	λ	NOUN
ap-4740	87	27	.	.	PUNCT
ap-4740	88	1	then	then	ADV
ap-4740	88	2	λ	λ	X
ap-4740	88	3	=	=	SYM
ap-4740	88	4	λn	λn	PROPN
ap-4740	88	5	,	,	PUNCT
ap-4740	88	6	where	where	SCONJ
ap-4740	88	7	,	,	PUNCT
ap-4740	88	8	in	in	ADP
ap-4740	88	9	accordance	accordance	NOUN
ap-4740	88	10	with	with	ADP
ap-4740	88	11	equation	equation	NOUN
ap-4740	88	12	(	(	PUNCT
ap-4740	88	13	2.7	2.7	NUM
ap-4740	88	14	)	)	PUNCT
ap-4740	88	15	,	,	PUNCT
ap-4740	88	16	λn	λn	NOUN
ap-4740	88	17	=	=	SYM
ap-4740	88	18	−	−	PROPN
ap-4740	88	19	1	1	NUM
ap-4740	88	20	2n(n−	2n(n−	NUM
ap-4740	88	21	1)x	1)x	NUM
ap-4740	88	22	′′(z)−	′′(z)−	PROPN
ap-4740	88	23	ny	ny	PROPN
ap-4740	88	24	′(z	′(z	NOUN
ap-4740	88	25	)	)	PUNCT
ap-4740	88	26	,	,	PUNCT
ap-4740	88	27	(	(	PUNCT
ap-4740	88	28	2.8	2.8	NUM
ap-4740	88	29	)	)	PUNCT
ap-4740	88	30	119	119	NUM
ap-4740	88	31	christiane	christiane	NOUN
ap-4740	88	32	quesne	quesne	NOUN
ap-4740	88	33	acta	acta	PROPN
ap-4740	88	34	polytechnica	polytechnica	PROPN
ap-4740	88	35	with	with	ADP
ap-4740	88	36	no	no	DET
ap-4740	88	37	integration	integration	NOUN
ap-4740	88	38	constant	constant	ADJ
ap-4740	88	39	,	,	PUNCT
ap-4740	88	40	which	which	PRON
ap-4740	88	41	is	be	AUX
ap-4740	88	42	a	a	DET
ap-4740	88	43	well	well	ADV
ap-4740	88	44	-	-	PUNCT
ap-4740	88	45	known	know	VERB
ap-4740	88	46	result	result	NOUN
ap-4740	89	1	[	[	X
ap-4740	89	2	3	3	NUM
ap-4740	89	3	]	]	PUNCT
ap-4740	89	4	.	.	PUNCT
ap-4740	90	1	in	in	ADP
ap-4740	90	2	the	the	DET
ap-4740	90	3	heun	heun	NOUN
ap-4740	90	4	-	-	PUNCT
ap-4740	90	5	type	type	NOUN
ap-4740	90	6	equation	equation	NOUN
ap-4740	90	7	case	case	NOUN
ap-4740	90	8	,	,	PUNCT
ap-4740	90	9	we	we	PRON
ap-4740	90	10	have	have	VERB
ap-4740	90	11	k	k	NOUN
ap-4740	90	12	=	=	SYM
ap-4740	90	13	3	3	NUM
ap-4740	90	14	and	and	CCONJ
ap-4740	90	15	the	the	DET
ap-4740	90	16	linear	linear	ADJ
ap-4740	90	17	polynomial	polynomial	ADJ
ap-4740	90	18	z(z	z(z	NOUN
ap-4740	90	19	)	)	PUNCT
ap-4740	90	20	=	=	SYM
ap-4740	90	21	zn(z	zn(z	NOUN
ap-4740	90	22	)	)	PUNCT
ap-4740	90	23	is	be	AUX
ap-4740	90	24	given	give	VERB
ap-4740	90	25	by	by	ADP
ap-4740	90	26	zn(z	zn(z	NOUN
ap-4740	90	27	)	)	PUNCT
ap-4740	90	28	=	=	PUNCT
ap-4740	91	1	−	−	PROPN
ap-4740	91	2	1	1	NUM
ap-4740	91	3	6n(n−	6n(n−	NUM
ap-4740	91	4	1)x	1)x	NUM
ap-4740	91	5	′′(z)−	′′(z)−	PROPN
ap-4740	91	6	1	1	NUM
ap-4740	91	7	2ny	2ny	ADJ
ap-4740	91	8	′(z	′(z	NOUN
ap-4740	91	9	)	)	PUNCT
ap-4740	92	1	+	+	CCONJ
ap-4740	92	2	cn	cn	X
ap-4740	92	3	(	(	PUNCT
ap-4740	92	4	2.9	2.9	NUM
ap-4740	92	5	)	)	PUNCT
ap-4740	92	6	in	in	ADP
ap-4740	92	7	terms	term	NOUN
ap-4740	92	8	of	of	ADP
ap-4740	92	9	a	a	DET
ap-4740	92	10	single	single	ADJ
ap-4740	92	11	integration	integration	NOUN
ap-4740	92	12	constant	constant	ADJ
ap-4740	92	13	cn	cn	PROPN
ap-4740	92	14	,	,	PUNCT
ap-4740	92	15	which	which	PRON
ap-4740	92	16	is	be	AUX
ap-4740	92	17	a	a	DET
ap-4740	92	18	result	result	NOUN
ap-4740	92	19	previously	previously	ADV
ap-4740	92	20	derived	derive	VERB
ap-4740	92	21	by	by	ADP
ap-4740	92	22	karayer	karayer	NOUN
ap-4740	92	23	,	,	PUNCT
ap-4740	92	24	demirhan	demirhan	ADV
ap-4740	92	25	,	,	PUNCT
ap-4740	92	26	and	and	CCONJ
ap-4740	92	27	büyükkılıç	büyükkılıç	NOUN
ap-4740	92	28	[	[	X
ap-4740	92	29	21	21	NUM
ap-4740	92	30	]	]	PUNCT
ap-4740	92	31	.	.	PUNCT
ap-4740	93	1	on	on	ADP
ap-4740	93	2	inserting	insert	VERB
ap-4740	93	3	now	now	ADV
ap-4740	93	4	equation	equation	NOUN
ap-4740	93	5	(	(	PUNCT
ap-4740	93	6	2.2	2.2	NUM
ap-4740	93	7	)	)	PUNCT
ap-4740	93	8	in	in	ADP
ap-4740	93	9	(	(	PUNCT
ap-4740	93	10	2.7	2.7	NUM
ap-4740	93	11	)	)	PUNCT
ap-4740	93	12	and	and	CCONJ
ap-4740	93	13	equating	equate	VERB
ap-4740	93	14	the	the	DET
ap-4740	93	15	coefficients	coefficient	NOUN
ap-4740	93	16	of	of	ADP
ap-4740	93	17	equal	equal	ADJ
ap-4740	93	18	powers	power	NOUN
ap-4740	93	19	of	of	ADP
ap-4740	93	20	z	z	NOUN
ap-4740	93	21	on	on	ADP
ap-4740	93	22	both	both	DET
ap-4740	93	23	sides	side	NOUN
ap-4740	93	24	,	,	PUNCT
ap-4740	93	25	we	we	PRON
ap-4740	93	26	obtain	obtain	VERB
ap-4740	93	27	the	the	DET
ap-4740	93	28	set	set	NOUN
ap-4740	93	29	of	of	ADP
ap-4740	93	30	relations	relation	NOUN
ap-4740	93	31	ck−2	ck−2	NOUN
ap-4740	94	1	=	=	PUNCT
ap-4740	95	1	−n(n−	−n(n−	X
ap-4740	96	1	1)ak	1)ak	NUM
ap-4740	97	1	−	−	ADP
ap-4740	97	2	nbk−1	nbk−1	NOUN
ap-4740	97	3	,	,	PUNCT
ap-4740	97	4	(	(	PUNCT
ap-4740	97	5	2.10	2.10	NUM
ap-4740	97	6	)	)	PUNCT
ap-4740	97	7	cl	cl	NOUN
ap-4740	97	8	=	=	SYM
ap-4740	97	9	−n(n−	−n(n−	NOUN
ap-4740	97	10	1	1	X
ap-4740	97	11	)	)	PUNCT
ap-4740	97	12	k(k	k(k	NOUN
ap-4740	97	13	−	−	NOUN
ap-4740	97	14	1	1	NUM
ap-4740	97	15	)	)	PUNCT
ap-4740	97	16	(	(	PUNCT
ap-4740	97	17	l	l	NOUN
ap-4740	97	18	+	+	X
ap-4740	97	19	2)(l	2)(l	NUM
ap-4740	97	20	+	+	CCONJ
ap-4740	97	21	1)al+2	1)al+2	NUM
ap-4740	97	22	−	−	NOUN
ap-4740	97	23	n	n	CCONJ
ap-4740	97	24	k	k	NOUN
ap-4740	97	25	−	−	PROPN
ap-4740	97	26	1(l	1(l	NUM
ap-4740	97	27	+	+	CCONJ
ap-4740	97	28	1)bl+1	1)bl+1	PROPN
ap-4740	97	29	+	+	CCONJ
ap-4740	97	30	ck−l−2,n	ck−l−2,n	PROPN
ap-4740	97	31	l	l	NOUN
ap-4740	97	32	!	!	PUNCT
ap-4740	97	33	,	,	PUNCT
ap-4740	97	34	l	l	NOUN
ap-4740	97	35	=	=	SYM
ap-4740	97	36	0	0	NUM
ap-4740	97	37	,	,	PUNCT
ap-4740	97	38	1	1	NUM
ap-4740	97	39	,	,	PUNCT
ap-4740	97	40	.	.	PUNCT
ap-4740	97	41	.	.	PUNCT
ap-4740	97	42	.	.	PUNCT
ap-4740	98	1	,	,	PUNCT
ap-4740	99	1	k	k	PROPN
ap-4740	99	2	−	−	NOUN
ap-4740	100	1	3	3	X
ap-4740	100	2	.	.	PUNCT
ap-4740	100	3	(	(	PUNCT
ap-4740	100	4	2.11	2.11	NUM
ap-4740	100	5	)	)	PUNCT
ap-4740	100	6	the	the	DET
ap-4740	100	7	nth	nth	NOUN
ap-4740	100	8	-	-	PUNCT
ap-4740	100	9	degree	degree	NOUN
ap-4740	100	10	polynomial	polynomial	ADJ
ap-4740	100	11	solutions	solution	NOUN
ap-4740	100	12	yn(z	yn(z	NOUN
ap-4740	100	13	)	)	PUNCT
ap-4740	100	14	of	of	ADP
ap-4740	100	15	equation	equation	NOUN
ap-4740	100	16	(	(	PUNCT
ap-4740	100	17	2.1	2.1	NUM
ap-4740	100	18	)	)	PUNCT
ap-4740	100	19	can	can	AUX
ap-4740	100	20	be	be	AUX
ap-4740	100	21	written	write	VERB
ap-4740	100	22	as	as	ADP
ap-4740	100	23	yn(z	yn(z	NOUN
ap-4740	100	24	)	)	PUNCT
ap-4740	100	25	=	=	PUNCT
ap-4740	100	26	n∏	n∏	PROPN
ap-4740	100	27	i=1	i=1	PROPN
ap-4740	100	28	(	(	PUNCT
ap-4740	100	29	z	z	NOUN
ap-4740	100	30	−	−	PROPN
ap-4740	100	31	zi	zi	PROPN
ap-4740	100	32	)	)	PUNCT
ap-4740	100	33	,	,	PUNCT
ap-4740	100	34	(	(	PUNCT
ap-4740	100	35	2.12	2.12	NUM
ap-4740	100	36	)	)	PUNCT
ap-4740	100	37	where	where	SCONJ
ap-4740	100	38	from	from	ADP
ap-4740	100	39	now	now	ADV
ap-4740	100	40	on	on	ADV
ap-4740	100	41	we	we	PRON
ap-4740	100	42	assume	assume	VERB
ap-4740	100	43	that	that	SCONJ
ap-4740	100	44	the	the	DET
ap-4740	100	45	roots	root	NOUN
ap-4740	100	46	z1	z1	VERB
ap-4740	100	47	,	,	PUNCT
ap-4740	100	48	z2	z2	PROPN
ap-4740	100	49	,	,	PUNCT
ap-4740	100	50	.	.	PUNCT
ap-4740	100	51	.	.	PUNCT
ap-4740	100	52	.	.	PUNCT
ap-4740	101	1	,	,	PUNCT
ap-4740	101	2	zn	zn	PROPN
ap-4740	101	3	are	be	AUX
ap-4740	101	4	real	real	ADJ
ap-4740	101	5	and	and	CCONJ
ap-4740	101	6	distinct	distinct	ADJ
ap-4740	101	7	.	.	PUNCT
ap-4740	102	1	we	we	PRON
ap-4740	102	2	now	now	ADV
ap-4740	102	3	plan	plan	VERB
ap-4740	102	4	to	to	PART
ap-4740	102	5	show	show	VERB
ap-4740	102	6	that	that	SCONJ
ap-4740	102	7	the	the	DET
ap-4740	102	8	integration	integration	NOUN
ap-4740	102	9	constants	constant	VERB
ap-4740	102	10	c1,n	c1,n	PROPN
ap-4740	102	11	,	,	PUNCT
ap-4740	102	12	c2,n	c2,n	PROPN
ap-4740	102	13	,	,	PUNCT
ap-4740	102	14	.	.	PUNCT
ap-4740	102	15	.	.	PUNCT
ap-4740	103	1	.	.	PUNCT
ap-4740	104	1	,	,	PUNCT
ap-4740	104	2	ck−2,n	ck−2,n	X
ap-4740	104	3	satisfy	satisfy	VERB
ap-4740	104	4	a	a	DET
ap-4740	104	5	system	system	NOUN
ap-4740	104	6	of	of	ADP
ap-4740	104	7	linear	linear	ADJ
ap-4740	104	8	equations	equation	NOUN
ap-4740	104	9	whose	whose	DET
ap-4740	104	10	coefficients	coefficient	NOUN
ap-4740	104	11	can	can	AUX
ap-4740	104	12	be	be	AUX
ap-4740	104	13	expressed	express	VERB
ap-4740	104	14	in	in	ADP
ap-4740	104	15	terms	term	NOUN
ap-4740	104	16	of	of	ADP
ap-4740	104	17	elementary	elementary	ADJ
ap-4740	104	18	symmetric	symmetric	ADJ
ap-4740	104	19	polynomials	polynomial	NOUN
ap-4740	104	20	in	in	ADP
ap-4740	104	21	z1	z1	NOUN
ap-4740	104	22	,	,	PUNCT
ap-4740	104	23	z2	z2	PROPN
ap-4740	104	24	,	,	PUNCT
ap-4740	104	25	.	.	PUNCT
ap-4740	104	26	.	.	PUNCT
ap-4740	105	1	.	.	PUNCT
ap-4740	106	1	,	,	PUNCT
ap-4740	106	2	zn	zn	PROPN
ap-4740	107	1	[	[	X
ap-4740	107	2	22	22	NUM
ap-4740	107	3	]	]	PUNCT
ap-4740	107	4	,	,	PUNCT
ap-4740	107	5	el	el	PROPN
ap-4740	107	6	≡	≡	PROPN
ap-4740	107	7	el(z1	el(z1	NOUN
ap-4740	107	8	,	,	PUNCT
ap-4740	107	9	z2	z2	PROPN
ap-4740	107	10	,	,	PUNCT
ap-4740	107	11	.	.	PUNCT
ap-4740	107	12	.	.	PUNCT
ap-4740	108	1	.	.	PUNCT
ap-4740	109	1	,	,	PUNCT
ap-4740	109	2	zn	zn	X
ap-4740	109	3	)	)	PUNCT
ap-4740	109	4	=	=	PUNCT
ap-4740	110	1	∑	∑	PUNCT
ap-4740	110	2	1≤i1	1≤i1	X
ap-4740	110	3	<	<	X
ap-4740	110	4	i2<···<il≤n	i2<···<il≤n	NOUN
ap-4740	110	5	zi1zi2	zi1zi2	X
ap-4740	110	6	.	.	PUNCT
ap-4740	110	7	.	.	PUNCT
ap-4740	110	8	.	.	PUNCT
ap-4740	111	1	zil	zil	NOUN
ap-4740	111	2	,	,	PUNCT
ap-4740	111	3	l	l	NOUN
ap-4740	111	4	=	=	SYM
ap-4740	111	5	1	1	NUM
ap-4740	111	6	,	,	PUNCT
ap-4740	111	7	2	2	NUM
ap-4740	111	8	,	,	PUNCT
ap-4740	111	9	.	.	PUNCT
ap-4740	111	10	.	.	PUNCT
ap-4740	111	11	.	.	PUNCT
ap-4740	112	1	,	,	PUNCT
ap-4740	112	2	n	n	CCONJ
ap-4740	112	3	,	,	PUNCT
ap-4740	112	4	e0	e0	PROPN
ap-4740	112	5	≡	≡	PROPN
ap-4740	112	6	1	1	NUM
ap-4740	112	7	.	.	PUNCT
ap-4740	113	1	(	(	PUNCT
ap-4740	113	2	2.13	2.13	NUM
ap-4740	113	3	)	)	PUNCT
ap-4740	113	4	we	we	PRON
ap-4740	113	5	can	can	AUX
ap-4740	113	6	indeed	indeed	ADV
ap-4740	113	7	rewrite	rewrite	VERB
ap-4740	113	8	yn(z	yn(z	NOUN
ap-4740	113	9	)	)	PUNCT
ap-4740	113	10	in	in	ADP
ap-4740	113	11	(	(	PUNCT
ap-4740	113	12	2.12	2.12	NUM
ap-4740	113	13	)	)	PUNCT
ap-4740	113	14	as	as	ADP
ap-4740	113	15	yn(z	yn(z	NOUN
ap-4740	113	16	)	)	PUNCT
ap-4740	114	1	=	=	SYM
ap-4740	114	2	n∑	n∑	PROPN
ap-4740	114	3	m=0	m=0	PROPN
ap-4740	114	4	(	(	PUNCT
ap-4740	114	5	−1)n−men−mzm	−1)n−men−mzm	ADV
ap-4740	114	6	,	,	PUNCT
ap-4740	114	7	(	(	PUNCT
ap-4740	114	8	2.14	2.14	NUM
ap-4740	114	9	)	)	PUNCT
ap-4740	114	10	so	so	SCONJ
ap-4740	114	11	that	that	SCONJ
ap-4740	114	12	y′n(z	y′n(z	VERB
ap-4740	114	13	)	)	PUNCT
ap-4740	115	1	=	=	SYM
ap-4740	115	2	n−1∑	n−1∑	PROPN
ap-4740	115	3	m=0	m=0	PROPN
ap-4740	115	4	(	(	PUNCT
ap-4740	115	5	−1)n−m−1(m+	−1)n−m−1(m+	X
ap-4740	115	6	1)en−m−1z	1)en−m−1z	NUM
ap-4740	115	7	m	m	NOUN
ap-4740	115	8	,	,	PUNCT
ap-4740	115	9	y′′n(z	y′′n(z	PROPN
ap-4740	115	10	)	)	PUNCT
ap-4740	115	11	=	=	PUNCT
ap-4740	115	12	n−2∑	n−2∑	NUM
ap-4740	115	13	m=0	m=0	PROPN
ap-4740	115	14	(	(	PUNCT
ap-4740	115	15	−1)n−m−2(m+	−1)n−m−2(m+	X
ap-4740	115	16	2)(m+	2)(m+	NUM
ap-4740	115	17	1)en−m−2z	1)en−m−2z	NUM
ap-4740	115	18	m.	m.	NOUN
ap-4740	115	19	(	(	PUNCT
ap-4740	115	20	2.15	2.15	NUM
ap-4740	115	21	)	)	PUNCT
ap-4740	115	22	on	on	ADP
ap-4740	115	23	inserting	insert	VERB
ap-4740	115	24	these	these	DET
ap-4740	115	25	expressions	expression	NOUN
ap-4740	115	26	in	in	ADP
ap-4740	115	27	equation	equation	NOUN
ap-4740	115	28	(	(	PUNCT
ap-4740	115	29	2.1	2.1	NUM
ap-4740	115	30	)	)	PUNCT
ap-4740	115	31	and	and	CCONJ
ap-4740	115	32	taking	take	VERB
ap-4740	115	33	equation	equation	NOUN
ap-4740	115	34	(	(	PUNCT
ap-4740	115	35	2.2	2.2	NUM
ap-4740	115	36	)	)	PUNCT
ap-4740	115	37	into	into	ADP
ap-4740	115	38	account	account	NOUN
ap-4740	115	39	,	,	PUNCT
ap-4740	115	40	we	we	PRON
ap-4740	115	41	get	get	AUX
ap-4740	115	42	k∑	k∑	VERB
ap-4740	115	43	l=0	l=0	PROPN
ap-4740	115	44	alz	alz	PROPN
ap-4740	116	1	l	l	PROPN
ap-4740	116	2	n−2∑	n−2∑	PROPN
ap-4740	116	3	m=0	m=0	PROPN
ap-4740	116	4	(	(	PUNCT
ap-4740	116	5	−1)n−m−2(m+	−1)n−m−2(m+	X
ap-4740	116	6	2)(m+	2)(m+	NUM
ap-4740	116	7	1)en−m−2z	1)en−m−2z	NUM
ap-4740	116	8	m	m	NOUN
ap-4740	116	9	+	+	CCONJ
ap-4740	116	10	k−1∑	k−1∑	PROPN
ap-4740	116	11	l=0	l=0	PROPN
ap-4740	116	12	blz	blz	PROPN
ap-4740	116	13	l	l	PROPN
ap-4740	116	14	n−1∑	n−1∑	PROPN
ap-4740	116	15	m=0	m=0	PROPN
ap-4740	116	16	(	(	PUNCT
ap-4740	116	17	−1)n−m−1(m+	−1)n−m−1(m+	X
ap-4740	116	18	1)en−m−1z	1)en−m−1z	NUM
ap-4740	116	19	m	m	NOUN
ap-4740	116	20	+	+	CCONJ
ap-4740	116	21	k−2∑	k−2∑	ADV
ap-4740	116	22	l=0	l=0	PROPN
ap-4740	116	23	clz	clz	NOUN
ap-4740	116	24	l	l	PROPN
ap-4740	116	25	n∑	n∑	PROPN
ap-4740	116	26	m=0	m=0	PROPN
ap-4740	116	27	(	(	PUNCT
ap-4740	116	28	−1)n−men−mzm	−1)n−men−mzm	ADV
ap-4740	116	29	=	=	SYM
ap-4740	116	30	0	0	X
ap-4740	116	31	.	.	PUNCT
ap-4740	117	1	(	(	PUNCT
ap-4740	117	2	2.16	2.16	NUM
ap-4740	117	3	)	)	PUNCT
ap-4740	117	4	here	here	ADV
ap-4740	117	5	l	l	PROPN
ap-4740	118	1	+	+	CCONJ
ap-4740	118	2	m	m	VERB
ap-4740	118	3	runs	run	NOUN
ap-4740	118	4	from	from	ADP
ap-4740	118	5	0	0	NUM
ap-4740	118	6	to	to	ADP
ap-4740	118	7	k	k	PROPN
ap-4740	118	8	+	+	CCONJ
ap-4740	118	9	n	n	CCONJ
ap-4740	118	10	−	−	PROPN
ap-4740	118	11	2	2	NUM
ap-4740	118	12	.	.	PUNCT
ap-4740	119	1	let	let	VERB
ap-4740	119	2	us	we	PRON
ap-4740	119	3	therefore	therefore	ADV
ap-4740	119	4	set	set	VERB
ap-4740	119	5	l	l	PROPN
ap-4740	120	1	+	+	X
ap-4740	120	2	m	m	VERB
ap-4740	120	3	=	=	SYM
ap-4740	120	4	k	k	PROPN
ap-4740	121	1	+	+	CCONJ
ap-4740	121	2	n	n	CCONJ
ap-4740	121	3	−	−	NOUN
ap-4740	121	4	r	r	NOUN
ap-4740	121	5	,	,	PUNCT
ap-4740	121	6	where	where	SCONJ
ap-4740	121	7	r	r	NOUN
ap-4740	121	8	=	=	SYM
ap-4740	121	9	2	2	NUM
ap-4740	121	10	,	,	PUNCT
ap-4740	121	11	3	3	NUM
ap-4740	121	12	,	,	PUNCT
ap-4740	121	13	.	.	PUNCT
ap-4740	121	14	.	.	PUNCT
ap-4740	122	1	.	.	PUNCT
ap-4740	123	1	,	,	PUNCT
ap-4740	123	2	k	k	PROPN
ap-4740	123	3	+	+	CCONJ
ap-4740	123	4	n.	n.	NOUN
ap-4740	123	5	equation	equation	NOUN
ap-4740	123	6	(	(	PUNCT
ap-4740	123	7	2.16	2.16	NUM
ap-4740	123	8	)	)	PUNCT
ap-4740	123	9	can	can	AUX
ap-4740	123	10	then	then	ADV
ap-4740	123	11	be	be	AUX
ap-4740	123	12	rewritten	rewrite	VERB
ap-4740	123	13	as	as	ADP
ap-4740	123	14	k∑	k∑	PROPN
ap-4740	123	15	r=2	r=2	PROPN
ap-4740	123	16	{	{	PUNCT
ap-4740	123	17	r−2∑	r−2∑	ADV
ap-4740	123	18	p=0	p=0	PROPN
ap-4740	123	19	(	(	PUNCT
ap-4740	123	20	−1)p	−1)p	PROPN
ap-4740	123	21	[	[	X
ap-4740	123	22	ak−r+2+p(n−	ak−r+2+p(n−	PROPN
ap-4740	123	23	p)(n−	p)(n−	NOUN
ap-4740	123	24	p−	p−	NOUN
ap-4740	123	25	1	1	NUM
ap-4740	123	26	)	)	PUNCT
ap-4740	123	27	+	+	CCONJ
ap-4740	124	1	bk−r+1+p(n−	bk−r+1+p(n−	PROPN
ap-4740	124	2	p	p	NOUN
ap-4740	124	3	)	)	PUNCT
ap-4740	124	4	+	+	CCONJ
ap-4740	124	5	ck−r+p	ck−r+p	ADJ
ap-4740	124	6	]	]	X
ap-4740	124	7	ep	ep	PROPN
ap-4740	124	8	}	}	PUNCT
ap-4740	124	9	zk+n−r	zk+n−r	PROPN
ap-4740	124	10	+	+	CCONJ
ap-4740	124	11	(	(	PUNCT
ap-4740	124	12	lower	low	ADJ
ap-4740	124	13	-	-	PUNCT
ap-4740	124	14	degree	degree	NOUN
ap-4740	124	15	terms	term	NOUN
ap-4740	124	16	with	with	ADP
ap-4740	124	17	k	k	PROPN
ap-4740	124	18	+	+	CCONJ
ap-4740	124	19	1	1	NUM
ap-4740	124	20	≤	≤	NUM
ap-4740	124	21	r	r	NOUN
ap-4740	124	22	≤	≤	PUNCT
ap-4740	124	23	k	k	NOUN
ap-4740	124	24	+	+	CCONJ
ap-4740	124	25	n	n	CCONJ
ap-4740	124	26	)	)	PUNCT
ap-4740	124	27	=	=	SYM
ap-4740	124	28	0	0	X
ap-4740	124	29	.	.	PUNCT
ap-4740	125	1	(	(	PUNCT
ap-4740	125	2	2.17	2.17	NUM
ap-4740	125	3	)	)	PUNCT
ap-4740	125	4	on	on	ADP
ap-4740	125	5	setting	set	VERB
ap-4740	125	6	to	to	ADP
ap-4740	125	7	zero	zero	NUM
ap-4740	125	8	the	the	DET
ap-4740	125	9	coefficients	coefficient	NOUN
ap-4740	125	10	of	of	ADP
ap-4740	125	11	zk+n−r	zk+n−r	PROPN
ap-4740	125	12	,	,	PUNCT
ap-4740	125	13	r	r	NOUN
ap-4740	125	14	=	=	SYM
ap-4740	125	15	2	2	NUM
ap-4740	125	16	,	,	PUNCT
ap-4740	125	17	3	3	NUM
ap-4740	125	18	,	,	PUNCT
ap-4740	125	19	.	.	PUNCT
ap-4740	125	20	.	.	PUNCT
ap-4740	126	1	.	.	PUNCT
ap-4740	127	1	,	,	PUNCT
ap-4740	127	2	k	k	X
ap-4740	127	3	,	,	PUNCT
ap-4740	127	4	we	we	PRON
ap-4740	127	5	obtain	obtain	VERB
ap-4740	127	6	the	the	DET
ap-4740	127	7	relations	relation	NOUN
ap-4740	127	8	r−2∑	r−2∑	ADV
ap-4740	127	9	p=0	p=0	PROPN
ap-4740	128	1	(	(	PUNCT
ap-4740	128	2	−1)p	−1)p	PROPN
ap-4740	128	3	[	[	X
ap-4740	128	4	ak−r+2+p(n−	ak−r+2+p(n−	PROPN
ap-4740	128	5	p)(n−	p)(n−	NOUN
ap-4740	128	6	p−	p−	NOUN
ap-4740	128	7	1	1	NUM
ap-4740	128	8	)	)	PUNCT
ap-4740	129	1	+	+	CCONJ
ap-4740	129	2	bk−r+1+p(n−	bk−r+1+p(n−	PROPN
ap-4740	129	3	p	p	NOUN
ap-4740	129	4	)	)	PUNCT
ap-4740	129	5	+	+	CCONJ
ap-4740	129	6	ck−r+p	ck−r+p	ADJ
ap-4740	129	7	]	]	X
ap-4740	129	8	ep	ep	PROPN
ap-4740	129	9	=	=	SYM
ap-4740	129	10	0	0	PROPN
ap-4740	129	11	,	,	PUNCT
ap-4740	129	12	r	r	NOUN
ap-4740	129	13	=	=	SYM
ap-4740	129	14	2	2	NUM
ap-4740	129	15	,	,	PUNCT
ap-4740	129	16	3	3	NUM
ap-4740	129	17	,	,	PUNCT
ap-4740	129	18	.	.	PUNCT
ap-4740	129	19	.	.	PUNCT
ap-4740	129	20	.	.	PUNCT
ap-4740	130	1	,	,	PUNCT
ap-4740	130	2	k.	k.	PROPN
ap-4740	130	3	(	(	PUNCT
ap-4740	130	4	2.18	2.18	NUM
ap-4740	130	5	)	)	PUNCT
ap-4740	130	6	for	for	ADP
ap-4740	130	7	r	r	NOUN
ap-4740	130	8	=	=	SYM
ap-4740	130	9	2	2	NUM
ap-4740	130	10	,	,	PUNCT
ap-4740	130	11	we	we	PRON
ap-4740	130	12	simply	simply	ADV
ap-4740	130	13	get	get	VERB
ap-4740	130	14	n(n−	n(n−	PROPN
ap-4740	130	15	1)ak	1)ak	PROPN
ap-4740	131	1	+	+	CCONJ
ap-4740	131	2	nbk−1	nbk−1	PROPN
ap-4740	131	3	+	+	NOUN
ap-4740	131	4	ck−2	ck−2	NOUN
ap-4740	131	5	=	=	SYM
ap-4740	131	6	0	0	PROPN
ap-4740	131	7	,	,	PUNCT
ap-4740	131	8	which	which	PRON
ap-4740	131	9	is	be	AUX
ap-4740	131	10	automatically	automatically	ADV
ap-4740	131	11	satisfied	satisfied	ADJ
ap-4740	131	12	due	due	ADP
ap-4740	131	13	to	to	ADP
ap-4740	131	14	equation	equation	NOUN
ap-4740	131	15	(	(	PUNCT
ap-4740	131	16	2.10	2.10	NUM
ap-4740	131	17	)	)	PUNCT
ap-4740	131	18	.	.	PUNCT
ap-4740	132	1	we	we	PRON
ap-4740	132	2	are	be	AUX
ap-4740	132	3	therefore	therefore	ADV
ap-4740	132	4	left	leave	VERB
ap-4740	132	5	with	with	ADP
ap-4740	132	6	the	the	DET
ap-4740	132	7	k	k	PROPN
ap-4740	132	8	−	−	PROPN
ap-4740	132	9	2	2	NUM
ap-4740	132	10	relations	relation	NOUN
ap-4740	132	11	r−3∑	r−3∑	PROPN
ap-4740	132	12	p=0	p=0	PROPN
ap-4740	132	13	(	(	PUNCT
ap-4740	132	14	−1)p	−1)p	X
ap-4740	132	15	[	[	PUNCT
ap-4740	132	16	ak−r+2+p(n−	ak−r+2+p(n−	PROPN
ap-4740	132	17	p)(n−	p)(n−	NOUN
ap-4740	132	18	p−	p−	NOUN
ap-4740	132	19	1	1	NUM
ap-4740	132	20	)	)	PUNCT
ap-4740	132	21	+	+	CCONJ
ap-4740	132	22	bk−r+1+p(n−	bk−r+1+p(n−	PROPN
ap-4740	132	23	p	p	NOUN
ap-4740	132	24	)	)	PUNCT
ap-4740	133	1	+	+	CCONJ
ap-4740	133	2	ck−r+p	ck−r+p	VERB
ap-4740	133	3	]	]	PUNCT
ap-4740	133	4	ep	ep	PROPN
ap-4740	134	1	+	+	CCONJ
ap-4740	134	2	(	(	PUNCT
ap-4740	134	3	−1)r−2[ak(n−	−1)r−2[ak(n−	ADJ
ap-4740	134	4	r	r	NOUN
ap-4740	134	5	+	+	CCONJ
ap-4740	134	6	2)(n−	2)(n−	NUM
ap-4740	134	7	r	r	NOUN
ap-4740	134	8	+	+	NOUN
ap-4740	134	9	1	1	NUM
ap-4740	134	10	)	)	PUNCT
ap-4740	134	11	+	+	CCONJ
ap-4740	134	12	bk−1(n−	bk−1(n−	NOUN
ap-4740	134	13	r	r	NOUN
ap-4740	134	14	+	+	NOUN
ap-4740	134	15	2	2	NUM
ap-4740	134	16	)	)	PUNCT
ap-4740	134	17	+	+	NUM
ap-4740	134	18	ck−2]er−2	ck−2]er−2	NOUN
ap-4740	134	19	=	=	SYM
ap-4740	134	20	0	0	NUM
ap-4740	134	21	,	,	PUNCT
ap-4740	134	22	r	r	NOUN
ap-4740	134	23	=	=	SYM
ap-4740	134	24	3	3	NUM
ap-4740	134	25	,	,	PUNCT
ap-4740	134	26	4	4	NUM
ap-4740	134	27	,	,	PUNCT
ap-4740	134	28	.	.	PUNCT
ap-4740	134	29	.	.	PUNCT
ap-4740	134	30	.	.	PUNCT
ap-4740	135	1	,	,	PUNCT
ap-4740	135	2	k.	k.	PROPN
ap-4740	135	3	(	(	PUNCT
ap-4740	135	4	2.19	2.19	NUM
ap-4740	135	5	)	)	PUNCT
ap-4740	135	6	120	120	NUM
ap-4740	135	7	vol	vol	NOUN
ap-4740	135	8	.	.	PUNCT
ap-4740	136	1	58	58	NUM
ap-4740	136	2	no	no	INTJ
ap-4740	136	3	.	.	PUNCT
ap-4740	137	1	2/2018	2/2018	NOUN
ap-4740	137	2	quasi	quasi	ADJ
ap-4740	137	3	-	-	ADJ
ap-4740	137	4	exactly	exactly	ADV
ap-4740	137	5	solvable	solvable	ADJ
ap-4740	137	6	schrödinger	schrödinger	ADJ
ap-4740	137	7	equations	equation	NOUN
ap-4740	137	8	after	after	ADP
ap-4740	137	9	substituting	substitute	VERB
ap-4740	137	10	the	the	DET
ap-4740	137	11	right	right	ADJ
ap-4740	137	12	-	-	PUNCT
ap-4740	137	13	hand	hand	NOUN
ap-4740	137	14	sides	side	NOUN
ap-4740	137	15	of	of	ADP
ap-4740	137	16	equations	equation	NOUN
ap-4740	137	17	(	(	PUNCT
ap-4740	137	18	2.10	2.10	NUM
ap-4740	137	19	)	)	PUNCT
ap-4740	137	20	and	and	CCONJ
ap-4740	137	21	(	(	PUNCT
ap-4740	137	22	2.11	2.11	NUM
ap-4740	137	23	)	)	PUNCT
ap-4740	137	24	for	for	ADP
ap-4740	137	25	ck−2	ck−2	PROPN
ap-4740	137	26	and	and	CCONJ
ap-4740	137	27	ck−r+p	ck−r+p	VERB
ap-4740	137	28	in	in	ADP
ap-4740	137	29	these	these	DET
ap-4740	137	30	relations	relation	NOUN
ap-4740	137	31	,	,	PUNCT
ap-4740	137	32	we	we	PRON
ap-4740	137	33	obtain	obtain	VERB
ap-4740	137	34	a	a	DET
ap-4740	137	35	system	system	NOUN
ap-4740	137	36	of	of	ADP
ap-4740	137	37	k	k	NOUN
ap-4740	137	38	−	−	PROPN
ap-4740	137	39	2	2	NUM
ap-4740	137	40	linear	linear	NOUN
ap-4740	137	41	equations	equation	NOUN
ap-4740	137	42	for	for	ADP
ap-4740	137	43	the	the	DET
ap-4740	137	44	k	k	NOUN
ap-4740	137	45	−	−	PROPN
ap-4740	137	46	2	2	NUM
ap-4740	137	47	integration	integration	NOUN
ap-4740	137	48	constants	constant	NOUN
ap-4740	137	49	c1,n	c1,n	PROPN
ap-4740	137	50	,	,	PUNCT
ap-4740	137	51	c2,n	c2,n	PROPN
ap-4740	137	52	,	,	PUNCT
ap-4740	137	53	.	.	PUNCT
ap-4740	137	54	.	.	PUNCT
ap-4740	138	1	.	.	PUNCT
ap-4740	139	1	,	,	PUNCT
ap-4740	139	2	ck−2,n	ck−2,n	ADV
ap-4740	139	3	,	,	PUNCT
ap-4740	139	4	r−3∑	r−3∑	PROPN
ap-4740	139	5	p=0	p=0	PROPN
ap-4740	139	6	(	(	PUNCT
ap-4740	139	7	−1)p	−1)p	PROPN
ap-4740	139	8	cr−2−p	cr−2−p	PROPN
ap-4740	139	9	,	,	PUNCT
ap-4740	139	10	n	n	PROPN
ap-4740	139	11	(	(	PUNCT
ap-4740	139	12	k	k	NOUN
ap-4740	139	13	−	−	PROPN
ap-4740	139	14	r	r	NOUN
ap-4740	139	15	+	+	NUM
ap-4740	139	16	p)!ep	p)!ep	NOUN
ap-4740	139	17	=	=	PUNCT
ap-4740	140	1	−	−	PROPN
ap-4740	140	2	r−3∑	r−3∑	PROPN
ap-4740	140	3	p=0	p=0	PROPN
ap-4740	140	4	(	(	PUNCT
ap-4740	140	5	−1)p	−1)p	NOUN
ap-4740	140	6	{	{	PUNCT
ap-4740	140	7	1	1	NUM
ap-4740	140	8	k(k	k(k	NOUN
ap-4740	140	9	−	−	NOUN
ap-4740	140	10	1	1	NUM
ap-4740	140	11	)	)	PUNCT
ap-4740	140	12	[	[	PUNCT
ap-4740	140	13	(	(	PUNCT
ap-4740	140	14	r	r	NOUN
ap-4740	140	15	−	−	PROPN
ap-4740	140	16	p−	p−	NOUN
ap-4740	140	17	2)(2k	2)(2k	NUM
ap-4740	140	18	−	−	NOUN
ap-4740	140	19	r	r	NOUN
ap-4740	140	20	+	+	NOUN
ap-4740	140	21	p+	p+	PROPN
ap-4740	140	22	1)n2	1)n2	NUM
ap-4740	140	23	−	−	PROPN
ap-4740	141	1	[	[	X
ap-4740	141	2	2pk2	2pk2	NUM
ap-4740	141	3	+	+	NUM
ap-4740	141	4	2k(r	2k(r	NOUN
ap-4740	141	5	−	−	NOUN
ap-4740	142	1	2p−	2p−	NOUN
ap-4740	142	2	2	2	NUM
ap-4740	142	3	)	)	PUNCT
ap-4740	142	4	−	−	PROPN
ap-4740	143	1	(	(	PUNCT
ap-4740	143	2	r	r	NOUN
ap-4740	143	3	−	−	NOUN
ap-4740	143	4	p−	p−	NOUN
ap-4740	143	5	2)(r	2)(r	NUM
ap-4740	143	6	−	−	NOUN
ap-4740	144	1	p−	p−	NOUN
ap-4740	144	2	1)]n+	1)]n+	NUM
ap-4740	144	3	k(k	k(k	NOUN
ap-4740	144	4	−	−	PROPN
ap-4740	145	1	1)p(p+	1)p(p+	PROPN
ap-4740	145	2	1	1	NUM
ap-4740	145	3	)	)	PUNCT
ap-4740	145	4	]	]	PUNCT
ap-4740	146	1	ak−r+2+p	ak−r+2+p	PROPN
ap-4740	146	2	+	+	X
ap-4740	146	3	1	1	NUM
ap-4740	146	4	k	k	NOUN
ap-4740	146	5	−	−	NOUN
ap-4740	146	6	1	1	NUM
ap-4740	147	1	[	[	X
ap-4740	147	2	(	(	PUNCT
ap-4740	147	3	r	r	NOUN
ap-4740	147	4	−	−	NOUN
ap-4740	147	5	p−	p−	NOUN
ap-4740	147	6	2)n−	2)n−	NUM
ap-4740	147	7	(	(	PUNCT
ap-4740	147	8	k	k	PROPN
ap-4740	147	9	−	−	PROPN
ap-4740	147	10	1)p]bk−r+1+p	1)p]bk−r+1+p	PROPN
ap-4740	147	11	}	}	PUNCT
ap-4740	147	12	ep	ep	PROPN
ap-4740	147	13	−	−	PROPN
ap-4740	148	1	(	(	PUNCT
ap-4740	148	2	−1)r−1(r	−1)r−1(r	NOUN
ap-4740	148	3	−	−	NOUN
ap-4740	148	4	2)[(2n−	2)[(2n−	NUM
ap-4740	148	5	r	r	NOUN
ap-4740	148	6	+	+	PROPN
ap-4740	148	7	1)ak	1)ak	PROPN
ap-4740	148	8	+	+	NUM
ap-4740	148	9	bk−1]er−2	bk−1]er−2	NOUN
ap-4740	148	10	,	,	PUNCT
ap-4740	148	11	r	r	NOUN
ap-4740	148	12	=	=	SYM
ap-4740	148	13	3	3	NUM
ap-4740	148	14	,	,	PUNCT
ap-4740	148	15	4	4	NUM
ap-4740	148	16	,	,	PUNCT
ap-4740	148	17	.	.	PUNCT
ap-4740	148	18	.	.	PUNCT
ap-4740	149	1	.	.	PUNCT
ap-4740	150	1	,	,	PUNCT
ap-4740	150	2	k	k	NOUN
ap-4740	150	3	,	,	PUNCT
ap-4740	150	4	(	(	PUNCT
ap-4740	150	5	2.20	2.20	NUM
ap-4740	150	6	)	)	PUNCT
ap-4740	150	7	whose	whose	DET
ap-4740	150	8	coefficients	coefficient	NOUN
ap-4740	150	9	are	be	AUX
ap-4740	150	10	expressed	express	VERB
ap-4740	150	11	in	in	ADP
ap-4740	150	12	terms	term	NOUN
ap-4740	150	13	of	of	ADP
ap-4740	150	14	elementary	elementary	ADJ
ap-4740	150	15	symmetric	symmetric	ADJ
ap-4740	150	16	polynomials	polynomial	NOUN
ap-4740	150	17	(	(	PUNCT
ap-4740	150	18	2.13	2.13	NUM
ap-4740	150	19	)	)	PUNCT
ap-4740	150	20	in	in	ADP
ap-4740	150	21	the	the	DET
ap-4740	150	22	roots	root	NOUN
ap-4740	150	23	of	of	ADP
ap-4740	150	24	the	the	DET
ap-4740	150	25	polynomial	polynomial	ADJ
ap-4740	150	26	solutions	solution	NOUN
ap-4740	150	27	of	of	ADP
ap-4740	150	28	equation	equation	NOUN
ap-4740	150	29	(	(	PUNCT
ap-4740	150	30	2.1	2.1	NUM
ap-4740	150	31	)	)	PUNCT
ap-4740	150	32	.	.	PUNCT
ap-4740	151	1	this	this	PRON
ap-4740	151	2	is	be	AUX
ap-4740	151	3	the	the	DET
ap-4740	151	4	second	second	ADJ
ap-4740	151	5	main	main	ADJ
ap-4740	151	6	result	result	NOUN
ap-4740	151	7	of	of	ADP
ap-4740	151	8	this	this	DET
ap-4740	151	9	paper	paper	NOUN
ap-4740	151	10	.	.	PUNCT
ap-4740	152	1	the	the	DET
ap-4740	152	2	determinant	determinant	NOUN
ap-4740	152	3	of	of	ADP
ap-4740	152	4	this	this	DET
ap-4740	152	5	system	system	NOUN
ap-4740	152	6	having	have	VERB
ap-4740	152	7	zeros	zero	NOUN
ap-4740	152	8	above	above	ADP
ap-4740	152	9	the	the	DET
ap-4740	152	10	diagonal	diagonal	NOUN
ap-4740	152	11	is	be	AUX
ap-4740	152	12	easily	easily	ADV
ap-4740	152	13	determined	determined	ADJ
ap-4740	152	14	to	to	PART
ap-4740	152	15	be	be	AUX
ap-4740	152	16	given	give	VERB
ap-4740	152	17	by[∏k	by[∏k	PROPN
ap-4740	152	18	r=3(k	r=3(k	ADP
ap-4740	152	19	−	−	NOUN
ap-4740	152	20	r	r	NOUN
ap-4740	152	21	)	)	PUNCT
ap-4740	152	22	!	!	PUNCT
ap-4740	153	1	]	]	X
ap-4740	153	2	−1	−1	NOUN
ap-4740	153	3	6=	6=	NOUN
ap-4740	153	4	0	0	X
ap-4740	153	5	.	.	PUNCT
ap-4740	154	1	it	it	PRON
ap-4740	154	2	is	be	AUX
ap-4740	154	3	therefore	therefore	ADV
ap-4740	154	4	obvious	obvious	ADJ
ap-4740	154	5	that	that	SCONJ
ap-4740	154	6	the	the	DET
ap-4740	154	7	constants	constant	NOUN
ap-4740	154	8	c1,n	c1,n	PROPN
ap-4740	154	9	,	,	PUNCT
ap-4740	154	10	c2,n	c2,n	PROPN
ap-4740	154	11	,	,	PUNCT
ap-4740	154	12	.	.	PUNCT
ap-4740	154	13	.	.	PUNCT
ap-4740	154	14	.	.	PUNCT
ap-4740	155	1	,	,	PUNCT
ap-4740	155	2	ck−2,n	ck−2,n	PROPN
ap-4740	155	3	can	can	AUX
ap-4740	155	4	be	be	AUX
ap-4740	155	5	calculated	calculate	VERB
ap-4740	155	6	successively	successively	ADV
ap-4740	155	7	from	from	ADP
ap-4740	155	8	the	the	DET
ap-4740	155	9	equations	equation	NOUN
ap-4740	155	10	corresponding	correspond	VERB
ap-4740	155	11	to	to	ADP
ap-4740	155	12	r	r	NOUN
ap-4740	155	13	=	=	SYM
ap-4740	155	14	3	3	NUM
ap-4740	155	15	,	,	PUNCT
ap-4740	155	16	4	4	NUM
ap-4740	155	17	,	,	PUNCT
ap-4740	155	18	.	.	PUNCT
ap-4740	155	19	.	.	PUNCT
ap-4740	156	1	.	.	PUNCT
ap-4740	157	1	,	,	PUNCT
ap-4740	157	2	k.	k.	PROPN
ap-4740	158	1	it	it	PRON
ap-4740	158	2	turns	turn	VERB
ap-4740	158	3	out	out	ADP
ap-4740	158	4	that	that	SCONJ
ap-4740	158	5	instead	instead	ADV
ap-4740	158	6	of	of	ADP
ap-4740	158	7	elementary	elementary	ADJ
ap-4740	158	8	symmetric	symmetric	ADJ
ap-4740	158	9	polynomials	polynomial	NOUN
ap-4740	158	10	el(z1	el(z1	NOUN
ap-4740	158	11	,	,	PUNCT
ap-4740	158	12	z2	z2	PROPN
ap-4740	158	13	,	,	PUNCT
ap-4740	158	14	.	.	PUNCT
ap-4740	158	15	.	.	PUNCT
ap-4740	158	16	.	.	PUNCT
ap-4740	159	1	,	,	PUNCT
ap-4740	159	2	zn	zn	X
ap-4740	159	3	)	)	PUNCT
ap-4740	159	4	,	,	PUNCT
ap-4740	159	5	defined	define	VERB
ap-4740	159	6	in	in	ADP
ap-4740	159	7	equation	equation	NOUN
ap-4740	159	8	(	(	PUNCT
ap-4740	159	9	2.13	2.13	NUM
ap-4740	159	10	)	)	PUNCT
ap-4740	159	11	,	,	PUNCT
ap-4740	159	12	it	it	PRON
ap-4740	159	13	is	be	AUX
ap-4740	159	14	more	more	ADV
ap-4740	159	15	appropriate	appropriate	ADJ
ap-4740	159	16	to	to	PART
ap-4740	159	17	express	express	VERB
ap-4740	159	18	the	the	DET
ap-4740	159	19	solution	solution	NOUN
ap-4740	159	20	in	in	ADP
ap-4740	159	21	terms	term	NOUN
ap-4740	159	22	of	of	ADP
ap-4740	159	23	monomial	monomial	ADJ
ap-4740	159	24	symmetric	symmetric	ADJ
ap-4740	159	25	polynomials	polynomial	NOUN
ap-4740	159	26	in	in	ADP
ap-4740	159	27	z1	z1	NOUN
ap-4740	159	28	,	,	PUNCT
ap-4740	159	29	z2	z2	PROPN
ap-4740	159	30	,	,	PUNCT
ap-4740	159	31	.	.	PUNCT
ap-4740	159	32	.	.	PUNCT
ap-4740	160	1	.	.	PUNCT
ap-4740	161	1	,	,	PUNCT
ap-4740	161	2	zn	zn	X
ap-4740	161	3	,	,	PUNCT
ap-4740	161	4	m(λ1,λ2,	m(λ1,λ2,	ADJ
ap-4740	161	5	...	...	PUNCT
ap-4740	161	6	,λn)(z1	,λn)(z1	ADJ
ap-4740	161	7	,	,	PUNCT
ap-4740	161	8	z2	z2	PROPN
ap-4740	161	9	,	,	PUNCT
ap-4740	161	10	.	.	PUNCT
ap-4740	161	11	.	.	PUNCT
ap-4740	162	1	.	.	PUNCT
ap-4740	163	1	,	,	PUNCT
ap-4740	163	2	zn	zn	X
ap-4740	163	3	)	)	PUNCT
ap-4740	163	4	=	=	SYM
ap-4740	163	5	∑	∑	PUNCT
ap-4740	163	6	π∈sλ	π∈sλ	NOUN
ap-4740	163	7	zλ1	zλ1	NOUN
ap-4740	163	8	π(1)z	π(1)z	PROPN
ap-4740	163	9	λ2	λ2	PROPN
ap-4740	163	10	π(2	π(2	PROPN
ap-4740	163	11	)	)	PUNCT
ap-4740	163	12	.	.	PUNCT
ap-4740	163	13	.	.	PUNCT
ap-4740	164	1	.	.	PUNCT
ap-4740	165	1	z	z	NOUN
ap-4740	165	2	λn	λn	PROPN
ap-4740	165	3	π(n	π(n	PROPN
ap-4740	165	4	)	)	PUNCT
ap-4740	165	5	,	,	PUNCT
ap-4740	165	6	(	(	PUNCT
ap-4740	165	7	2.21	2.21	NUM
ap-4740	165	8	)	)	PUNCT
ap-4740	165	9	where	where	SCONJ
ap-4740	165	10	(	(	PUNCT
ap-4740	165	11	λ1	λ1	ADJ
ap-4740	165	12	,	,	PUNCT
ap-4740	165	13	λ2	λ2	NOUN
ap-4740	165	14	,	,	PUNCT
ap-4740	165	15	.	.	PUNCT
ap-4740	165	16	.	.	PUNCT
ap-4740	166	1	.	.	PUNCT
ap-4740	167	1	,	,	PUNCT
ap-4740	167	2	λn	λn	NOUN
ap-4740	167	3	)	)	PUNCT
ap-4740	167	4	denotes	denote	VERB
ap-4740	167	5	a	a	DET
ap-4740	167	6	partition	partition	NOUN
ap-4740	167	7	and	and	CCONJ
ap-4740	167	8	sλ	sλ	NOUN
ap-4740	167	9	is	be	AUX
ap-4740	167	10	the	the	DET
ap-4740	167	11	set	set	NOUN
ap-4740	167	12	of	of	ADP
ap-4740	167	13	permutations	permutation	NOUN
ap-4740	167	14	giving	give	VERB
ap-4740	167	15	distinct	distinct	ADJ
ap-4740	167	16	terms	term	NOUN
ap-4740	167	17	in	in	ADP
ap-4740	167	18	the	the	DET
ap-4740	167	19	sum	sum	NOUN
ap-4740	167	20	[	[	X
ap-4740	167	21	22	22	NUM
ap-4740	167	22	]	]	PUNCT
ap-4740	167	23	.	.	PUNCT
ap-4740	168	1	the	the	DET
ap-4740	168	2	derivation	derivation	NOUN
ap-4740	168	3	of	of	ADP
ap-4740	168	4	the	the	DET
ap-4740	168	5	first	first	ADJ
ap-4740	168	6	three	three	NUM
ap-4740	168	7	constants	constant	NOUN
ap-4740	168	8	c1,n	c1,n	PROPN
ap-4740	168	9	,	,	PUNCT
ap-4740	168	10	c2,n	c2,n	PROPN
ap-4740	168	11	,	,	PUNCT
ap-4740	168	12	and	and	CCONJ
ap-4740	168	13	c3,n	c3,n	PROPN
ap-4740	168	14	is	be	AUX
ap-4740	168	15	outlined	outline	VERB
ap-4740	168	16	in	in	ADP
ap-4740	168	17	appendix	appendix	NOUN
ap-4740	168	18	.	.	PUNCT
ap-4740	169	1	in	in	ADP
ap-4740	169	2	particular	particular	ADJ
ap-4740	169	3	,	,	PUNCT
ap-4740	169	4	it	it	PRON
ap-4740	169	5	is	be	AUX
ap-4740	169	6	shown	show	VERB
ap-4740	169	7	there	there	ADV
ap-4740	169	8	that	that	SCONJ
ap-4740	169	9	m(13,0̇	m(13,0̇	NOUN
ap-4740	169	10	)	)	PUNCT
ap-4740	169	11	(	(	PUNCT
ap-4740	169	12	a	a	DET
ap-4740	169	13	dot	dot	NOUN
ap-4740	169	14	over	over	ADP
ap-4740	169	15	zero	zero	NUM
ap-4740	169	16	meaning	mean	VERB
ap-4740	169	17	that	that	SCONJ
ap-4740	169	18	it	it	PRON
ap-4740	169	19	is	be	AUX
ap-4740	169	20	repeated	repeat	VERB
ap-4740	169	21	as	as	ADV
ap-4740	169	22	often	often	ADV
ap-4740	169	23	as	as	ADP
ap-4740	169	24	necessary	necessary	ADJ
ap-4740	169	25	)	)	PUNCT
ap-4740	169	26	,	,	PUNCT
ap-4740	169	27	corresponding	correspond	VERB
ap-4740	169	28	to	to	ADP
ap-4740	169	29	a	a	DET
ap-4740	169	30	partition	partition	NOUN
ap-4740	169	31	into	into	ADP
ap-4740	169	32	more	more	ADJ
ap-4740	169	33	than	than	ADP
ap-4740	169	34	two	two	NUM
ap-4740	169	35	parts	part	NOUN
ap-4740	169	36	and	and	CCONJ
ap-4740	169	37	which	which	PRON
ap-4740	169	38	in	in	ADP
ap-4740	169	39	principle	principle	NOUN
ap-4740	169	40	might	might	AUX
ap-4740	169	41	appear	appear	VERB
ap-4740	169	42	in	in	ADP
ap-4740	169	43	c3,n	c3,n	PROPN
ap-4740	169	44	,	,	PUNCT
ap-4740	169	45	actually	actually	ADV
ap-4740	169	46	does	do	AUX
ap-4740	169	47	not	not	PART
ap-4740	169	48	occur	occur	VERB
ap-4740	169	49	because	because	SCONJ
ap-4740	169	50	it	it	PRON
ap-4740	169	51	has	have	VERB
ap-4740	169	52	a	a	DET
ap-4740	169	53	vanishing	vanish	VERB
ap-4740	169	54	coefficient	coefficient	NOUN
ap-4740	169	55	.	.	PUNCT
ap-4740	170	1	this	this	PRON
ap-4740	170	2	is	be	AUX
ap-4740	170	3	a	a	DET
ap-4740	170	4	general	general	ADJ
ap-4740	170	5	property	property	NOUN
ap-4740	170	6	that	that	PRON
ap-4740	170	7	we	we	PRON
ap-4740	170	8	have	have	AUX
ap-4740	170	9	observed	observe	VERB
ap-4740	170	10	for	for	ADP
ap-4740	170	11	the	the	DET
ap-4740	170	12	first	first	ADJ
ap-4740	170	13	six	six	NUM
ap-4740	170	14	constants	constant	NOUN
ap-4740	170	15	that	that	PRON
ap-4740	170	16	we	we	PRON
ap-4740	170	17	have	have	AUX
ap-4740	170	18	computed	compute	VERB
ap-4740	170	19	explicitly	explicitly	ADV
ap-4740	170	20	and	and	CCONJ
ap-4740	170	21	which	which	PRON
ap-4740	170	22	all	all	PRON
ap-4740	170	23	agree	agree	VERB
ap-4740	170	24	with	with	ADP
ap-4740	170	25	the	the	DET
ap-4740	170	26	general	general	ADJ
ap-4740	170	27	formula	formula	NOUN
ap-4740	170	28	cq	cq	PROPN
ap-4740	170	29	,	,	PUNCT
ap-4740	170	30	n	n	PROPN
ap-4740	170	31	(	(	PUNCT
ap-4740	170	32	k	k	PROPN
ap-4740	170	33	−	−	PROPN
ap-4740	170	34	2−	2−	NUM
ap-4740	170	35	q	q	NOUN
ap-4740	170	36	)	)	PUNCT
ap-4740	170	37	!	!	PUNCT
ap-4740	171	1	=	=	PUNCT
ap-4740	172	1	−	−	PROPN
ap-4740	172	2	q−1∑	q−1∑	NUM
ap-4740	172	3	t=0	t=0	PROPN
ap-4740	173	1	[	[	X
ap-4740	173	2	2(n−	2(n−	NUM
ap-4740	173	3	1)ak−t	1)ak−t	NUM
ap-4740	173	4	+	+	NUM
ap-4740	173	5	bk−t−1]m(q−t,0̇	bk−t−1]m(q−t,0̇	NOUN
ap-4740	173	6	)	)	PUNCT
ap-4740	173	7	−	−	PUNCT
ap-4740	174	1	[	[	X
ap-4740	174	2	q/2]∑	q/2]∑	VERB
ap-4740	174	3	s=1	s=1	ADP
ap-4740	174	4	q−2s∑	q−2s∑	PROPN
ap-4740	174	5	t=0	t=0	X
ap-4740	174	6	2ak−tm(q−t−s	2ak−tm(q−t−s	PROPN
ap-4740	174	7	,	,	PUNCT
ap-4740	174	8	s,0̇	s,0̇	NOUN
ap-4740	174	9	)	)	PUNCT
ap-4740	174	10	−	−	PROPN
ap-4740	174	11	n(n−	n(n−	NOUN
ap-4740	174	12	1	1	NUM
ap-4740	174	13	)	)	PUNCT
ap-4740	174	14	k(k	k(k	NOUN
ap-4740	174	15	−	−	NOUN
ap-4740	174	16	1	1	NUM
ap-4740	174	17	)	)	PUNCT
ap-4740	174	18	q(2k	q(2k	ADJ
ap-4740	174	19	−	−	PROPN
ap-4740	174	20	q	q	NOUN
ap-4740	174	21	−	−	PROPN
ap-4740	174	22	1)ak−q	1)ak−q	PROPN
ap-4740	174	23	−	−	PROPN
ap-4740	174	24	n	n	CCONJ
ap-4740	174	25	k	k	NOUN
ap-4740	175	1	−	−	PROPN
ap-4740	176	1	1qbk−q−1	1qbk−q−1	NUM
ap-4740	176	2	,	,	PUNCT
ap-4740	176	3	q	q	NOUN
ap-4740	176	4	=	=	SYM
ap-4740	176	5	1	1	NUM
ap-4740	176	6	,	,	PUNCT
ap-4740	176	7	2	2	NUM
ap-4740	176	8	,	,	PUNCT
ap-4740	176	9	.	.	PUNCT
ap-4740	176	10	.	.	PUNCT
ap-4740	176	11	.	.	PUNCT
ap-4740	177	1	,	,	PUNCT
ap-4740	178	1	k	k	PROPN
ap-4740	178	2	−	−	PROPN
ap-4740	178	3	2	2	NUM
ap-4740	178	4	,	,	PUNCT
ap-4740	178	5	(	(	PUNCT
ap-4740	178	6	2.22	2.22	NUM
ap-4740	178	7	)	)	PUNCT
ap-4740	178	8	where	where	SCONJ
ap-4740	178	9	[	[	X
ap-4740	178	10	q/2	q/2	NUM
ap-4740	178	11	]	]	X
ap-4740	178	12	denotes	denote	VERB
ap-4740	178	13	the	the	DET
ap-4740	178	14	largest	large	ADJ
ap-4740	178	15	integer	integer	NOUN
ap-4740	178	16	contained	contain	VERB
ap-4740	178	17	in	in	ADP
ap-4740	178	18	q/2	q/2	PROPN
ap-4740	178	19	.	.	PUNCT
ap-4740	179	1	at	at	ADP
ap-4740	179	2	this	this	DET
ap-4740	179	3	stage	stage	NOUN
ap-4740	179	4	,	,	PUNCT
ap-4740	179	5	equation	equation	NOUN
ap-4740	179	6	(	(	PUNCT
ap-4740	179	7	2.22	2.22	NUM
ap-4740	179	8	)	)	PUNCT
ap-4740	179	9	is	be	AUX
ap-4740	179	10	a	a	DET
ap-4740	179	11	conjecture	conjecture	NOUN
ap-4740	179	12	,	,	PUNCT
ap-4740	179	13	which	which	PRON
ap-4740	179	14	might	might	AUX
ap-4740	179	15	be	be	AUX
ap-4740	179	16	proved	prove	VERB
ap-4740	179	17	from	from	ADP
ap-4740	179	18	(	(	PUNCT
ap-4740	179	19	2.20	2.20	NUM
ap-4740	179	20	)	)	PUNCT
ap-4740	179	21	by	by	ADP
ap-4740	179	22	determining	determine	VERB
ap-4740	179	23	cq	cq	PROPN
ap-4740	179	24	,	,	PUNCT
ap-4740	179	25	n	n	PROPN
ap-4740	179	26	for	for	ADP
ap-4740	179	27	any	any	DET
ap-4740	179	28	q	q	NOUN
ap-4740	179	29	∈	∈	PROPN
ap-4740	179	30	{	{	PUNCT
ap-4740	179	31	1	1	NUM
ap-4740	179	32	,	,	PUNCT
ap-4740	179	33	2	2	NUM
ap-4740	179	34	,	,	PUNCT
ap-4740	179	35	.	.	PUNCT
ap-4740	179	36	.	.	PUNCT
ap-4740	180	1	.	.	PUNCT
ap-4740	181	1	,	,	PUNCT
ap-4740	182	1	k	k	PROPN
ap-4740	183	1	−	−	PROPN
ap-4740	184	1	2	2	NUM
ap-4740	184	2	}	}	PUNCT
ap-4740	184	3	.	.	PUNCT
ap-4740	185	1	this	this	PRON
ap-4740	185	2	would	would	AUX
ap-4740	185	3	,	,	PUNCT
ap-4740	185	4	however	however	ADV
ap-4740	185	5	,	,	PUNCT
ap-4740	185	6	be	be	AUX
ap-4740	185	7	a	a	DET
ap-4740	185	8	rather	rather	ADV
ap-4740	185	9	complicated	complicated	ADJ
ap-4740	185	10	derivation	derivation	NOUN
ap-4740	185	11	.	.	PUNCT
ap-4740	186	1	in	in	ADP
ap-4740	186	2	section	section	NOUN
ap-4740	186	3	4	4	NUM
ap-4740	186	4	,	,	PUNCT
ap-4740	186	5	we	we	PRON
ap-4740	186	6	will	will	AUX
ap-4740	186	7	proceed	proceed	VERB
ap-4740	186	8	to	to	PART
ap-4740	186	9	show	show	VERB
ap-4740	186	10	that	that	SCONJ
ap-4740	186	11	a	a	DET
ap-4740	186	12	much	much	ADV
ap-4740	186	13	easier	easy	ADJ
ap-4740	186	14	proof	proof	NOUN
ap-4740	186	15	of	of	ADP
ap-4740	186	16	(	(	PUNCT
ap-4740	186	17	2.22	2.22	NUM
ap-4740	186	18	)	)	PUNCT
ap-4740	186	19	can	can	AUX
ap-4740	186	20	be	be	AUX
ap-4740	186	21	found	find	VERB
ap-4740	186	22	by	by	ADP
ap-4740	186	23	comparing	compare	VERB
ap-4740	186	24	the	the	DET
ap-4740	186	25	results	result	NOUN
ap-4740	186	26	of	of	ADP
ap-4740	186	27	the	the	DET
ap-4740	186	28	present	present	ADJ
ap-4740	186	29	approach	approach	NOUN
ap-4740	186	30	with	with	ADP
ap-4740	186	31	those	those	PRON
ap-4740	186	32	of	of	ADP
ap-4740	186	33	the	the	DET
ap-4740	186	34	fba	fba	PROPN
ap-4740	186	35	one	one	NUM
ap-4740	186	36	.	.	PUNCT
ap-4740	187	1	3	3	X
ap-4740	187	2	.	.	X
ap-4740	187	3	functional	functional	ADJ
ap-4740	187	4	bethe	bethe	ADJ
ap-4740	187	5	ansatz	ansatz	ADJ
ap-4740	187	6	method	method	NOUN
ap-4740	187	7	in	in	ADP
ap-4740	187	8	its	its	PRON
ap-4740	187	9	most	most	ADV
ap-4740	187	10	general	general	ADJ
ap-4740	187	11	form	form	NOUN
ap-4740	187	12	,	,	PUNCT
ap-4740	187	13	the	the	DET
ap-4740	187	14	fba	fba	PROPN
ap-4740	187	15	method	method	NOUN
ap-4740	187	16	also	also	ADV
ap-4740	187	17	starts	start	VERB
ap-4740	187	18	from	from	ADP
ap-4740	187	19	equation	equation	NOUN
ap-4740	187	20	(	(	PUNCT
ap-4740	187	21	2.1	2.1	NUM
ap-4740	187	22	)	)	PUNCT
ap-4740	187	23	,	,	PUNCT
ap-4740	187	24	with	with	ADP
ap-4740	187	25	x(z	x(z	PROPN
ap-4740	187	26	)	)	PUNCT
ap-4740	187	27	,	,	PUNCT
ap-4740	187	28	y	y	PROPN
ap-4740	187	29	(	(	PUNCT
ap-4740	187	30	z	z	NOUN
ap-4740	187	31	)	)	PUNCT
ap-4740	187	32	,	,	PUNCT
ap-4740	187	33	z(z	z(z	NOUN
ap-4740	187	34	)	)	PUNCT
ap-4740	187	35	given	give	VERB
ap-4740	187	36	in	in	ADP
ap-4740	187	37	(	(	PUNCT
ap-4740	187	38	2.2	2.2	NUM
ap-4740	187	39	)	)	PUNCT
ap-4740	187	40	,	,	PUNCT
ap-4740	187	41	and	and	CCONJ
ap-4740	187	42	considers	consider	VERB
ap-4740	187	43	polynomial	polynomial	ADJ
ap-4740	187	44	solutions	solution	NOUN
ap-4740	187	45	of	of	ADP
ap-4740	187	46	type	type	NOUN
ap-4740	187	47	(	(	PUNCT
ap-4740	187	48	2.12	2.12	NUM
ap-4740	187	49	)	)	PUNCT
ap-4740	187	50	with	with	ADP
ap-4740	187	51	real	real	ADJ
ap-4740	187	52	and	and	CCONJ
ap-4740	187	53	distinct	distinct	ADJ
ap-4740	187	54	roots	root	NOUN
ap-4740	187	55	z1	z1	VERB
ap-4740	187	56	,	,	PUNCT
ap-4740	187	57	z2	z2	PROPN
ap-4740	187	58	,	,	PUNCT
ap-4740	187	59	.	.	PUNCT
ap-4740	187	60	.	.	PUNCT
ap-4740	188	1	.	.	PUNCT
ap-4740	189	1	,	,	PUNCT
ap-4740	189	2	zn	zn	PROPN
ap-4740	190	1	[	[	X
ap-4740	190	2	11–13	11–13	NUM
ap-4740	190	3	]	]	X
ap-4740	190	4	.	.	PUNCT
ap-4740	191	1	equation	equation	NOUN
ap-4740	191	2	(	(	PUNCT
ap-4740	191	3	2.1	2.1	NUM
ap-4740	191	4	)	)	PUNCT
ap-4740	191	5	is	be	AUX
ap-4740	191	6	then	then	ADV
ap-4740	191	7	rewritten	rewrite	VERB
ap-4740	191	8	as	as	ADP
ap-4740	191	9	−	−	PROPN
ap-4740	191	10	c0	c0	NOUN
ap-4740	191	11	=	=	PUNCT
ap-4740	191	12	(	(	PUNCT
ap-4740	191	13	k∑	k∑	NOUN
ap-4740	191	14	l=0	l=0	PROPN
ap-4740	191	15	alz	alz	PROPN
ap-4740	191	16	l	l	PROPN
ap-4740	191	17	)	)	PUNCT
ap-4740	192	1	n∑	n∑	PROPN
ap-4740	192	2	i=1	i=1	PROPN
ap-4740	193	1	1	1	NUM
ap-4740	193	2	z	z	NOUN
ap-4740	193	3	−	−	PROPN
ap-4740	193	4	zi	zi	NOUN
ap-4740	193	5	n∑	n∑	PROPN
ap-4740	194	1	j=1	j=1	PROPN
ap-4740	195	1	j	j	PROPN
ap-4740	195	2	6	6	NUM
ap-4740	195	3	=	=	NOUN
ap-4740	195	4	i	i	PROPN
ap-4740	195	5	2	2	NUM
ap-4740	195	6	zi	zi	NOUN
ap-4740	195	7	−	−	PROPN
ap-4740	195	8	zj	zj	PROPN
ap-4740	195	9	+	+	CCONJ
ap-4740	195	10	(	(	PUNCT
ap-4740	195	11	k−1∑	k−1∑	PROPN
ap-4740	195	12	l=0	l=0	PROPN
ap-4740	195	13	blz	blz	PROPN
ap-4740	195	14	l	l	PROPN
ap-4740	195	15	)	)	PUNCT
ap-4740	196	1	n∑	n∑	PROPN
ap-4740	196	2	i=1	i=1	PROPN
ap-4740	197	1	1	1	NUM
ap-4740	197	2	z	z	NOUN
ap-4740	197	3	−	−	PROPN
ap-4740	197	4	zi	zi	NOUN
ap-4740	197	5	+	+	CCONJ
ap-4740	197	6	k−2∑	k−2∑	PROPN
ap-4740	198	1	l=1	l=1	NOUN
ap-4740	198	2	clz	clz	NOUN
ap-4740	198	3	l.	l.	NOUN
ap-4740	198	4	(	(	PUNCT
ap-4740	198	5	3.1	3.1	NUM
ap-4740	198	6	)	)	PUNCT
ap-4740	198	7	the	the	DET
ap-4740	198	8	left	left	ADJ
ap-4740	198	9	-	-	PUNCT
ap-4740	198	10	hand	hand	NOUN
ap-4740	198	11	side	side	NOUN
ap-4740	198	12	of	of	ADP
ap-4740	198	13	this	this	DET
ap-4740	198	14	equation	equation	NOUN
ap-4740	198	15	is	be	AUX
ap-4740	198	16	a	a	DET
ap-4740	198	17	constant	constant	ADJ
ap-4740	198	18	,	,	PUNCT
ap-4740	198	19	while	while	SCONJ
ap-4740	198	20	the	the	DET
ap-4740	198	21	right	right	ADJ
ap-4740	198	22	-	-	PUNCT
ap-4740	198	23	hand	hand	NOUN
ap-4740	198	24	one	one	NOUN
ap-4740	198	25	is	be	AUX
ap-4740	198	26	a	a	DET
ap-4740	198	27	meromorphic	meromorphic	ADJ
ap-4740	198	28	function	function	NOUN
ap-4740	198	29	with	with	ADP
ap-4740	198	30	simple	simple	ADJ
ap-4740	198	31	poles	pole	NOUN
ap-4740	198	32	at	at	ADP
ap-4740	198	33	z	z	PROPN
ap-4740	198	34	=	=	SYM
ap-4740	198	35	zi	zi	PROPN
ap-4740	198	36	and	and	CCONJ
ap-4740	198	37	a	a	DET
ap-4740	198	38	singularity	singularity	NOUN
ap-4740	198	39	at	at	ADP
ap-4740	198	40	z	z	PROPN
ap-4740	198	41	=	=	PRON
ap-4740	198	42	∞.	∞.	PROPN
ap-4740	198	43	since	since	SCONJ
ap-4740	198	44	the	the	DET
ap-4740	198	45	residues	residue	NOUN
ap-4740	198	46	at	at	ADP
ap-4740	198	47	the	the	DET
ap-4740	198	48	simple	simple	ADJ
ap-4740	198	49	poles	pole	NOUN
ap-4740	198	50	are	be	AUX
ap-4740	198	51	given	give	VERB
ap-4740	198	52	by	by	ADP
ap-4740	198	53	res(−c0)z	res(−c0)z	NOUN
ap-4740	198	54	=	=	NOUN
ap-4740	198	55	zi	zi	NOUN
ap-4740	198	56	=	=	PUNCT
ap-4740	198	57	(	(	PUNCT
ap-4740	198	58	k∑	k∑	NOUN
ap-4740	198	59	l=0	l=0	PROPN
ap-4740	199	1	alz	alz	PROPN
ap-4740	200	1	l	l	NOUN
ap-4740	200	2	i	i	NOUN
ap-4740	200	3	)	)	PUNCT
ap-4740	201	1	n∑	n∑	NOUN
ap-4740	202	1	j=1	j=1	PROPN
ap-4740	202	2	j	j	PROPN
ap-4740	202	3	6	6	NUM
ap-4740	202	4	=	=	NOUN
ap-4740	202	5	i	i	PROPN
ap-4740	202	6	2	2	NUM
ap-4740	202	7	zi	zi	NOUN
ap-4740	202	8	−	−	PROPN
ap-4740	202	9	zj	zj	PROPN
ap-4740	202	10	+	+	CCONJ
ap-4740	202	11	k−1∑	k−1∑	PROPN
ap-4740	202	12	l=0	l=0	PROPN
ap-4740	202	13	blz	blz	PROPN
ap-4740	203	1	l	l	PROPN
ap-4740	204	1	i	i	PRON
ap-4740	204	2	,	,	PUNCT
ap-4740	204	3	(	(	PUNCT
ap-4740	204	4	3.2	3.2	NUM
ap-4740	204	5	)	)	PUNCT
ap-4740	204	6	equation	equation	NOUN
ap-4740	204	7	(	(	PUNCT
ap-4740	204	8	3.1	3.1	NUM
ap-4740	204	9	)	)	PUNCT
ap-4740	204	10	yields	yield	NOUN
ap-4740	204	11	−	−	PROPN
ap-4740	204	12	c0	c0	PROPN
ap-4740	204	13	=	=	SYM
ap-4740	204	14	k∑	k∑	PROPN
ap-4740	205	1	l=1	l=1	X
ap-4740	205	2	al	al	PROPN
ap-4740	205	3	n∑	n∑	PROPN
ap-4740	205	4	i=1	i=1	PROPN
ap-4740	206	1	l−1∑	l−1∑	PROPN
ap-4740	206	2	m=0	m=0	PROPN
ap-4740	206	3	zmi	zmi	PROPN
ap-4740	207	1	z	z	PROPN
ap-4740	207	2	l−m−1	l−m−1	PROPN
ap-4740	207	3	n∑	n∑	PROPN
ap-4740	208	1	j=1	j=1	PROPN
ap-4740	208	2	j	j	PROPN
ap-4740	208	3	6	6	NUM
ap-4740	208	4	=	=	NOUN
ap-4740	208	5	i	i	PROPN
ap-4740	208	6	2	2	NUM
ap-4740	208	7	zi	zi	NOUN
ap-4740	208	8	−	−	PROPN
ap-4740	208	9	zj	zj	PROPN
ap-4740	208	10	+	+	CCONJ
ap-4740	208	11	k−1∑	k−1∑	PROPN
ap-4740	209	1	l=1	l=1	INTJ
ap-4740	209	2	bl	bl	INTJ
ap-4740	209	3	n∑	n∑	PROPN
ap-4740	209	4	i=1	i=1	PROPN
ap-4740	210	1	l−1∑	l−1∑	PROPN
ap-4740	210	2	m=0	m=0	PROPN
ap-4740	210	3	zmi	zmi	PROPN
ap-4740	210	4	z	z	PROPN
ap-4740	210	5	l−m−1	l−m−1	NOUN
ap-4740	211	1	+	+	CCONJ
ap-4740	211	2	k−2∑	k−2∑	PROPN
ap-4740	211	3	l=1	l=1	NOUN
ap-4740	211	4	clz	clz	NOUN
ap-4740	211	5	l	l	NOUN
ap-4740	212	1	+	+	CCONJ
ap-4740	212	2	n∑	n∑	PROPN
ap-4740	212	3	i=1	i=1	PROPN
ap-4740	212	4	res(−c0)z	res(−c0)z	NOUN
ap-4740	212	5	=	=	PROPN
ap-4740	212	6	zi	zi	NOUN
ap-4740	212	7	z	z	NOUN
ap-4740	212	8	−	−	PROPN
ap-4740	212	9	zi	zi	NOUN
ap-4740	212	10	.	.	PUNCT
ap-4740	213	1	(	(	PUNCT
ap-4740	213	2	3.3	3.3	NUM
ap-4740	213	3	)	)	PUNCT
ap-4740	213	4	121	121	NUM
ap-4740	213	5	christiane	christiane	NOUN
ap-4740	213	6	quesne	quesne	NOUN
ap-4740	213	7	acta	acta	PROPN
ap-4740	213	8	polytechnica	polytechnica	PROPN
ap-4740	213	9	on	on	ADP
ap-4740	213	10	defining	define	VERB
ap-4740	213	11	sm	sm	PROPN
ap-4740	213	12	=	=	PUNCT
ap-4740	213	13	n∑	n∑	PROPN
ap-4740	213	14	i=1	i=1	PROPN
ap-4740	213	15	n∑	n∑	PROPN
ap-4740	214	1	j=1	j=1	PROPN
ap-4740	214	2	j	j	PROPN
ap-4740	215	1	6	6	NUM
ap-4740	215	2	=	=	NOUN
ap-4740	215	3	i	i	PROPN
ap-4740	215	4	zmi	zmi	PROPN
ap-4740	215	5	zi	zi	PROPN
ap-4740	215	6	−	−	PROPN
ap-4740	216	1	zj	zj	PROPN
ap-4740	216	2	,	,	PUNCT
ap-4740	216	3	tm	tm	PROPN
ap-4740	216	4	=	=	PROPN
ap-4740	216	5	n∑	n∑	PROPN
ap-4740	216	6	i=1	i=1	PROPN
ap-4740	216	7	zmi	zmi	PROPN
ap-4740	216	8	,	,	PUNCT
ap-4740	216	9	(	(	PUNCT
ap-4740	216	10	3.4	3.4	NUM
ap-4740	216	11	)	)	PUNCT
ap-4740	216	12	and	and	CCONJ
ap-4740	216	13	observing	observe	VERB
ap-4740	216	14	that	that	DET
ap-4740	216	15	s0	s0	NOUN
ap-4740	216	16	=	=	PUNCT
ap-4740	216	17	0	0	PROPN
ap-4740	216	18	,	,	PUNCT
ap-4740	216	19	this	this	DET
ap-4740	216	20	relation	relation	NOUN
ap-4740	216	21	becomes	become	VERB
ap-4740	216	22	−	−	PROPN
ap-4740	216	23	c0	c0	NOUN
ap-4740	216	24	=	=	SYM
ap-4740	216	25	2	2	NUM
ap-4740	216	26	k∑	k∑	NOUN
ap-4740	216	27	l=2	l=2	PUNCT
ap-4740	216	28	al	al	PROPN
ap-4740	216	29	l−1∑	l−1∑	PROPN
ap-4740	216	30	m=1	m=1	PROPN
ap-4740	216	31	smz	smz	NOUN
ap-4740	216	32	l−m−1	l−m−1	PROPN
ap-4740	216	33	+	+	CCONJ
ap-4740	216	34	k−1∑	k−1∑	PROPN
ap-4740	216	35	l=1	l=1	X
ap-4740	216	36	bl	bl	PROPN
ap-4740	216	37	l−1∑	l−1∑	PROPN
ap-4740	216	38	m=0	m=0	PROPN
ap-4740	216	39	tmz	tmz	PROPN
ap-4740	216	40	l−m−1	l−m−1	NOUN
ap-4740	216	41	+	+	CCONJ
ap-4740	217	1	k−2∑	k−2∑	PROPN
ap-4740	217	2	l=1	l=1	NOUN
ap-4740	217	3	clz	clz	NOUN
ap-4740	217	4	l	l	NOUN
ap-4740	218	1	+	+	CCONJ
ap-4740	218	2	n∑	n∑	PROPN
ap-4740	218	3	i=1	i=1	PROPN
ap-4740	218	4	res(−c0)z	res(−c0)z	NOUN
ap-4740	218	5	=	=	PROPN
ap-4740	218	6	zi	zi	NOUN
ap-4740	218	7	z	z	PROPN
ap-4740	218	8	−	−	PROPN
ap-4740	218	9	zi	zi	NOUN
ap-4740	218	10	,	,	PUNCT
ap-4740	218	11	(	(	PUNCT
ap-4740	218	12	3.5	3.5	NUM
ap-4740	218	13	)	)	PUNCT
ap-4740	218	14	or	or	CCONJ
ap-4740	218	15	,	,	PUNCT
ap-4740	218	16	with	with	ADP
ap-4740	218	17	q	q	PROPN
ap-4740	218	18	≡	≡	PROPN
ap-4740	218	19	l	l	NOUN
ap-4740	218	20	−m−	−m−	NOUN
ap-4740	218	21	1	1	NUM
ap-4740	218	22	in	in	ADP
ap-4740	218	23	the	the	DET
ap-4740	218	24	first	first	ADJ
ap-4740	218	25	two	two	NUM
ap-4740	218	26	terms	term	NOUN
ap-4740	218	27	and	and	CCONJ
ap-4740	218	28	q	q	DET
ap-4740	218	29	≡	≡	PROPN
ap-4740	218	30	l	l	PROPN
ap-4740	218	31	in	in	ADP
ap-4740	218	32	the	the	DET
ap-4740	218	33	third	third	ADJ
ap-4740	218	34	one	one	NUM
ap-4740	218	35	,	,	PUNCT
ap-4740	218	36	−	−	PROPN
ap-4740	218	37	c0	c0	NOUN
ap-4740	218	38	=	=	SYM
ap-4740	218	39	2	2	NUM
ap-4740	218	40	k−2∑	k−2∑	PROPN
ap-4740	218	41	q=0	q=0	NOUN
ap-4740	218	42	zq	zq	PROPN
ap-4740	218	43	k−1−q∑	k−1−q∑	PROPN
ap-4740	218	44	m=1	m=1	X
ap-4740	218	45	aq+m+1sm	aq+m+1sm	X
ap-4740	218	46	+	+	CCONJ
ap-4740	218	47	k−2∑	k−2∑	PROPN
ap-4740	218	48	q=0	q=0	NOUN
ap-4740	218	49	zq	zq	PROPN
ap-4740	218	50	k−2−q∑	k−2−q∑	PROPN
ap-4740	218	51	m=0	m=0	PROPN
ap-4740	218	52	bq+m+1tm	bq+m+1tm	PUNCT
ap-4740	218	53	+	+	CCONJ
ap-4740	218	54	k−2∑	k−2∑	PROPN
ap-4740	218	55	q=1	q=1	X
ap-4740	218	56	zqcq	zqcq	NOUN
ap-4740	219	1	+	+	CCONJ
ap-4740	219	2	n∑	n∑	PROPN
ap-4740	219	3	i=1	i=1	PROPN
ap-4740	219	4	res(−c0)z	res(−c0)z	NOUN
ap-4740	220	1	=	=	PROPN
ap-4740	220	2	zi	zi	NOUN
ap-4740	220	3	z	z	NOUN
ap-4740	220	4	−	−	PROPN
ap-4740	220	5	zi	zi	NOUN
ap-4740	220	6	.	.	PUNCT
ap-4740	221	1	(	(	PUNCT
ap-4740	221	2	3.6	3.6	NUM
ap-4740	221	3	)	)	PUNCT
ap-4740	221	4	the	the	DET
ap-4740	221	5	right	right	ADJ
ap-4740	221	6	-	-	PUNCT
ap-4740	221	7	hand	hand	NOUN
ap-4740	221	8	side	side	NOUN
ap-4740	221	9	of	of	ADP
ap-4740	221	10	this	this	DET
ap-4740	221	11	equation	equation	NOUN
ap-4740	221	12	will	will	AUX
ap-4740	221	13	be	be	AUX
ap-4740	221	14	a	a	DET
ap-4740	221	15	constant	constant	ADJ
ap-4740	221	16	if	if	SCONJ
ap-4740	222	1	and	and	CCONJ
ap-4740	222	2	only	only	ADV
ap-4740	222	3	if	if	SCONJ
ap-4740	222	4	the	the	DET
ap-4740	222	5	coefficients	coefficient	NOUN
ap-4740	222	6	of	of	ADP
ap-4740	222	7	zq	zq	PROPN
ap-4740	222	8	,	,	PUNCT
ap-4740	222	9	q	q	PROPN
ap-4740	222	10	=	=	SYM
ap-4740	222	11	1	1	NUM
ap-4740	222	12	,	,	PUNCT
ap-4740	222	13	2	2	NUM
ap-4740	222	14	,	,	PUNCT
ap-4740	222	15	.	.	PUNCT
ap-4740	222	16	.	.	PUNCT
ap-4740	223	1	.	.	PUNCT
ap-4740	224	1	,	,	PUNCT
ap-4740	224	2	k−	k−	PROPN
ap-4740	224	3	2	2	NUM
ap-4740	224	4	,	,	PUNCT
ap-4740	224	5	and	and	CCONJ
ap-4740	224	6	all	all	DET
ap-4740	224	7	the	the	DET
ap-4740	224	8	residues	residue	NOUN
ap-4740	224	9	at	at	ADP
ap-4740	224	10	the	the	DET
ap-4740	224	11	simple	simple	ADJ
ap-4740	224	12	poles	pole	NOUN
ap-4740	224	13	vanish	vanish	VERB
ap-4740	224	14	.	.	PUNCT
ap-4740	225	1	this	this	DET
ap-4740	225	2	yields	yield	NOUN
ap-4740	225	3	cq	cq	PROPN
ap-4740	225	4	,	,	PUNCT
ap-4740	225	5	q	q	NOUN
ap-4740	226	1	=	=	NOUN
ap-4740	226	2	1	1	NUM
ap-4740	226	3	,	,	PUNCT
ap-4740	226	4	2	2	NUM
ap-4740	226	5	,	,	PUNCT
ap-4740	226	6	.	.	PUNCT
ap-4740	226	7	.	.	PUNCT
ap-4740	227	1	.	.	PUNCT
ap-4740	228	1	,	,	PUNCT
ap-4740	229	1	k	k	PROPN
ap-4740	230	1	−	−	PROPN
ap-4740	230	2	2	2	NUM
ap-4740	230	3	,	,	PUNCT
ap-4740	230	4	in	in	ADP
ap-4740	230	5	terms	term	NOUN
ap-4740	230	6	of	of	ADP
ap-4740	230	7	the	the	DET
ap-4740	230	8	coefficients	coefficient	NOUN
ap-4740	230	9	of	of	ADP
ap-4740	230	10	x(z	x(z	PROPN
ap-4740	230	11	)	)	PUNCT
ap-4740	230	12	,	,	PUNCT
ap-4740	230	13	y	y	PROPN
ap-4740	230	14	(	(	PUNCT
ap-4740	230	15	z	z	NOUN
ap-4740	230	16	)	)	PUNCT
ap-4740	230	17	,	,	PUNCT
ap-4740	230	18	and	and	CCONJ
ap-4740	230	19	the	the	DET
ap-4740	230	20	roots	root	NOUN
ap-4740	230	21	of	of	ADP
ap-4740	230	22	yn(z	yn(z	NOUN
ap-4740	230	23	)	)	PUNCT
ap-4740	230	24	,	,	PUNCT
ap-4740	230	25	cq	cq	PROPN
ap-4740	230	26	=	=	SYM
ap-4740	230	27	−2	−2	PROPN
ap-4740	230	28	k−1−q∑	k−1−q∑	PROPN
ap-4740	230	29	m=1	m=1	X
ap-4740	230	30	aq+m+1sm	aq+m+1sm	X
ap-4740	230	31	−	−	PROPN
ap-4740	230	32	k−2−q∑	k−2−q∑	PROPN
ap-4740	230	33	m=0	m=0	PROPN
ap-4740	230	34	bq+m+1tm	bq+m+1tm	PUNCT
ap-4740	230	35	,	,	PUNCT
ap-4740	230	36	q	q	X
ap-4740	230	37	=	=	SYM
ap-4740	230	38	1	1	NUM
ap-4740	230	39	,	,	PUNCT
ap-4740	230	40	2	2	NUM
ap-4740	230	41	,	,	PUNCT
ap-4740	230	42	.	.	PUNCT
ap-4740	230	43	.	.	PUNCT
ap-4740	231	1	.	.	PUNCT
ap-4740	232	1	,	,	PUNCT
ap-4740	233	1	k	k	PROPN
ap-4740	233	2	−	−	PROPN
ap-4740	233	3	2	2	NUM
ap-4740	233	4	,	,	PUNCT
ap-4740	233	5	(	(	PUNCT
ap-4740	233	6	3.7	3.7	NUM
ap-4740	233	7	)	)	PUNCT
ap-4740	233	8	as	as	ADV
ap-4740	233	9	well	well	ADV
ap-4740	233	10	as	as	ADP
ap-4740	233	11	the	the	DET
ap-4740	233	12	n	n	PRON
ap-4740	233	13	algebraic	algebraic	ADJ
ap-4740	233	14	equations	equation	NOUN
ap-4740	233	15	determining	determine	VERB
ap-4740	233	16	the	the	DET
ap-4740	233	17	roots	root	NOUN
ap-4740	233	18	,	,	PUNCT
ap-4740	233	19	i.e.	i.e.	X
ap-4740	233	20	,	,	PUNCT
ap-4740	233	21	the	the	DET
ap-4740	233	22	bethe	bethe	ADJ
ap-4740	233	23	ansatz	ansatz	ADJ
ap-4740	233	24	equations	equation	NOUN
ap-4740	233	25	,	,	PUNCT
ap-4740	233	26	n∑	n∑	NOUN
ap-4740	233	27	j=1	j=1	PROPN
ap-4740	234	1	j	j	PROPN
ap-4740	234	2	6	6	NUM
ap-4740	234	3	=	=	NOUN
ap-4740	234	4	i	i	PROPN
ap-4740	234	5	2	2	NUM
ap-4740	234	6	zi	zi	NOUN
ap-4740	234	7	−	−	PROPN
ap-4740	234	8	zj	zj	PROPN
ap-4740	234	9	+	+	CCONJ
ap-4740	234	10	∑k−1	∑k−1	X
ap-4740	234	11	l=0	l=0	PROPN
ap-4740	234	12	blz	blz	PROPN
ap-4740	234	13	l	l	NOUN
ap-4740	234	14	i∑k	i∑k	NOUN
ap-4740	235	1	l=0	l=0	PROPN
ap-4740	235	2	alz	alz	NOUN
ap-4740	236	1	l	l	NOUN
ap-4740	236	2	i	i	NOUN
ap-4740	236	3	=	=	NOUN
ap-4740	236	4	0	0	PROPN
ap-4740	236	5	,	,	PUNCT
ap-4740	236	6	i	i	PRON
ap-4740	236	7	=	=	NOUN
ap-4740	236	8	1	1	NUM
ap-4740	236	9	,	,	PUNCT
ap-4740	236	10	2	2	NUM
ap-4740	236	11	,	,	PUNCT
ap-4740	236	12	.	.	PUNCT
ap-4740	236	13	.	.	PUNCT
ap-4740	236	14	.	.	PUNCT
ap-4740	237	1	,	,	PUNCT
ap-4740	237	2	n.	n.	NOUN
ap-4740	237	3	(	(	PUNCT
ap-4740	237	4	3.8	3.8	NUM
ap-4740	237	5	)	)	PUNCT
ap-4740	237	6	the	the	DET
ap-4740	237	7	remaining	remain	VERB
ap-4740	237	8	constant	constant	ADJ
ap-4740	237	9	leads	lead	NOUN
ap-4740	237	10	to	to	ADP
ap-4740	237	11	the	the	DET
ap-4740	237	12	value	value	NOUN
ap-4740	237	13	of	of	ADP
ap-4740	237	14	c0	c0	PROPN
ap-4740	237	15	,	,	PUNCT
ap-4740	238	1	c0	c0	PROPN
ap-4740	238	2	=	=	PROPN
ap-4740	238	3	−2	−2	PROPN
ap-4740	238	4	k−1∑	k−1∑	PROPN
ap-4740	238	5	m=1	m=1	PROPN
ap-4740	238	6	am+1sm	am+1sm	NOUN
ap-4740	238	7	−	−	NOUN
ap-4740	238	8	k−2∑	k−2∑	PROPN
ap-4740	238	9	m=0	m=0	PROPN
ap-4740	238	10	bm+1tm	bm+1tm	PROPN
ap-4740	238	11	.	.	PUNCT
ap-4740	239	1	(	(	PUNCT
ap-4740	239	2	3.9	3.9	NUM
ap-4740	239	3	)	)	PUNCT
ap-4740	239	4	it	it	PRON
ap-4740	239	5	remains	remain	VERB
ap-4740	239	6	to	to	PART
ap-4740	239	7	find	find	VERB
ap-4740	239	8	the	the	DET
ap-4740	239	9	explicit	explicit	ADJ
ap-4740	239	10	expressions	expression	NOUN
ap-4740	239	11	of	of	ADP
ap-4740	239	12	sm	sm	PROPN
ap-4740	239	13	and	and	CCONJ
ap-4740	239	14	tm	tm	PROPN
ap-4740	239	15	.	.	PROPN
ap-4740	240	1	for	for	ADP
ap-4740	240	2	the	the	DET
ap-4740	240	3	smallest	small	ADJ
ap-4740	240	4	allowed	allow	VERB
ap-4740	240	5	m	m	VERB
ap-4740	240	6	values	value	NOUN
ap-4740	240	7	,	,	PUNCT
ap-4740	240	8	it	it	PRON
ap-4740	240	9	is	be	AUX
ap-4740	240	10	obvious	obvious	ADJ
ap-4740	240	11	that	that	SCONJ
ap-4740	240	12	s1	s1	NOUN
ap-4740	240	13	=	=	SYM
ap-4740	240	14	1	1	NUM
ap-4740	240	15	2n(n−	2n(n−	NUM
ap-4740	240	16	1	1	NUM
ap-4740	240	17	)	)	PUNCT
ap-4740	240	18	,	,	PUNCT
ap-4740	240	19	t0	t0	X
ap-4740	241	1	=	=	PUNCT
ap-4740	242	1	n.	n.	PROPN
ap-4740	242	2	(	(	PUNCT
ap-4740	242	3	3.10	3.10	NUM
ap-4740	242	4	)	)	PUNCT
ap-4740	242	5	for	for	ADP
ap-4740	242	6	higher	high	ADJ
ap-4740	242	7	m	m	PROPN
ap-4740	242	8	values	value	NOUN
ap-4740	242	9	,	,	PUNCT
ap-4740	242	10	sm	sm	PROPN
ap-4740	242	11	can	can	AUX
ap-4740	242	12	be	be	AUX
ap-4740	242	13	written	write	VERB
ap-4740	242	14	as	as	ADP
ap-4740	242	15	a	a	DET
ap-4740	242	16	linear	linear	ADJ
ap-4740	242	17	combination	combination	NOUN
ap-4740	242	18	of	of	ADP
ap-4740	242	19	monomial	monomial	ADJ
ap-4740	242	20	symmetric	symmetric	ADJ
ap-4740	242	21	polynomials	polynomial	NOUN
ap-4740	242	22	in	in	ADP
ap-4740	242	23	z1	z1	NOUN
ap-4740	242	24	,	,	PUNCT
ap-4740	242	25	z2	z2	PROPN
ap-4740	242	26	,	,	PUNCT
ap-4740	242	27	.	.	PUNCT
ap-4740	242	28	.	.	PUNCT
ap-4740	242	29	.	.	PUNCT
ap-4740	243	1	,	,	PUNCT
ap-4740	243	2	zn	zn	X
ap-4740	243	3	.	.	PUNCT
ap-4740	244	1	from	from	ADP
ap-4740	244	2	sm	sm	PROPN
ap-4740	244	3	=	=	SYM
ap-4740	244	4	1	1	NUM
ap-4740	244	5	2	2	NUM
ap-4740	244	6	n∑	n∑	NOUN
ap-4740	244	7	i=1	i=1	PROPN
ap-4740	244	8	n∑	n∑	PROPN
ap-4740	245	1	j=1	j=1	PROPN
ap-4740	245	2	j	j	PROPN
ap-4740	246	1	6	6	NUM
ap-4740	246	2	=	=	NOUN
ap-4740	246	3	i	i	PRON
ap-4740	246	4	zmi	zmi	VERB
ap-4740	246	5	−	−	VERB
ap-4740	247	1	zmj	zmj	NOUN
ap-4740	247	2	zi	zi	NOUN
ap-4740	247	3	−	−	PROPN
ap-4740	247	4	zj	zj	X
ap-4740	247	5	=	=	SYM
ap-4740	247	6	1	1	NUM
ap-4740	247	7	2	2	NUM
ap-4740	247	8	n∑	n∑	NOUN
ap-4740	247	9	i=1	i=1	PROPN
ap-4740	248	1	n∑	n∑	PROPN
ap-4740	249	1	j=1	j=1	PROPN
ap-4740	249	2	j	j	PROPN
ap-4740	250	1	6	6	NUM
ap-4740	251	1	=	=	NOUN
ap-4740	252	1	i	i	PRON
ap-4740	252	2	m−1∑	m−1∑	NUM
ap-4740	252	3	p=0	p=0	PROPN
ap-4740	252	4	zm−1−p	zm−1−p	NUM
ap-4740	252	5	i	i	PRON
ap-4740	252	6	zpj	zpj	PROPN
ap-4740	252	7	,	,	PUNCT
ap-4740	252	8	(	(	PUNCT
ap-4740	252	9	3.11	3.11	NUM
ap-4740	252	10	)	)	PUNCT
ap-4740	252	11	we	we	PRON
ap-4740	252	12	get	get	VERB
ap-4740	252	13	for	for	ADP
ap-4740	252	14	odd	odd	ADJ
ap-4740	252	15	m	m	PROPN
ap-4740	252	16	≥	≥	NOUN
ap-4740	252	17	3	3	NUM
ap-4740	252	18	,	,	PUNCT
ap-4740	252	19	sm	sm	PROPN
ap-4740	252	20	=	=	SYM
ap-4740	252	21	1	1	NUM
ap-4740	252	22	2	2	NUM
ap-4740	252	23	n∑	n∑	NOUN
ap-4740	252	24	i=1	i=1	PROPN
ap-4740	252	25	n∑	n∑	PROPN
ap-4740	253	1	j=1	j=1	PROPN
ap-4740	253	2	j	j	PROPN
ap-4740	254	1	6	6	NUM
ap-4740	254	2	=	=	NOUN
ap-4740	254	3	i	i	PRON
ap-4740	254	4	[	[	PUNCT
ap-4740	254	5	zm−1	zm−1	NOUN
ap-4740	254	6	i	i	PRON
ap-4740	254	7	+	+	CCONJ
ap-4740	254	8	zm−1	zm−1	PROPN
ap-4740	254	9	j	j	PROPN
ap-4740	254	10	+	+	CCONJ
ap-4740	254	11	(	(	PUNCT
ap-4740	254	12	m−3)/2∑	m−3)/2∑	NOUN
ap-4740	254	13	p=1	p=1	PROPN
ap-4740	254	14	(	(	PUNCT
ap-4740	254	15	zm−1−p	zm−1−p	NUM
ap-4740	254	16	i	i	PRON
ap-4740	254	17	zpj	zpj	VERB
ap-4740	255	1	+	+	CCONJ
ap-4740	255	2	zpi	zpi	PROPN
ap-4740	255	3	z	z	PROPN
ap-4740	255	4	m−1−p	m−1−p	X
ap-4740	255	5	j	j	PROPN
ap-4740	255	6	)	)	PUNCT
ap-4740	256	1	+	+	CCONJ
ap-4740	256	2	z	z	NOUN
ap-4740	256	3	(	(	PUNCT
ap-4740	256	4	m−1)/2	m−1)/2	NOUN
ap-4740	256	5	i	i	PRON
ap-4740	256	6	z	z	PROPN
ap-4740	256	7	(	(	PUNCT
ap-4740	256	8	m−1)/2	m−1)/2	X
ap-4740	256	9	j	j	X
ap-4740	256	10	]	]	X
ap-4740	257	1	=	=	PUNCT
ap-4740	257	2	(	(	PUNCT
ap-4740	257	3	n−	n−	NOUN
ap-4740	257	4	1	1	NUM
ap-4740	257	5	)	)	PUNCT
ap-4740	257	6	n∑	n∑	NOUN
ap-4740	258	1	i=1	i=1	PROPN
ap-4740	259	1	zm−1	zm−1	PROPN
ap-4740	260	1	i	i	PRON
ap-4740	260	2	+	+	PROPN
ap-4740	260	3	n∑	n∑	NOUN
ap-4740	260	4	i	i	PROPN
ap-4740	260	5	,	,	PUNCT
ap-4740	260	6	j=1	j=1	PROPN
ap-4740	260	7	i	i	PRON
ap-4740	260	8	6	6	NUM
ap-4740	260	9	=	=	SYM
ap-4740	260	10	j	j	X
ap-4740	260	11	(	(	PUNCT
ap-4740	260	12	m−3)/2∑	m−3)/2∑	PROPN
ap-4740	260	13	p=1	p=1	PROPN
ap-4740	260	14	zm−1−p	zm−1−p	NUM
ap-4740	260	15	i	i	PRON
ap-4740	260	16	zpj	zpj	VERB
ap-4740	261	1	+	+	CCONJ
ap-4740	261	2	n∑	n∑	PROPN
ap-4740	261	3	i	i	PROPN
ap-4740	261	4	,	,	PUNCT
ap-4740	261	5	j=1	j=1	PROPN
ap-4740	262	1	i	i	PRON
ap-4740	262	2	<	<	X
ap-4740	262	3	j	j	PROPN
ap-4740	262	4	z	z	PROPN
ap-4740	262	5	(	(	PUNCT
ap-4740	262	6	m−1)/2	m−1)/2	ADP
ap-4740	262	7	i	i	PRON
ap-4740	262	8	z	z	PROPN
ap-4740	262	9	(	(	PUNCT
ap-4740	262	10	m−1)/2	m−1)/2	X
ap-4740	262	11	j	j	PROPN
ap-4740	263	1	=	=	PUNCT
ap-4740	264	1	(	(	PUNCT
ap-4740	264	2	n−	n−	NOUN
ap-4740	264	3	1)m(m−1,0̇	1)m(m−1,0̇	NUM
ap-4740	264	4	)	)	PUNCT
ap-4740	265	1	+	+	CCONJ
ap-4740	265	2	(	(	PUNCT
ap-4740	265	3	m−1)/2∑	m−1)/2∑	INTJ
ap-4740	265	4	p=1	p=1	PROPN
ap-4740	265	5	m(m−1−p	m(m−1−p	PROPN
ap-4740	265	6	,	,	PUNCT
ap-4740	265	7	p,0̇	p,0̇	NOUN
ap-4740	265	8	)	)	PUNCT
ap-4740	265	9	,	,	PUNCT
ap-4740	265	10	(	(	PUNCT
ap-4740	265	11	3.12	3.12	NUM
ap-4740	265	12	)	)	PUNCT
ap-4740	265	13	and	and	CCONJ
ap-4740	265	14	for	for	ADP
ap-4740	265	15	even	even	ADV
ap-4740	265	16	m	m	PRON
ap-4740	265	17	≥	≥	NOUN
ap-4740	265	18	2	2	NUM
ap-4740	265	19	,	,	PUNCT
ap-4740	265	20	sm	sm	NOUN
ap-4740	265	21	=	=	NOUN
ap-4740	265	22	1	1	NUM
ap-4740	265	23	2	2	NUM
ap-4740	265	24	n∑	n∑	NOUN
ap-4740	265	25	i=1	i=1	PROPN
ap-4740	265	26	n∑	n∑	PROPN
ap-4740	266	1	j=1	j=1	PROPN
ap-4740	266	2	j	j	PROPN
ap-4740	267	1	6	6	NUM
ap-4740	267	2	=	=	NOUN
ap-4740	267	3	i	i	PRON
ap-4740	267	4	[	[	PUNCT
ap-4740	267	5	zm−1	zm−1	NOUN
ap-4740	267	6	i	i	PRON
ap-4740	267	7	+	+	CCONJ
ap-4740	267	8	zm−1	zm−1	PROPN
ap-4740	267	9	j	j	PROPN
ap-4740	267	10	+	+	CCONJ
ap-4740	267	11	(	(	PUNCT
ap-4740	267	12	m−2)/2∑	m−2)/2∑	PROPN
ap-4740	267	13	p=1	p=1	PROPN
ap-4740	267	14	(	(	PUNCT
ap-4740	267	15	zm−1−p	zm−1−p	NUM
ap-4740	267	16	i	i	PRON
ap-4740	267	17	zpj	zpj	VERB
ap-4740	268	1	+	+	CCONJ
ap-4740	268	2	zpi	zpi	PROPN
ap-4740	268	3	z	z	PROPN
ap-4740	268	4	m−1−p	m−1−p	PROPN
ap-4740	268	5	j	j	PROPN
ap-4740	268	6	)	)	PUNCT
ap-4740	268	7	]	]	PUNCT
ap-4740	269	1	=	=	PUNCT
ap-4740	269	2	(	(	PUNCT
ap-4740	269	3	n−	n−	NOUN
ap-4740	269	4	1	1	NUM
ap-4740	269	5	)	)	PUNCT
ap-4740	269	6	n∑	n∑	NOUN
ap-4740	270	1	i=1	i=1	PROPN
ap-4740	271	1	zm−1	zm−1	PROPN
ap-4740	272	1	i	i	PRON
ap-4740	272	2	+	+	PROPN
ap-4740	272	3	n∑	n∑	NOUN
ap-4740	272	4	i	i	PROPN
ap-4740	272	5	,	,	PUNCT
ap-4740	272	6	j=1	j=1	ADJ
ap-4740	272	7	i6	i6	NOUN
ap-4740	272	8	=	=	SYM
ap-4740	272	9	j	j	PROPN
ap-4740	272	10	(	(	PUNCT
ap-4740	272	11	m−2)/2∑	m−2)/2∑	PROPN
ap-4740	272	12	p=1	p=1	PROPN
ap-4740	272	13	zm−1−p	zm−1−p	PROPN
ap-4740	272	14	i	i	PRON
ap-4740	272	15	zpj	zpj	PUNCT
ap-4740	272	16	=	=	PUNCT
ap-4740	272	17	(	(	PUNCT
ap-4740	272	18	n−	n−	NOUN
ap-4740	272	19	1)m(m−1,0̇	1)m(m−1,0̇	NUM
ap-4740	272	20	)	)	PUNCT
ap-4740	272	21	+	+	CCONJ
ap-4740	272	22	(	(	PUNCT
ap-4740	272	23	m−2)/2∑	m−2)/2∑	PROPN
ap-4740	272	24	p=1	p=1	PROPN
ap-4740	272	25	m(m−1−p	m(m−1−p	PROPN
ap-4740	272	26	,	,	PUNCT
ap-4740	272	27	p,0̇	p,0̇	NOUN
ap-4740	272	28	)	)	PUNCT
ap-4740	272	29	.	.	PUNCT
ap-4740	273	1	(	(	PUNCT
ap-4740	273	2	3.13	3.13	NUM
ap-4740	273	3	)	)	PUNCT
ap-4740	273	4	122	122	NUM
ap-4740	273	5	vol	vol	NOUN
ap-4740	273	6	.	.	PUNCT
ap-4740	274	1	58	58	NUM
ap-4740	275	1	no	no	INTJ
ap-4740	275	2	.	.	PUNCT
ap-4740	276	1	2/2018	2/2018	NOUN
ap-4740	276	2	quasi	quasi	ADJ
ap-4740	276	3	-	-	ADJ
ap-4740	276	4	exactly	exactly	ADV
ap-4740	276	5	solvable	solvable	ADJ
ap-4740	276	6	schrödinger	schrödinger	ADJ
ap-4740	276	7	equations	equation	NOUN
ap-4740	276	8	hence	hence	ADV
ap-4740	276	9	,	,	PUNCT
ap-4740	276	10	sm	sm	PROPN
ap-4740	276	11	=	=	PUNCT
ap-4740	276	12	(	(	PUNCT
ap-4740	276	13	n−	n−	NOUN
ap-4740	276	14	1)m(m−1,0̇	1)m(m−1,0̇	NUM
ap-4740	276	15	)	)	PUNCT
ap-4740	276	16	+	+	CCONJ
ap-4740	277	1	[	[	X
ap-4740	277	2	(	(	PUNCT
ap-4740	277	3	m−1)/2]∑	m−1)/2]∑	PROPN
ap-4740	277	4	p=1	p=1	PROPN
ap-4740	277	5	m(m−1−p	m(m−1−p	PROPN
ap-4740	277	6	,	,	PUNCT
ap-4740	277	7	p,0̇	p,0̇	NOUN
ap-4740	277	8	)	)	PUNCT
ap-4740	277	9	,	,	PUNCT
ap-4740	277	10	m	m	VERB
ap-4740	277	11	≥	≥	NOUN
ap-4740	277	12	2	2	NUM
ap-4740	277	13	.	.	PUNCT
ap-4740	277	14	(	(	PUNCT
ap-4740	277	15	3.14	3.14	NUM
ap-4740	277	16	)	)	PUNCT
ap-4740	277	17	furthermore	furthermore	ADV
ap-4740	277	18	,	,	PUNCT
ap-4740	277	19	it	it	PRON
ap-4740	277	20	is	be	AUX
ap-4740	277	21	obvious	obvious	ADJ
ap-4740	277	22	that	that	SCONJ
ap-4740	277	23	tm	tm	PROPN
ap-4740	277	24	=	=	PROPN
ap-4740	277	25	m(m,0̇	m(m,0̇	PROPN
ap-4740	277	26	)	)	PUNCT
ap-4740	277	27	,	,	PUNCT
ap-4740	277	28	m	m	VERB
ap-4740	277	29	≥	≥	NOUN
ap-4740	277	30	1	1	NUM
ap-4740	277	31	.	.	PUNCT
ap-4740	278	1	(	(	PUNCT
ap-4740	278	2	3.15	3.15	NUM
ap-4740	278	3	)	)	PUNCT
ap-4740	278	4	on	on	ADP
ap-4740	278	5	replacing	replace	VERB
ap-4740	278	6	sm	sm	ADV
ap-4740	278	7	and	and	CCONJ
ap-4740	278	8	tm	tm	NOUN
ap-4740	278	9	by	by	ADP
ap-4740	278	10	their	their	PRON
ap-4740	278	11	explicit	explicit	ADJ
ap-4740	278	12	values	value	NOUN
ap-4740	278	13	in	in	ADP
ap-4740	278	14	(	(	PUNCT
ap-4740	278	15	3.7	3.7	NUM
ap-4740	278	16	)	)	PUNCT
ap-4740	278	17	and	and	CCONJ
ap-4740	278	18	(	(	PUNCT
ap-4740	278	19	3.9	3.9	NUM
ap-4740	278	20	)	)	PUNCT
ap-4740	278	21	,	,	PUNCT
ap-4740	278	22	we	we	PRON
ap-4740	278	23	get	get	VERB
ap-4740	278	24	ck−2	ck−2	NOUN
ap-4740	278	25	=	=	PRON
ap-4740	278	26	−n(n−	−n(n−	X
ap-4740	279	1	1)ak	1)ak	NUM
ap-4740	280	1	−	−	ADP
ap-4740	280	2	nbk−1	nbk−1	NOUN
ap-4740	280	3	,	,	PUNCT
ap-4740	280	4	(	(	PUNCT
ap-4740	280	5	3.16	3.16	NUM
ap-4740	280	6	)	)	PUNCT
ap-4740	280	7	cl	cl	NOUN
ap-4740	280	8	=	=	SYM
ap-4740	280	9	−n(n−	−n(n−	PUNCT
ap-4740	280	10	1)al+2	1)al+2	NUM
ap-4740	280	11	−	−	ADP
ap-4740	280	12	nbl+1	nbl+1	PRON
ap-4740	280	13	−	−	PROPN
ap-4740	280	14	2	2	NUM
ap-4740	280	15	k−1−l∑	k−1−l∑	PROPN
ap-4740	280	16	m=2	m=2	PROPN
ap-4740	280	17	al+m+1	al+m+1	PROPN
ap-4740	280	18	[	[	PUNCT
ap-4740	280	19	(	(	PUNCT
ap-4740	280	20	n−	n−	NOUN
ap-4740	280	21	1)m(m−1,0̇	1)m(m−1,0̇	NUM
ap-4740	280	22	)	)	PUNCT
ap-4740	280	23	+	+	CCONJ
ap-4740	281	1	[	[	X
ap-4740	281	2	(	(	PUNCT
ap-4740	281	3	m−1)/2]∑	m−1)/2]∑	PROPN
ap-4740	281	4	p=1	p=1	PROPN
ap-4740	281	5	m(m−1−p	m(m−1−p	PROPN
ap-4740	281	6	,	,	PUNCT
ap-4740	281	7	p,0̇	p,0̇	NOUN
ap-4740	281	8	)	)	PUNCT
ap-4740	281	9	]	]	PUNCT
ap-4740	282	1	−	−	PROPN
ap-4740	282	2	k−2−l∑	k−2−l∑	PROPN
ap-4740	282	3	m=1	m=1	PROPN
ap-4740	282	4	bl+m+1m(m,0̇	bl+m+1m(m,0̇	PROPN
ap-4740	282	5	)	)	PUNCT
ap-4740	282	6	,	,	PUNCT
ap-4740	282	7	l	l	NOUN
ap-4740	282	8	=	=	SYM
ap-4740	282	9	0	0	NUM
ap-4740	282	10	,	,	PUNCT
ap-4740	282	11	1	1	NUM
ap-4740	282	12	,	,	PUNCT
ap-4740	282	13	.	.	PUNCT
ap-4740	282	14	.	.	PUNCT
ap-4740	282	15	.	.	PUNCT
ap-4740	283	1	,	,	PUNCT
ap-4740	284	1	k	k	PROPN
ap-4740	284	2	−	−	PROPN
ap-4740	284	3	3	3	NUM
ap-4740	284	4	,	,	PUNCT
ap-4740	284	5	(	(	PUNCT
ap-4740	284	6	3.17	3.17	NUM
ap-4740	284	7	)	)	PUNCT
ap-4740	284	8	in	in	ADP
ap-4740	284	9	terms	term	NOUN
ap-4740	284	10	of	of	ADP
ap-4740	284	11	monomial	monomial	ADJ
ap-4740	284	12	symmetric	symmetric	ADJ
ap-4740	284	13	polynomials	polynomial	NOUN
ap-4740	284	14	in	in	ADP
ap-4740	284	15	the	the	DET
ap-4740	284	16	polynomial	polynomial	ADJ
ap-4740	284	17	roots	root	NOUN
ap-4740	284	18	.	.	PUNCT
ap-4740	285	1	this	this	PRON
ap-4740	285	2	is	be	AUX
ap-4740	285	3	the	the	DET
ap-4740	285	4	third	third	ADJ
ap-4740	285	5	main	main	ADJ
ap-4740	285	6	result	result	NOUN
ap-4740	285	7	of	of	ADP
ap-4740	285	8	this	this	DET
ap-4740	285	9	paper	paper	NOUN
ap-4740	285	10	.	.	PUNCT
ap-4740	286	1	4	4	X
ap-4740	286	2	.	.	X
ap-4740	286	3	comparison	comparison	NOUN
ap-4740	286	4	between	between	ADP
ap-4740	286	5	the	the	DET
ap-4740	286	6	two	two	NUM
ap-4740	286	7	approaches	approach	NOUN
ap-4740	286	8	direct	direct	ADJ
ap-4740	286	9	comparison	comparison	NOUN
ap-4740	286	10	between	between	ADP
ap-4740	286	11	equations	equation	NOUN
ap-4740	286	12	(	(	PUNCT
ap-4740	286	13	2.10	2.10	NUM
ap-4740	286	14	)	)	PUNCT
ap-4740	286	15	,	,	PUNCT
ap-4740	286	16	(	(	PUNCT
ap-4740	286	17	2.11	2.11	NUM
ap-4740	286	18	)	)	PUNCT
ap-4740	286	19	and	and	CCONJ
ap-4740	286	20	equations	equation	NOUN
ap-4740	286	21	(	(	PUNCT
ap-4740	286	22	3.16	3.16	NUM
ap-4740	286	23	)	)	PUNCT
ap-4740	286	24	,	,	PUNCT
ap-4740	286	25	(	(	PUNCT
ap-4740	286	26	3.17	3.17	NUM
ap-4740	286	27	)	)	PUNCT
ap-4740	286	28	shows	show	VERB
ap-4740	286	29	that	that	SCONJ
ap-4740	286	30	ck−2	ck−2	PROPN
ap-4740	286	31	is	be	AUX
ap-4740	286	32	given	give	VERB
ap-4740	286	33	by	by	ADP
ap-4740	286	34	the	the	DET
ap-4740	286	35	same	same	ADJ
ap-4740	286	36	expression	expression	NOUN
ap-4740	286	37	in	in	ADP
ap-4740	286	38	both	both	DET
ap-4740	286	39	approaches	approach	NOUN
ap-4740	286	40	,	,	PUNCT
ap-4740	286	41	while	while	SCONJ
ap-4740	286	42	for	for	ADP
ap-4740	286	43	l	l	NOUN
ap-4740	286	44	=	=	SYM
ap-4740	286	45	0	0	NUM
ap-4740	286	46	,	,	PUNCT
ap-4740	286	47	1	1	NUM
ap-4740	286	48	,	,	PUNCT
ap-4740	286	49	.	.	PUNCT
ap-4740	286	50	.	.	PUNCT
ap-4740	287	1	.	.	PUNCT
ap-4740	288	1	,	,	PUNCT
ap-4740	289	1	k	k	PROPN
ap-4740	290	1	−	−	PROPN
ap-4740	290	2	3	3	NUM
ap-4740	290	3	,	,	PUNCT
ap-4740	290	4	cl	cl	NOUN
ap-4740	290	5	is	be	AUX
ap-4740	290	6	written	write	VERB
ap-4740	290	7	in	in	ADP
ap-4740	290	8	terms	term	NOUN
ap-4740	290	9	of	of	ADP
ap-4740	290	10	al+2	al+2	NOUN
ap-4740	290	11	and	and	CCONJ
ap-4740	290	12	bl+1	bl+1	NOUN
ap-4740	290	13	,	,	PUNCT
ap-4740	290	14	as	as	ADV
ap-4740	290	15	well	well	ADV
ap-4740	290	16	as	as	SCONJ
ap-4740	290	17	the	the	DET
ap-4740	290	18	integration	integration	NOUN
ap-4740	290	19	constant	constant	ADJ
ap-4740	290	20	ck−l−2,n	ck−l−2,n	ADV
ap-4740	290	21	in	in	ADP
ap-4740	290	22	the	the	DET
ap-4740	290	23	first	first	ADJ
ap-4740	290	24	one	one	NUM
ap-4740	290	25	or	or	CCONJ
ap-4740	290	26	a	a	DET
ap-4740	290	27	linear	linear	ADJ
ap-4740	290	28	combination	combination	NOUN
ap-4740	290	29	of	of	ADP
ap-4740	290	30	monomial	monomial	ADJ
ap-4740	290	31	symmetric	symmetric	ADJ
ap-4740	290	32	polynomials	polynomial	NOUN
ap-4740	290	33	in	in	ADP
ap-4740	290	34	z1	z1	NOUN
ap-4740	290	35	,	,	PUNCT
ap-4740	290	36	z2	z2	PROPN
ap-4740	290	37	,	,	PUNCT
ap-4740	290	38	.	.	PUNCT
ap-4740	290	39	.	.	PUNCT
ap-4740	290	40	.	.	PUNCT
ap-4740	291	1	,	,	PUNCT
ap-4740	291	2	zn	zn	X
ap-4740	291	3	in	in	ADP
ap-4740	291	4	the	the	DET
ap-4740	291	5	second	second	ADJ
ap-4740	291	6	one	one	NUM
ap-4740	291	7	.	.	PUNCT
ap-4740	292	1	equating	equate	VERB
ap-4740	292	2	the	the	DET
ap-4740	292	3	two	two	NUM
ap-4740	292	4	expressions	expression	NOUN
ap-4740	292	5	for	for	ADP
ap-4740	292	6	cl	cl	NOUN
ap-4740	292	7	,	,	PUNCT
ap-4740	292	8	l	l	NOUN
ap-4740	292	9	=	=	SYM
ap-4740	292	10	0	0	NUM
ap-4740	292	11	,	,	PUNCT
ap-4740	292	12	1	1	NUM
ap-4740	292	13	,	,	PUNCT
ap-4740	292	14	.	.	PUNCT
ap-4740	292	15	.	.	PUNCT
ap-4740	293	1	.	.	PUNCT
ap-4740	294	1	,	,	PUNCT
ap-4740	295	1	k	k	PROPN
ap-4740	295	2	−	−	PROPN
ap-4740	295	3	3	3	NUM
ap-4740	295	4	,	,	PUNCT
ap-4740	295	5	yields	yield	NOUN
ap-4740	295	6	ck−2−l	ck−2−l	ADV
ap-4740	295	7	,	,	PUNCT
ap-4740	295	8	n	n	PRON
ap-4740	295	9	l	l	NOUN
ap-4740	295	10	!	!	PUNCT
ap-4740	296	1	=	=	PRON
ap-4740	296	2	−2	−2	NOUN
ap-4740	297	1	k−1−l∑	k−1−l∑	NOUN
ap-4740	297	2	m=2	m=2	PROPN
ap-4740	297	3	al+m+1	al+m+1	PROPN
ap-4740	297	4	[	[	PUNCT
ap-4740	297	5	(	(	PUNCT
ap-4740	297	6	n−	n−	NOUN
ap-4740	297	7	1)m(m−1,0̇	1)m(m−1,0̇	NUM
ap-4740	297	8	)	)	PUNCT
ap-4740	297	9	+	+	CCONJ
ap-4740	298	1	[	[	X
ap-4740	298	2	(	(	PUNCT
ap-4740	298	3	m−1)/2]∑	m−1)/2]∑	PROPN
ap-4740	298	4	p=1	p=1	PROPN
ap-4740	298	5	m(m−1−p	m(m−1−p	PROPN
ap-4740	298	6	,	,	PUNCT
ap-4740	298	7	p,0̇	p,0̇	NOUN
ap-4740	298	8	)	)	PUNCT
ap-4740	298	9	]	]	PUNCT
ap-4740	299	1	−	−	PROPN
ap-4740	299	2	k−2−l∑	k−2−l∑	PROPN
ap-4740	299	3	m=1	m=1	PROPN
ap-4740	299	4	bl+m+1m(m,0̇	bl+m+1m(m,0̇	PROPN
ap-4740	299	5	)	)	PUNCT
ap-4740	300	1	−	−	PROPN
ap-4740	300	2	n(n−	n(n−	PROPN
ap-4740	300	3	1	1	NUM
ap-4740	300	4	)	)	PUNCT
ap-4740	300	5	k(k	k(k	NOUN
ap-4740	300	6	−	−	NOUN
ap-4740	300	7	1	1	NUM
ap-4740	300	8	)	)	PUNCT
ap-4740	300	9	(	(	PUNCT
ap-4740	300	10	k	k	NOUN
ap-4740	301	1	−	−	PROPN
ap-4740	301	2	l	l	NOUN
ap-4740	301	3	−	−	PROPN
ap-4740	301	4	2)(k	2)(k	NUM
ap-4740	302	1	+	+	CCONJ
ap-4740	302	2	l	l	NOUN
ap-4740	303	1	+	+	CCONJ
ap-4740	303	2	1)al+2	1)al+2	NUM
ap-4740	303	3	−	−	NOUN
ap-4740	304	1	n	n	CCONJ
ap-4740	304	2	k	k	NOUN
ap-4740	304	3	−	−	PROPN
ap-4740	305	1	1(k	1(k	NUM
ap-4740	305	2	−	−	PROPN
ap-4740	305	3	l	l	NOUN
ap-4740	305	4	−	−	PROPN
ap-4740	305	5	2)bl+1	2)bl+1	NUM
ap-4740	305	6	,	,	PUNCT
ap-4740	305	7	l	l	PROPN
ap-4740	305	8	=	=	SYM
ap-4740	305	9	0	0	NUM
ap-4740	305	10	,	,	PUNCT
ap-4740	305	11	1	1	NUM
ap-4740	305	12	,	,	PUNCT
ap-4740	305	13	.	.	PUNCT
ap-4740	305	14	.	.	PUNCT
ap-4740	305	15	.	.	PUNCT
ap-4740	306	1	,	,	PUNCT
ap-4740	307	1	k	k	PROPN
ap-4740	307	2	−	−	NOUN
ap-4740	308	1	3	3	X
ap-4740	308	2	.	.	PUNCT
ap-4740	308	3	(	(	PUNCT
ap-4740	308	4	4.1	4.1	NUM
ap-4740	308	5	)	)	PUNCT
ap-4740	308	6	on	on	ADP
ap-4740	308	7	setting	set	VERB
ap-4740	308	8	q	q	PROPN
ap-4740	308	9	=	=	SYM
ap-4740	308	10	k	k	NOUN
ap-4740	308	11	−	−	PROPN
ap-4740	308	12	2−	2−	NUM
ap-4740	308	13	l	l	NOUN
ap-4740	308	14	in	in	ADP
ap-4740	308	15	equation	equation	NOUN
ap-4740	308	16	(	(	PUNCT
ap-4740	308	17	4.1	4.1	NUM
ap-4740	308	18	)	)	PUNCT
ap-4740	308	19	,	,	PUNCT
ap-4740	308	20	the	the	DET
ap-4740	308	21	latter	latter	ADJ
ap-4740	308	22	becomes	become	VERB
ap-4740	308	23	cq	cq	PROPN
ap-4740	308	24	,	,	PUNCT
ap-4740	308	25	n	n	PROPN
ap-4740	308	26	(	(	PUNCT
ap-4740	308	27	k	k	PROPN
ap-4740	308	28	−	−	PROPN
ap-4740	308	29	2−	2−	NUM
ap-4740	308	30	q	q	NOUN
ap-4740	308	31	)	)	PUNCT
ap-4740	308	32	!	!	PUNCT
ap-4740	309	1	=	=	PRON
ap-4740	310	1	−2	−2	NOUN
ap-4740	311	1	q+1∑	q+1∑	PROPN
ap-4740	311	2	m=2	m=2	PROPN
ap-4740	311	3	ak+m−1−q	ak+m−1−q	PROPN
ap-4740	311	4	[	[	PUNCT
ap-4740	311	5	(	(	PUNCT
ap-4740	311	6	n−	n−	NOUN
ap-4740	311	7	1)m(m−1,0̇	1)m(m−1,0̇	NUM
ap-4740	311	8	)	)	PUNCT
ap-4740	311	9	+	+	CCONJ
ap-4740	312	1	[	[	X
ap-4740	312	2	(	(	PUNCT
ap-4740	312	3	m−1)/2]∑	m−1)/2]∑	PROPN
ap-4740	312	4	p=1	p=1	PROPN
ap-4740	312	5	m(m−1−p	m(m−1−p	PROPN
ap-4740	312	6	,	,	PUNCT
ap-4740	312	7	p,0̇	p,0̇	NOUN
ap-4740	312	8	)	)	PUNCT
ap-4740	312	9	]	]	PUNCT
ap-4740	313	1	−	−	PROPN
ap-4740	313	2	q∑	q∑	PROPN
ap-4740	313	3	m=1	m=1	X
ap-4740	313	4	bk+m−1−qm(m,0̇	bk+m−1−qm(m,0̇	PROPN
ap-4740	313	5	)	)	PUNCT
ap-4740	313	6	−	−	PROPN
ap-4740	313	7	n(n−	n(n−	NOUN
ap-4740	313	8	1	1	NUM
ap-4740	313	9	)	)	PUNCT
ap-4740	313	10	k(k	k(k	NOUN
ap-4740	313	11	−	−	NOUN
ap-4740	313	12	1	1	NUM
ap-4740	313	13	)	)	PUNCT
ap-4740	313	14	q(2k	q(2k	ADJ
ap-4740	313	15	−	−	PROPN
ap-4740	313	16	q	q	NOUN
ap-4740	313	17	−	−	PROPN
ap-4740	313	18	1)ak−q	1)ak−q	PROPN
ap-4740	313	19	−	−	PROPN
ap-4740	313	20	n	n	CCONJ
ap-4740	313	21	k	k	NOUN
ap-4740	313	22	−	−	PROPN
ap-4740	314	1	1qbk−q−1	1qbk−q−1	NUM
ap-4740	314	2	,	,	PUNCT
ap-4740	314	3	l	l	NOUN
ap-4740	314	4	=	=	SYM
ap-4740	314	5	0	0	NUM
ap-4740	314	6	,	,	PUNCT
ap-4740	314	7	1	1	NUM
ap-4740	314	8	,	,	PUNCT
ap-4740	314	9	.	.	PUNCT
ap-4740	314	10	.	.	PUNCT
ap-4740	314	11	.	.	PUNCT
ap-4740	315	1	,	,	PUNCT
ap-4740	316	1	k	k	PROPN
ap-4740	316	2	−	−	PROPN
ap-4740	316	3	3	3	NUM
ap-4740	316	4	,	,	PUNCT
ap-4740	316	5	(	(	PUNCT
ap-4740	316	6	4.2	4.2	NUM
ap-4740	316	7	)	)	PUNCT
ap-4740	316	8	where	where	SCONJ
ap-4740	316	9	we	we	PRON
ap-4740	316	10	see	see	VERB
ap-4740	316	11	that	that	SCONJ
ap-4740	316	12	the	the	DET
ap-4740	316	13	last	last	ADJ
ap-4740	316	14	two	two	NUM
ap-4740	316	15	terms	term	NOUN
ap-4740	316	16	on	on	ADP
ap-4740	316	17	the	the	DET
ap-4740	316	18	right	right	ADJ
ap-4740	316	19	-	-	PUNCT
ap-4740	316	20	hand	hand	NOUN
ap-4740	316	21	side	side	NOUN
ap-4740	316	22	coincide	coincide	NOUN
ap-4740	316	23	with	with	ADP
ap-4740	316	24	the	the	DET
ap-4740	316	25	corresponding	corresponding	ADJ
ap-4740	316	26	ones	one	NOUN
ap-4740	316	27	in	in	ADP
ap-4740	316	28	equation	equation	NOUN
ap-4740	316	29	(	(	PUNCT
ap-4740	316	30	2.22	2.22	NUM
ap-4740	316	31	)	)	PUNCT
ap-4740	316	32	.	.	PUNCT
ap-4740	317	1	the	the	DET
ap-4740	317	2	other	other	ADJ
ap-4740	317	3	terms	term	NOUN
ap-4740	317	4	can	can	AUX
ap-4740	317	5	also	also	ADV
ap-4740	317	6	be	be	AUX
ap-4740	317	7	easily	easily	ADV
ap-4740	317	8	converted	convert	VERB
ap-4740	317	9	into	into	ADP
ap-4740	317	10	those	those	PRON
ap-4740	317	11	of	of	ADP
ap-4740	317	12	equation	equation	NOUN
ap-4740	317	13	(	(	PUNCT
ap-4740	317	14	2.22	2.22	NUM
ap-4740	317	15	)	)	PUNCT
ap-4740	317	16	by	by	ADP
ap-4740	317	17	changing	change	VERB
ap-4740	317	18	the	the	DET
ap-4740	317	19	summation	summation	NOUN
ap-4740	317	20	indices	index	NOUN
ap-4740	317	21	.	.	PUNCT
ap-4740	318	1	with	with	ADP
ap-4740	318	2	t	t	PROPN
ap-4740	318	3	=	=	PUNCT
ap-4740	318	4	q	q	PROPN
ap-4740	319	1	+	+	NUM
ap-4740	319	2	1−m	1−m	NUM
ap-4740	319	3	and	and	CCONJ
ap-4740	319	4	t	t	NOUN
ap-4740	319	5	=	=	SYM
ap-4740	319	6	q	q	NOUN
ap-4740	319	7	−m	−m	NOUN
ap-4740	319	8	,	,	PUNCT
ap-4740	319	9	we	we	PRON
ap-4740	319	10	can	can	AUX
ap-4740	319	11	indeed	indeed	ADV
ap-4740	319	12	rewrite	rewrite	VERB
ap-4740	319	13	q+1∑	q+1∑	PROPN
ap-4740	319	14	m=2	m=2	PROPN
ap-4740	319	15	ak+m−1−qm(m−1,0̇	ak+m−1−qm(m−1,0̇	NOUN
ap-4740	319	16	)	)	PUNCT
ap-4740	319	17	=	=	SYM
ap-4740	319	18	q−1∑	q−1∑	NUM
ap-4740	319	19	t=0	t=0	ADJ
ap-4740	319	20	ak−tm(q−t,0̇	ak−tm(q−t,0̇	NOUN
ap-4740	319	21	)	)	PUNCT
ap-4740	319	22	(	(	PUNCT
ap-4740	319	23	4.3	4.3	NUM
ap-4740	319	24	)	)	PUNCT
ap-4740	319	25	and	and	CCONJ
ap-4740	319	26	q∑	q∑	PROPN
ap-4740	319	27	m=1	m=1	X
ap-4740	319	28	bk+m−1−qm(m,0̇	bk+m−1−qm(m,0̇	PROPN
ap-4740	319	29	)	)	PUNCT
ap-4740	319	30	=	=	SYM
ap-4740	319	31	q−1∑	q−1∑	NUM
ap-4740	319	32	t=0	t=0	PUNCT
ap-4740	319	33	bk−t−1m(q−t,0̇	bk−t−1m(q−t,0̇	PROPN
ap-4740	319	34	)	)	PUNCT
ap-4740	319	35	,	,	PUNCT
ap-4740	319	36	(	(	PUNCT
ap-4740	319	37	4.4	4.4	NUM
ap-4740	319	38	)	)	PUNCT
ap-4740	319	39	respectively	respectively	ADV
ap-4740	319	40	.	.	PUNCT
ap-4740	320	1	furthermore	furthermore	ADV
ap-4740	320	2	,	,	PUNCT
ap-4740	320	3	t	t	PROPN
ap-4740	320	4	=	=	PUNCT
ap-4740	320	5	q	q	PROPN
ap-4740	321	1	+	+	NUM
ap-4740	321	2	1−m	1−m	NUM
ap-4740	321	3	and	and	CCONJ
ap-4740	321	4	s	s	NOUN
ap-4740	321	5	=	=	NOUN
ap-4740	321	6	p	p	NOUN
ap-4740	321	7	lead	lead	NOUN
ap-4740	321	8	to	to	ADP
ap-4740	321	9	q+1∑	q+1∑	PROPN
ap-4740	321	10	m=2	m=2	PROPN
ap-4740	321	11	ak+m−1−q	ak+m−1−q	PROPN
ap-4740	322	1	[	[	X
ap-4740	322	2	(	(	PUNCT
ap-4740	322	3	m−1)/2]∑	m−1)/2]∑	PROPN
ap-4740	322	4	p=1	p=1	PROPN
ap-4740	322	5	m(m−1−p	m(m−1−p	PROPN
ap-4740	322	6	,	,	PUNCT
ap-4740	322	7	p,0̇	p,0̇	X
ap-4740	322	8	)	)	PUNCT
ap-4740	323	1	=	=	SYM
ap-4740	323	2	q−1∑	q−1∑	NUM
ap-4740	323	3	t=0	t=0	ADJ
ap-4740	323	4	ak−t	ak−t	NOUN
ap-4740	323	5	[	[	X
ap-4740	323	6	(	(	PUNCT
ap-4740	323	7	q−t)/2]∑	q−t)/2]∑	ADJ
ap-4740	323	8	s=1	s=1	X
ap-4740	323	9	m(q−t−s	m(q−t−	NOUN
ap-4740	323	10	,	,	PUNCT
ap-4740	323	11	s,0̇	s,0̇	NOUN
ap-4740	323	12	)	)	PUNCT
ap-4740	323	13	=	=	PUNCT
ap-4740	324	1	[	[	X
ap-4740	324	2	q/2]∑	q/2]∑	VERB
ap-4740	324	3	s=1	s=1	ADP
ap-4740	324	4	q−2s∑	q−2s∑	PROPN
ap-4740	324	5	t=0	t=0	PROPN
ap-4740	324	6	ak−tm(q−t−s	ak−tm(q−t−s	PROPN
ap-4740	324	7	,	,	PUNCT
ap-4740	324	8	s,0̇	s,0̇	NOUN
ap-4740	324	9	)	)	PUNCT
ap-4740	324	10	.	.	PUNCT
ap-4740	325	1	(	(	PUNCT
ap-4740	325	2	4.5	4.5	X
ap-4740	325	3	)	)	PUNCT
ap-4740	325	4	collecting	collect	VERB
ap-4740	325	5	all	all	DET
ap-4740	325	6	the	the	DET
ap-4740	325	7	terms	term	NOUN
ap-4740	325	8	shows	show	VERB
ap-4740	325	9	that	that	SCONJ
ap-4740	325	10	equation	equation	NOUN
ap-4740	325	11	(	(	PUNCT
ap-4740	325	12	4.2	4.2	NUM
ap-4740	325	13	)	)	PUNCT
ap-4740	325	14	coincides	coincide	VERB
ap-4740	325	15	with	with	ADP
ap-4740	325	16	equation	equation	NOUN
ap-4740	325	17	(	(	PUNCT
ap-4740	325	18	2.22	2.22	NUM
ap-4740	325	19	)	)	PUNCT
ap-4740	325	20	,	,	PUNCT
ap-4740	325	21	which	which	PRON
ap-4740	325	22	is	be	AUX
ap-4740	325	23	therefore	therefore	ADV
ap-4740	325	24	proved	prove	VERB
ap-4740	325	25	.	.	PUNCT
ap-4740	326	1	this	this	PRON
ap-4740	326	2	is	be	AUX
ap-4740	326	3	the	the	DET
ap-4740	326	4	fourth	fourth	ADJ
ap-4740	326	5	main	main	ADJ
ap-4740	326	6	result	result	NOUN
ap-4740	326	7	of	of	ADP
ap-4740	326	8	the	the	DET
ap-4740	326	9	present	present	ADJ
ap-4740	326	10	paper	paper	NOUN
ap-4740	326	11	.	.	PUNCT
ap-4740	327	1	123	123	NUM
ap-4740	327	2	christiane	christiane	PROPN
ap-4740	327	3	quesne	quesne	NOUN
ap-4740	327	4	acta	acta	PROPN
ap-4740	327	5	polytechnica	polytechnica	PROPN
ap-4740	327	6	5	5	NUM
ap-4740	327	7	.	.	PUNCT
ap-4740	327	8	example	example	NOUN
ap-4740	327	9	:	:	PUNCT
ap-4740	327	10	qes	qes	NOUN
ap-4740	327	11	extension	extension	NOUN
ap-4740	327	12	of	of	ADP
ap-4740	327	13	the	the	DET
ap-4740	327	14	mathews	mathews	NOUN
ap-4740	327	15	-	-	PUNCT
ap-4740	327	16	lakshmanan	lakshmanan	PROPN
ap-4740	327	17	nonlinear	nonlinear	ADJ
ap-4740	327	18	oscillator	oscillator	NOUN
ap-4740	327	19	the	the	DET
ap-4740	327	20	purpose	purpose	NOUN
ap-4740	327	21	of	of	ADP
ap-4740	327	22	the	the	DET
ap-4740	327	23	present	present	ADJ
ap-4740	327	24	section	section	NOUN
ap-4740	327	25	is	be	AUX
ap-4740	327	26	to	to	PART
ap-4740	327	27	illustrate	illustrate	VERB
ap-4740	327	28	the	the	DET
ap-4740	327	29	results	result	NOUN
ap-4740	327	30	of	of	ADP
ap-4740	327	31	previous	previous	ADJ
ap-4740	327	32	ones	one	NOUN
ap-4740	327	33	by	by	ADP
ap-4740	327	34	considering	consider	VERB
ap-4740	327	35	a	a	DET
ap-4740	327	36	qes	qes	NOUN
ap-4740	327	37	extension	extension	NOUN
ap-4740	327	38	of	of	ADP
ap-4740	327	39	the	the	DET
ap-4740	327	40	mathews	mathews	NOUN
ap-4740	327	41	-	-	PUNCT
ap-4740	327	42	lakshmanan	lakshmanan	PROPN
ap-4740	327	43	nonlinear	nonlinear	ADJ
ap-4740	327	44	oscillator	oscillator	NOUN
ap-4740	327	45	in	in	ADP
ap-4740	327	46	the	the	DET
ap-4740	327	47	simplest	simple	ADJ
ap-4740	327	48	case	case	NOUN
ap-4740	327	49	not	not	PART
ap-4740	327	50	amenable	amenable	ADJ
ap-4740	327	51	to	to	ADP
ap-4740	327	52	an	an	DET
ap-4740	327	53	sl(2,r	sl(2,r	NOUN
ap-4740	327	54	)	)	PUNCT
ap-4740	327	55	description	description	NOUN
ap-4740	327	56	,	,	PUNCT
ap-4740	327	57	and	and	CCONJ
ap-4740	327	58	which	which	PRON
ap-4740	327	59	corresponds	correspond	VERB
ap-4740	327	60	to	to	ADP
ap-4740	327	61	k	k	PROPN
ap-4740	327	62	=	=	PUNCT
ap-4740	327	63	4	4	X
ap-4740	327	64	.	.	PUNCT
ap-4740	328	1	the	the	DET
ap-4740	328	2	quantum	quantum	ADJ
ap-4740	328	3	version	version	NOUN
ap-4740	328	4	of	of	ADP
ap-4740	328	5	the	the	DET
ap-4740	328	6	classical	classical	ADJ
ap-4740	328	7	mathews	mathews	NOUN
ap-4740	328	8	-	-	PUNCT
ap-4740	328	9	lakshmanan	lakshmanan	ADJ
ap-4740	328	10	nonlinear	nonlinear	ADJ
ap-4740	328	11	oscillator	oscillator	NOUN
ap-4740	328	12	[	[	X
ap-4740	328	13	23	23	NUM
ap-4740	328	14	]	]	PUNCT
ap-4740	328	15	is	be	AUX
ap-4740	328	16	described	describe	VERB
ap-4740	328	17	by	by	ADP
ap-4740	328	18	the	the	DET
ap-4740	328	19	hamiltonian	hamiltonian	PROPN
ap-4740	329	1	[	[	X
ap-4740	329	2	24	24	NUM
ap-4740	329	3	,	,	PUNCT
ap-4740	329	4	25	25	NUM
ap-4740	329	5	]	]	PUNCT
ap-4740	329	6	h	h	NOUN
ap-4740	329	7	=	=	PUNCT
ap-4740	330	1	−(1	−(1	NOUN
ap-4740	330	2	+	+	NUM
ap-4740	330	3	λx2	λx2	NOUN
ap-4740	330	4	)	)	PUNCT
ap-4740	330	5	d	d	ADP
ap-4740	330	6	2	2	NUM
ap-4740	330	7	dx2	dx2	NOUN
ap-4740	330	8	−	−	PROPN
ap-4740	330	9	λx	λx	PROPN
ap-4740	331	1	d	d	X
ap-4740	331	2	dx	dx	PROPN
ap-4740	332	1	+	+	X
ap-4740	332	2	β(β	β(β	PUNCT
ap-4740	333	1	+	+	CCONJ
ap-4740	333	2	λ)x2	λ)x2	NOUN
ap-4740	333	3	1	1	NUM
ap-4740	333	4	+	+	CCONJ
ap-4740	333	5	λx2	λx2	NOUN
ap-4740	333	6	,	,	PUNCT
ap-4740	333	7	(	(	PUNCT
ap-4740	333	8	5.1	5.1	NUM
ap-4740	333	9	)	)	PUNCT
ap-4740	333	10	where	where	SCONJ
ap-4740	333	11	β	β	X
ap-4740	333	12	plays	play	VERB
ap-4740	333	13	the	the	DET
ap-4740	333	14	role	role	NOUN
ap-4740	333	15	of	of	ADP
ap-4740	333	16	the	the	DET
ap-4740	333	17	frequency	frequency	NOUN
ap-4740	333	18	ω	ω	PROPN
ap-4740	333	19	in	in	ADP
ap-4740	333	20	the	the	DET
ap-4740	333	21	standard	standard	ADJ
ap-4740	333	22	oscillator	oscillator	NOUN
ap-4740	333	23	and	and	CCONJ
ap-4740	333	24	the	the	DET
ap-4740	333	25	nonlinearity	nonlinearity	NOUN
ap-4740	333	26	parameter	parameter	NOUN
ap-4740	333	27	λ	λ	PROPN
ap-4740	333	28	6=	6=	ADP
ap-4740	333	29	0	0	NUM
ap-4740	333	30	enters	enter	VERB
ap-4740	333	31	both	both	CCONJ
ap-4740	333	32	the	the	DET
ap-4740	333	33	potential	potential	ADJ
ap-4740	333	34	energy	energy	NOUN
ap-4740	333	35	term	term	NOUN
ap-4740	333	36	and	and	CCONJ
ap-4740	333	37	the	the	DET
ap-4740	333	38	kinetic	kinetic	ADJ
ap-4740	333	39	energy	energy	NOUN
ap-4740	333	40	one	one	NOUN
ap-4740	333	41	,	,	PUNCT
ap-4740	333	42	giving	give	VERB
ap-4740	333	43	rise	rise	NOUN
ap-4740	333	44	there	there	ADV
ap-4740	333	45	to	to	ADP
ap-4740	333	46	the	the	DET
ap-4740	333	47	position	position	NOUN
ap-4740	333	48	-	-	PUNCT
ap-4740	333	49	dependent	dependent	ADJ
ap-4740	333	50	mass	mass	NOUN
ap-4740	333	51	m(x	m(x	PROPN
ap-4740	333	52	)	)	PUNCT
ap-4740	333	53	=	=	PUNCT
ap-4740	334	1	(	(	PUNCT
ap-4740	334	2	1	1	NUM
ap-4740	334	3	+	+	NUM
ap-4740	334	4	λx2)−1	λx2)−1	X
ap-4740	334	5	.	.	PUNCT
ap-4740	335	1	according	accord	VERB
ap-4740	335	2	to	to	ADP
ap-4740	335	3	whether	whether	SCONJ
ap-4740	335	4	λ	λ	PROPN
ap-4740	335	5	>	>	X
ap-4740	335	6	0	0	PUNCT
ap-4740	335	7	or	or	CCONJ
ap-4740	335	8	λ	λ	X
ap-4740	335	9	<	<	X
ap-4740	335	10	0	0	PROPN
ap-4740	335	11	,	,	PUNCT
ap-4740	335	12	the	the	DET
ap-4740	335	13	range	range	NOUN
ap-4740	335	14	of	of	ADP
ap-4740	335	15	the	the	DET
ap-4740	335	16	coordinate	coordinate	NOUN
ap-4740	335	17	x	x	X
ap-4740	335	18	is	be	AUX
ap-4740	335	19	(	(	PUNCT
ap-4740	335	20	−∞,∞	−∞,∞	VERB
ap-4740	335	21	)	)	PUNCT
ap-4740	335	22	or	or	CCONJ
ap-4740	335	23	(	(	PUNCT
ap-4740	335	24	−1/	−1/	PROPN
ap-4740	335	25	√	√	PROPN
ap-4740	335	26	|λ|	|λ|	PROPN
ap-4740	335	27	,	,	PUNCT
ap-4740	335	28	1/	1/	NUM
ap-4740	335	29	√	√	NUM
ap-4740	335	30	|λ|	|λ|	NOUN
ap-4740	335	31	)	)	PUNCT
ap-4740	335	32	.	.	PUNCT
ap-4740	336	1	such	such	DET
ap-4740	336	2	a	a	DET
ap-4740	336	3	hamiltonian	hamiltonian	NOUN
ap-4740	336	4	is	be	AUX
ap-4740	336	5	formally	formally	ADV
ap-4740	336	6	self	self	NOUN
ap-4740	336	7	-	-	PUNCT
ap-4740	336	8	adjoint	adjoint	NOUN
ap-4740	336	9	with	with	ADP
ap-4740	336	10	respect	respect	NOUN
ap-4740	336	11	to	to	ADP
ap-4740	336	12	the	the	DET
ap-4740	336	13	measure	measure	NOUN
ap-4740	336	14	dµ	dµ	ADJ
ap-4740	336	15	=	=	PUNCT
ap-4740	336	16	(	(	PUNCT
ap-4740	336	17	1+λx2)−1/2dx	1+λx2)−1/2dx	X
ap-4740	336	18	.	.	PUNCT
ap-4740	337	1	the	the	DET
ap-4740	337	2	corresponding	correspond	VERB
ap-4740	337	3	schrödinger	schrödinger	ADJ
ap-4740	337	4	equation	equation	NOUN
ap-4740	337	5	is	be	AUX
ap-4740	337	6	es	es	X
ap-4740	337	7	[	[	PUNCT
ap-4740	337	8	24	24	NUM
ap-4740	337	9	,	,	PUNCT
ap-4740	337	10	25	25	NUM
ap-4740	337	11	]	]	PUNCT
ap-4740	337	12	and	and	CCONJ
ap-4740	337	13	its	its	PRON
ap-4740	337	14	bound	bind	VERB
ap-4740	337	15	-	-	PUNCT
ap-4740	337	16	state	state	NOUN
ap-4740	337	17	wavefunctions	wavefunction	NOUN
ap-4740	337	18	can	can	AUX
ap-4740	337	19	be	be	AUX
ap-4740	337	20	expressed	express	VERB
ap-4740	337	21	in	in	ADP
ap-4740	337	22	terms	term	NOUN
ap-4740	337	23	of	of	ADP
ap-4740	337	24	gegenbauer	gegenbauer	NOUN
ap-4740	337	25	polynomials	polynomial	NOUN
ap-4740	337	26	[	[	X
ap-4740	337	27	26	26	NUM
ap-4740	337	28	]	]	PUNCT
ap-4740	337	29	.	.	PUNCT
ap-4740	338	1	noting	note	VERB
ap-4740	338	2	that	that	SCONJ
ap-4740	338	3	the	the	DET
ap-4740	338	4	potential	potential	ADJ
ap-4740	338	5	energy	energy	NOUN
ap-4740	338	6	term	term	NOUN
ap-4740	338	7	in	in	ADP
ap-4740	338	8	(	(	PUNCT
ap-4740	338	9	5.1	5.1	NUM
ap-4740	338	10	)	)	PUNCT
ap-4740	338	11	can	can	AUX
ap-4740	338	12	also	also	ADV
ap-4740	338	13	be	be	AUX
ap-4740	338	14	written	write	VERB
ap-4740	338	15	as	as	ADP
ap-4740	338	16	v0(x	v0(x	NOUN
ap-4740	338	17	)	)	PUNCT
ap-4740	338	18	=	=	SYM
ap-4740	338	19	λa−	λa−	PUNCT
ap-4740	338	20	λa	λa	X
ap-4740	338	21	1	1	NUM
ap-4740	338	22	+	+	CCONJ
ap-4740	338	23	λx2	λx2	NOUN
ap-4740	338	24	,	,	PUNCT
ap-4740	338	25	where	where	SCONJ
ap-4740	338	26	a	a	DET
ap-4740	338	27	=	=	X
ap-4740	338	28	β	β	X
ap-4740	338	29	λ	λ	X
ap-4740	338	30	(	(	PUNCT
ap-4740	338	31	β	β	X
ap-4740	338	32	λ	λ	X
ap-4740	338	33	+	+	PROPN
ap-4740	338	34	1	1	NUM
ap-4740	338	35	)	)	PUNCT
ap-4740	338	36	,	,	PUNCT
ap-4740	338	37	(	(	PUNCT
ap-4740	338	38	5.2	5.2	NUM
ap-4740	338	39	)	)	PUNCT
ap-4740	338	40	let	let	VERB
ap-4740	338	41	us	we	PRON
ap-4740	338	42	extend	extend	VERB
ap-4740	338	43	it	it	PRON
ap-4740	338	44	to	to	ADP
ap-4740	338	45	vm(x	vm(x	PUNCT
ap-4740	338	46	)	)	PUNCT
ap-4740	339	1	=	=	PUNCT
ap-4740	339	2	λa−	λa−	PUNCT
ap-4740	340	1	λa	λa	X
ap-4740	340	2	1	1	NUM
ap-4740	341	1	+	+	NUM
ap-4740	341	2	λx2	λx2	NOUN
ap-4740	341	3	+	+	CCONJ
ap-4740	341	4	λ	λ	X
ap-4740	341	5	2m∑	2m∑	NUM
ap-4740	341	6	k=1	k=1	X
ap-4740	341	7	bk(1	bk(1	PROPN
ap-4740	341	8	+	+	CCONJ
ap-4740	341	9	λx2)k	λx2)k	PROPN
ap-4740	341	10	,	,	PUNCT
ap-4740	341	11	(	(	PUNCT
ap-4740	341	12	5.3	5.3	NUM
ap-4740	341	13	)	)	PUNCT
ap-4740	341	14	where	where	SCONJ
ap-4740	341	15	m	m	NOUN
ap-4740	341	16	may	may	AUX
ap-4740	341	17	take	take	VERB
ap-4740	341	18	the	the	DET
ap-4740	341	19	values	value	NOUN
ap-4740	341	20	m	m	VERB
ap-4740	341	21	=	=	NOUN
ap-4740	341	22	1	1	NUM
ap-4740	341	23	,	,	PUNCT
ap-4740	341	24	2	2	NUM
ap-4740	341	25	,	,	PUNCT
ap-4740	341	26	3	3	NUM
ap-4740	341	27	,	,	PUNCT
ap-4740	341	28	.	.	PUNCT
ap-4740	341	29	.	.	PUNCT
ap-4740	342	1	.	.	PUNCT
ap-4740	343	1	,	,	PUNCT
ap-4740	343	2	a	a	DET
ap-4740	343	3	,	,	PUNCT
ap-4740	343	4	b1	b1	NOUN
ap-4740	343	5	,	,	PUNCT
ap-4740	343	6	b2	b2	NOUN
ap-4740	343	7	,	,	PUNCT
ap-4740	343	8	.	.	PUNCT
ap-4740	343	9	.	.	PUNCT
ap-4740	344	1	.	.	PUNCT
ap-4740	345	1	,	,	PUNCT
ap-4740	345	2	b2	b2	NOUN
ap-4740	345	3	m	m	NOUN
ap-4740	345	4	are	be	AUX
ap-4740	345	5	2m+	2m+	NUM
ap-4740	345	6	1	1	NUM
ap-4740	345	7	parameters	parameter	NOUN
ap-4740	345	8	,	,	PUNCT
ap-4740	345	9	and	and	CCONJ
ap-4740	345	10	the	the	DET
ap-4740	345	11	range	range	NOUN
ap-4740	345	12	of	of	ADP
ap-4740	345	13	x	x	SYM
ap-4740	345	14	is	be	AUX
ap-4740	345	15	the	the	DET
ap-4740	345	16	same	same	ADJ
ap-4740	345	17	as	as	ADP
ap-4740	345	18	before	before	ADV
ap-4740	345	19	.	.	PUNCT
ap-4740	346	1	the	the	DET
ap-4740	346	2	starting	start	VERB
ap-4740	346	3	schrödinger	schrödinger	ADJ
ap-4740	346	4	equation	equation	NOUN
ap-4740	346	5	therefore	therefore	ADV
ap-4740	346	6	reads	read	VERB
ap-4740	346	7	(	(	PUNCT
ap-4740	346	8	−(1	−(1	NOUN
ap-4740	346	9	+	+	CCONJ
ap-4740	346	10	λx2	λx2	NOUN
ap-4740	346	11	)	)	PUNCT
ap-4740	347	1	d	d	ADP
ap-4740	347	2	2	2	NUM
ap-4740	347	3	dx2	dx2	NOUN
ap-4740	347	4	−	−	PROPN
ap-4740	347	5	λx	λx	PROPN
ap-4740	347	6	d	d	X
ap-4740	347	7	dx	dx	PROPN
ap-4740	347	8	+	+	PROPN
ap-4740	347	9	λa−	λa−	PUNCT
ap-4740	347	10	λa	λa	X
ap-4740	347	11	1	1	NUM
ap-4740	347	12	+	+	CCONJ
ap-4740	347	13	λx2	λx2	NOUN
ap-4740	347	14	+	+	CCONJ
ap-4740	347	15	λ	λ	X
ap-4740	347	16	2m∑	2m∑	NUM
ap-4740	347	17	k=1	k=1	X
ap-4740	347	18	bk(1	bk(1	PROPN
ap-4740	347	19	+	+	CCONJ
ap-4740	347	20	λx2)k	λx2)k	PROPN
ap-4740	347	21	−	−	PROPN
ap-4740	347	22	e	e	PROPN
ap-4740	347	23	)	)	PUNCT
ap-4740	347	24	ψ(x	ψ(x	PROPN
ap-4740	347	25	)	)	PUNCT
ap-4740	348	1	=	=	SYM
ap-4740	348	2	0	0	X
ap-4740	348	3	.	.	PUNCT
ap-4740	349	1	(	(	PUNCT
ap-4740	349	2	5.4	5.4	NUM
ap-4740	349	3	)	)	PUNCT
ap-4740	349	4	to	to	PART
ap-4740	349	5	reduce	reduce	VERB
ap-4740	349	6	it	it	PRON
ap-4740	349	7	to	to	ADP
ap-4740	349	8	an	an	DET
ap-4740	349	9	equation	equation	NOUN
ap-4740	349	10	of	of	ADP
ap-4740	349	11	type	type	NOUN
ap-4740	349	12	(	(	PUNCT
ap-4740	349	13	2.1	2.1	NUM
ap-4740	349	14	)	)	PUNCT
ap-4740	349	15	,	,	PUNCT
ap-4740	349	16	let	let	VERB
ap-4740	349	17	us	we	PRON
ap-4740	349	18	make	make	VERB
ap-4740	349	19	the	the	DET
ap-4740	349	20	change	change	NOUN
ap-4740	349	21	of	of	ADP
ap-4740	349	22	variable	variable	ADJ
ap-4740	349	23	z	z	NOUN
ap-4740	349	24	=	=	SYM
ap-4740	349	25	1	1	NUM
ap-4740	349	26	1	1	NUM
ap-4740	349	27	+	+	CCONJ
ap-4740	349	28	λx2	λx2	NOUN
ap-4740	349	29	(	(	PUNCT
ap-4740	349	30	5.5	5.5	NUM
ap-4740	349	31	)	)	PUNCT
ap-4740	349	32	and	and	CCONJ
ap-4740	349	33	the	the	DET
ap-4740	349	34	gauge	gauge	ADJ
ap-4740	349	35	transformation	transformation	NOUN
ap-4740	349	36	ψ(x	ψ(x	NOUN
ap-4740	349	37	)	)	PUNCT
ap-4740	349	38	=	=	SYM
ap-4740	349	39	xpza	xpza	PROPN
ap-4740	349	40	exp	exp	NOUN
ap-4740	349	41	(	(	PUNCT
ap-4740	349	42	−	−	PROPN
ap-4740	349	43	m∑	m∑	ADV
ap-4740	349	44	j=1	j=1	PROPN
ap-4740	349	45	bj	bj	VERB
ap-4740	349	46	zj	zj	PROPN
ap-4740	349	47	)	)	PUNCT
ap-4740	349	48	y(z	y(z	PROPN
ap-4740	349	49	)	)	PUNCT
ap-4740	349	50	,	,	PUNCT
ap-4740	349	51	(	(	PUNCT
ap-4740	349	52	5.6	5.6	NUM
ap-4740	349	53	)	)	PUNCT
ap-4740	349	54	where	where	SCONJ
ap-4740	349	55	p	p	NOUN
ap-4740	349	56	=	=	NOUN
ap-4740	349	57	0	0	NUM
ap-4740	349	58	,	,	PUNCT
ap-4740	349	59	1	1	NUM
ap-4740	349	60	is	be	AUX
ap-4740	349	61	related	relate	VERB
ap-4740	349	62	to	to	ADP
ap-4740	349	63	the	the	DET
ap-4740	349	64	parity	parity	NOUN
ap-4740	349	65	(	(	PUNCT
ap-4740	349	66	−1)p	−1)p	PROPN
ap-4740	349	67	=	=	SYM
ap-4740	349	68	+1,−1	+1,−1	PROPN
ap-4740	349	69	,	,	PUNCT
ap-4740	349	70	and	and	CCONJ
ap-4740	349	71	a	a	DET
ap-4740	349	72	,	,	PUNCT
ap-4740	349	73	b1	b1	NOUN
ap-4740	349	74	,	,	PUNCT
ap-4740	349	75	b2	b2	NOUN
ap-4740	349	76	,	,	PUNCT
ap-4740	349	77	.	.	PUNCT
ap-4740	349	78	.	.	PUNCT
ap-4740	350	1	.	.	PUNCT
ap-4740	351	1	,	,	PUNCT
ap-4740	351	2	bm	bm	PROPN
ap-4740	351	3	are	be	AUX
ap-4740	351	4	m+	m+	NUM
ap-4740	351	5	1	1	NUM
ap-4740	351	6	parameters	parameter	NOUN
ap-4740	351	7	connected	connect	VERB
ap-4740	351	8	with	with	ADP
ap-4740	351	9	the	the	DET
ap-4740	351	10	previous	previous	ADJ
ap-4740	351	11	ones	one	NOUN
ap-4740	351	12	.	.	PUNCT
ap-4740	352	1	it	it	PRON
ap-4740	352	2	turns	turn	VERB
ap-4740	352	3	out	out	ADP
ap-4740	352	4	that	that	SCONJ
ap-4740	352	5	k	k	PROPN
ap-4740	352	6	in	in	ADP
ap-4740	352	7	(	(	PUNCT
ap-4740	352	8	2.2	2.2	NUM
ap-4740	352	9	)	)	PUNCT
ap-4740	352	10	is	be	AUX
ap-4740	352	11	related	relate	VERB
ap-4740	352	12	to	to	ADP
ap-4740	352	13	m	m	PROPN
ap-4740	352	14	in	in	ADP
ap-4740	352	15	(	(	PUNCT
ap-4740	352	16	5.3	5.3	NUM
ap-4740	352	17	)	)	PUNCT
ap-4740	352	18	by	by	ADP
ap-4740	352	19	the	the	DET
ap-4740	352	20	relation	relation	NOUN
ap-4740	352	21	k	k	PROPN
ap-4740	353	1	=	=	PUNCT
ap-4740	353	2	m+	m+	NUM
ap-4740	353	3	2	2	NUM
ap-4740	353	4	.	.	PUNCT
ap-4740	354	1	for	for	ADP
ap-4740	354	2	m	m	PROPN
ap-4740	354	3	=	=	SYM
ap-4740	354	4	2	2	NUM
ap-4740	354	5	,	,	PUNCT
ap-4740	354	6	for	for	ADP
ap-4740	354	7	instance	instance	NOUN
ap-4740	354	8	,	,	PUNCT
ap-4740	354	9	equation	equation	NOUN
ap-4740	354	10	(	(	PUNCT
ap-4740	354	11	5.4	5.4	NUM
ap-4740	354	12	)	)	PUNCT
ap-4740	354	13	yields	yield	NOUN
ap-4740	354	14	{	{	PUNCT
ap-4740	354	15	−4z3(1−	−4z3(1−	PROPN
ap-4740	354	16	z	z	PROPN
ap-4740	354	17	)	)	PUNCT
ap-4740	354	18	d	d	ADP
ap-4740	354	19	2	2	NUM
ap-4740	354	20	dz2	dz2	NOUN
ap-4740	354	21	+	+	CCONJ
ap-4740	354	22	2[(4a+	2[(4a+	NUM
ap-4740	354	23	3)z3	3)z3	NUM
ap-4740	354	24	−	−	NUM
ap-4740	354	25	2(2a−	2(2a−	NUM
ap-4740	354	26	2b1	2b1	NUM
ap-4740	354	27	+	+	CCONJ
ap-4740	354	28	1−	1−	NUM
ap-4740	354	29	p)z2	p)z2	NOUN
ap-4740	354	30	−	−	PROPN
ap-4740	354	31	4(b1	4(b1	NOUN
ap-4740	354	32	−	−	PROPN
ap-4740	354	33	2b2)z	2b2)z	NUM
ap-4740	354	34	−	−	NOUN
ap-4740	354	35	8b2	8b2	NUM
ap-4740	354	36	]	]	X
ap-4740	354	37	d	d	X
ap-4740	354	38	dz	dz	X
ap-4740	354	39	+	+	X
ap-4740	355	1	[	[	X
ap-4740	355	2	2a(2a+	2a(2a+	NUM
ap-4740	355	3	1)−a]z2	1)−a]z2	NOUN
ap-4740	356	1	+	+	CCONJ
ap-4740	357	1	[	[	X
ap-4740	357	2	−4a2	−4a2	X
ap-4740	357	3	+	+	NUM
ap-4740	357	4	8ab1	8ab1	NUM
ap-4740	357	5	+	+	CCONJ
ap-4740	357	6	4ap−	4ap−	NUM
ap-4740	357	7	2b1	2b1	NUM
ap-4740	357	8	−	−	NOUN
ap-4740	357	9	p−	p−	NOUN
ap-4740	357	10	ε]z	ε]z	NOUN
ap-4740	357	11	+	+	SYM
ap-4740	357	12	b1	b1	NOUN
ap-4740	357	13	−	−	PROPN
ap-4740	357	14	4b1(2a−	4b1(2a−	NUM
ap-4740	357	15	b1	b1	NOUN
ap-4740	357	16	−	−	PROPN
ap-4740	357	17	1−	1−	NUM
ap-4740	357	18	p	p	NOUN
ap-4740	357	19	)	)	PUNCT
ap-4740	357	20	+	+	CCONJ
ap-4740	357	21	4b2(4a−	4b2(4a−	NUM
ap-4740	357	22	3	3	NUM
ap-4740	357	23	)	)	PUNCT
ap-4740	357	24	}	}	PUNCT
ap-4740	357	25	y(z	y(z	NOUN
ap-4740	357	26	)	)	PUNCT
ap-4740	357	27	=	=	SYM
ap-4740	357	28	0	0	NUM
ap-4740	357	29	,	,	PUNCT
ap-4740	357	30	(	(	PUNCT
ap-4740	357	31	5.7	5.7	NUM
ap-4740	357	32	)	)	PUNCT
ap-4740	357	33	after	after	ADP
ap-4740	357	34	setting	set	VERB
ap-4740	357	35	e	e	NOUN
ap-4740	357	36	=	=	PUNCT
ap-4740	357	37	λ(ε+a	λ(ε+a	PROPN
ap-4740	357	38	)	)	PUNCT
ap-4740	357	39	and	and	CCONJ
ap-4740	357	40	b2	b2	NOUN
ap-4740	357	41	=	=	SYM
ap-4740	357	42	4[b2	4[b2	NOUN
ap-4740	357	43	1	1	NUM
ap-4740	357	44	+	+	CCONJ
ap-4740	357	45	2b2(2a−	2b2(2a−	NUM
ap-4740	357	46	2b1	2b1	NUM
ap-4740	357	47	−	−	NUM
ap-4740	357	48	2−	2−	NUM
ap-4740	357	49	p	p	NOUN
ap-4740	357	50	)	)	PUNCT
ap-4740	357	51	]	]	PUNCT
ap-4740	357	52	,	,	PUNCT
ap-4740	357	53	b3	b3	PROPN
ap-4740	357	54	=	=	SYM
ap-4740	357	55	16b2(b1	16b2(b1	NUM
ap-4740	357	56	−	−	PROPN
ap-4740	357	57	b2	b2	NOUN
ap-4740	357	58	)	)	PUNCT
ap-4740	357	59	,	,	PUNCT
ap-4740	357	60	b4	b4	NOUN
ap-4740	357	61	=	=	PUNCT
ap-4740	357	62	16b2	16b2	NUM
ap-4740	357	63	2	2	NUM
ap-4740	357	64	.	.	PUNCT
ap-4740	357	65	(	(	PUNCT
ap-4740	357	66	5.8	5.8	NUM
ap-4740	357	67	)	)	PUNCT
ap-4740	357	68	with	with	ADP
ap-4740	357	69	the	the	DET
ap-4740	357	70	identifications	identification	NOUN
ap-4740	357	71	a4	a4	NOUN
ap-4740	357	72	→	→	SYM
ap-4740	357	73	4	4	NUM
ap-4740	357	74	,	,	PUNCT
ap-4740	357	75	a3	a3	NOUN
ap-4740	357	76	→	→	SYM
ap-4740	357	77	−4	−4	PROPN
ap-4740	357	78	,	,	PUNCT
ap-4740	357	79	a2	a2	PROPN
ap-4740	357	80	,	,	PUNCT
ap-4740	357	81	a1	a1	NOUN
ap-4740	357	82	,	,	PUNCT
ap-4740	357	83	a0	a0	PROPN
ap-4740	357	84	→	→	SYM
ap-4740	357	85	0	0	NUM
ap-4740	357	86	,	,	PUNCT
ap-4740	357	87	b3	b3	PROPN
ap-4740	357	88	→	→	SYM
ap-4740	357	89	2(4a+	2(4a+	NUM
ap-4740	357	90	3	3	NUM
ap-4740	357	91	)	)	PUNCT
ap-4740	357	92	,	,	PUNCT
ap-4740	357	93	b2	b2	NOUN
ap-4740	357	94	→	→	SYM
ap-4740	357	95	−4(2a−	−4(2a−	NUM
ap-4740	357	96	2b1	2b1	NUM
ap-4740	357	97	+	+	CCONJ
ap-4740	357	98	1−	1−	NUM
ap-4740	357	99	p	p	NOUN
ap-4740	357	100	)	)	PUNCT
ap-4740	357	101	,	,	PUNCT
ap-4740	357	102	b1	b1	PROPN
ap-4740	357	103	→	→	SYM
ap-4740	357	104	−8(b1	−8(b1	NUM
ap-4740	357	105	−	−	PROPN
ap-4740	357	106	2b2	2b2	NUM
ap-4740	357	107	)	)	PUNCT
ap-4740	357	108	,	,	PUNCT
ap-4740	357	109	b0	b0	NOUN
ap-4740	357	110	→	→	SYM
ap-4740	357	111	−16b2	−16b2	PROPN
ap-4740	357	112	,	,	PUNCT
ap-4740	357	113	c2	c2	PROPN
ap-4740	357	114	→	→	SYM
ap-4740	357	115	2a(2a+	2a(2a+	NUM
ap-4740	357	116	1)−a	1)−a	NUM
ap-4740	357	117	,	,	PUNCT
ap-4740	357	118	c1	c1	PROPN
ap-4740	357	119	→	→	SYM
ap-4740	357	120	−4a2	−4a2	PROPN
ap-4740	358	1	+	+	CCONJ
ap-4740	358	2	8ab1	8ab1	NUM
ap-4740	358	3	+	+	CCONJ
ap-4740	358	4	4ap−	4ap−	NUM
ap-4740	358	5	2b1	2b1	NUM
ap-4740	358	6	−	−	NOUN
ap-4740	358	7	p−	p−	NOUN
ap-4740	358	8	ε	ε	PROPN
ap-4740	358	9	,	,	PUNCT
ap-4740	358	10	c0	c0	PROPN
ap-4740	358	11	→	→	SYM
ap-4740	358	12	b1	b1	PROPN
ap-4740	358	13	−	−	PROPN
ap-4740	358	14	4b1(2a−	4b1(2a−	NUM
ap-4740	358	15	b1	b1	NOUN
ap-4740	358	16	−	−	PROPN
ap-4740	358	17	1−	1−	NUM
ap-4740	358	18	p	p	NOUN
ap-4740	358	19	)	)	PUNCT
ap-4740	358	20	+	+	CCONJ
ap-4740	358	21	4b2(4a−	4b2(4a−	NUM
ap-4740	358	22	3	3	X
ap-4740	358	23	)	)	PUNCT
ap-4740	358	24	(	(	PUNCT
ap-4740	358	25	5.9	5.9	NUM
ap-4740	358	26	)	)	PUNCT
ap-4740	358	27	in	in	ADP
ap-4740	358	28	equation	equation	NOUN
ap-4740	358	29	(	(	PUNCT
ap-4740	358	30	2.2	2.2	NUM
ap-4740	358	31	)	)	PUNCT
ap-4740	358	32	,	,	PUNCT
ap-4740	358	33	from	from	ADP
ap-4740	358	34	equations	equation	NOUN
ap-4740	358	35	(	(	PUNCT
ap-4740	358	36	2.10	2.10	NUM
ap-4740	358	37	)	)	PUNCT
ap-4740	358	38	and	and	CCONJ
ap-4740	358	39	(	(	PUNCT
ap-4740	358	40	2.11	2.11	NUM
ap-4740	358	41	)	)	PUNCT
ap-4740	358	42	we	we	PRON
ap-4740	358	43	obtain	obtain	VERB
ap-4740	358	44	2a(2a+	2a(2a+	NUM
ap-4740	358	45	1)−a	1)−a	NUM
ap-4740	358	46	=	=	PUNCT
ap-4740	358	47	−4n(n−	−4n(n−	PROPN
ap-4740	358	48	1)−	1)−	PROPN
ap-4740	358	49	2n(4a+	2n(4a+	NUM
ap-4740	358	50	3	3	NUM
ap-4740	358	51	)	)	PUNCT
ap-4740	358	52	,	,	PUNCT
ap-4740	358	53	−4a2	−4a2	PROPN
ap-4740	359	1	+	+	CCONJ
ap-4740	359	2	8ab1	8ab1	NUM
ap-4740	359	3	+	+	CCONJ
ap-4740	359	4	4ap−	4ap−	NUM
ap-4740	359	5	2b1	2b1	NUM
ap-4740	359	6	−	−	NOUN
ap-4740	359	7	p−	p−	NOUN
ap-4740	359	8	ε	ε	NOUN
ap-4740	359	9	=	=	SYM
ap-4740	359	10	2n(n−	2n(n−	NUM
ap-4740	359	11	1	1	NUM
ap-4740	359	12	)	)	PUNCT
ap-4740	359	13	+	+	CCONJ
ap-4740	359	14	8	8	NUM
ap-4740	359	15	3n(2a−	3n(2a−	NUM
ap-4740	359	16	2b1	2b1	NUM
ap-4740	359	17	+	+	CCONJ
ap-4740	359	18	1−	1−	NUM
ap-4740	359	19	p	p	NOUN
ap-4740	359	20	)	)	PUNCT
ap-4740	359	21	+	+	CCONJ
ap-4740	359	22	c1,n	c1,n	PROPN
ap-4740	359	23	,	,	PUNCT
ap-4740	359	24	b1	b1	NOUN
ap-4740	359	25	−	−	PROPN
ap-4740	359	26	4b1(2a−	4b1(2a−	NUM
ap-4740	359	27	b1	b1	PROPN
ap-4740	359	28	−	−	PROPN
ap-4740	359	29	1−	1−	NUM
ap-4740	359	30	p	p	NOUN
ap-4740	359	31	)	)	PUNCT
ap-4740	359	32	+	+	CCONJ
ap-4740	359	33	4b2(4a−	4b2(4a−	NUM
ap-4740	359	34	3	3	X
ap-4740	359	35	)	)	PUNCT
ap-4740	359	36	=	=	SYM
ap-4740	359	37	8	8	NUM
ap-4740	359	38	3n(b1	3n(b1	NUM
ap-4740	359	39	−	−	PROPN
ap-4740	359	40	2b2	2b2	NUM
ap-4740	359	41	)	)	PUNCT
ap-4740	359	42	+	+	CCONJ
ap-4740	359	43	c2,n	c2,n	ADJ
ap-4740	359	44	,	,	PUNCT
ap-4740	359	45	(	(	PUNCT
ap-4740	359	46	5.10	5.10	NUM
ap-4740	359	47	)	)	PUNCT
ap-4740	359	48	124	124	NUM
ap-4740	359	49	vol	vol	NOUN
ap-4740	359	50	.	.	PUNCT
ap-4740	360	1	58	58	NUM
ap-4740	360	2	no	no	INTJ
ap-4740	360	3	.	.	PUNCT
ap-4740	361	1	2/2018	2/2018	NOUN
ap-4740	361	2	quasi	quasi	ADJ
ap-4740	361	3	-	-	ADJ
ap-4740	361	4	exactly	exactly	ADV
ap-4740	361	5	solvable	solvable	ADJ
ap-4740	361	6	schrödinger	schrödinger	ADJ
ap-4740	361	7	equations	equation	NOUN
ap-4740	361	8	where	where	SCONJ
ap-4740	361	9	,	,	PUNCT
ap-4740	361	10	from	from	ADP
ap-4740	361	11	(	(	PUNCT
ap-4740	361	12	2.22	2.22	NUM
ap-4740	361	13	)	)	PUNCT
ap-4740	361	14	,	,	PUNCT
ap-4740	361	15	the	the	DET
ap-4740	361	16	integration	integration	NOUN
ap-4740	361	17	constants	constant	VERB
ap-4740	361	18	c1,n	c1,n	PROPN
ap-4740	361	19	and	and	CCONJ
ap-4740	361	20	c2,n	c2,n	PROPN
ap-4740	361	21	are	be	AUX
ap-4740	361	22	given	give	VERB
ap-4740	361	23	by	by	ADP
ap-4740	361	24	c1,n	c1,n	X
ap-4740	361	25	=	=	PUNCT
ap-4740	361	26	−2[4(n−	−2[4(n−	VERB
ap-4740	361	27	1	1	NUM
ap-4740	361	28	)	)	PUNCT
ap-4740	361	29	+	+	CCONJ
ap-4740	361	30	4a+	4a+	NUM
ap-4740	361	31	3]m(1,0̇	3]m(1,0̇	NUM
ap-4740	361	32	)	)	PUNCT
ap-4740	361	33	+	+	CCONJ
ap-4740	361	34	2n(n−	2n(n−	NUM
ap-4740	361	35	1	1	NUM
ap-4740	361	36	)	)	PUNCT
ap-4740	361	37	+	+	CCONJ
ap-4740	361	38	4	4	NUM
ap-4740	361	39	3n(2a−	3n(2a−	NUM
ap-4740	361	40	2b1	2b1	NUM
ap-4740	361	41	+	+	CCONJ
ap-4740	361	42	1−	1−	NUM
ap-4740	361	43	p	p	NOUN
ap-4740	361	44	)	)	PUNCT
ap-4740	361	45	,	,	PUNCT
ap-4740	361	46	c2,n	c2,n	PROPN
ap-4740	361	47	=	=	SYM
ap-4740	361	48	−2[4(n−	−2[4(n−	VERB
ap-4740	361	49	1	1	NUM
ap-4740	361	50	)	)	PUNCT
ap-4740	361	51	+	+	CCONJ
ap-4740	361	52	4a+	4a+	NUM
ap-4740	361	53	3]m(2,0̇	3]m(2,0̇	NUM
ap-4740	361	54	)	)	PUNCT
ap-4740	362	1	+	+	CCONJ
ap-4740	363	1	4[2(n−	4[2(n−	NUM
ap-4740	363	2	1	1	NUM
ap-4740	363	3	)	)	PUNCT
ap-4740	363	4	+	+	CCONJ
ap-4740	363	5	2a−	2a−	NUM
ap-4740	363	6	2b1	2b1	NUM
ap-4740	363	7	+	+	CCONJ
ap-4740	363	8	1−	1−	NUM
ap-4740	363	9	p]m(1,0̇	p]m(1,0̇	NOUN
ap-4740	363	10	)	)	PUNCT
ap-4740	363	11	−	−	ADP
ap-4740	363	12	8m(12,0̇	8m(12,0̇	NUM
ap-4740	363	13	)	)	PUNCT
ap-4740	364	1	+	+	CCONJ
ap-4740	364	2	16	16	NUM
ap-4740	364	3	3	3	NUM
ap-4740	364	4	n(b1	n(b1	NOUN
ap-4740	364	5	−	−	PROPN
ap-4740	364	6	2b2	2b2	NUM
ap-4740	364	7	)	)	PUNCT
ap-4740	364	8	.	.	PUNCT
ap-4740	365	1	(	(	PUNCT
ap-4740	365	2	5.11	5.11	NUM
ap-4740	365	3	)	)	PUNCT
ap-4740	365	4	on	on	ADP
ap-4740	365	5	the	the	DET
ap-4740	365	6	other	other	ADJ
ap-4740	365	7	hand	hand	NOUN
ap-4740	365	8	,	,	PUNCT
ap-4740	365	9	the	the	DET
ap-4740	365	10	direct	direct	ADJ
ap-4740	365	11	application	application	NOUN
ap-4740	365	12	of	of	ADP
ap-4740	365	13	the	the	DET
ap-4740	365	14	fba	fba	PROPN
ap-4740	365	15	relations	relation	NOUN
ap-4740	365	16	(	(	PUNCT
ap-4740	365	17	3.16	3.16	NUM
ap-4740	365	18	)	)	PUNCT
ap-4740	365	19	and	and	CCONJ
ap-4740	365	20	(	(	PUNCT
ap-4740	365	21	3.17	3.17	NUM
ap-4740	365	22	)	)	PUNCT
ap-4740	365	23	yields	yield	VERB
ap-4740	365	24	the	the	DET
ap-4740	365	25	equivalent	equivalent	ADJ
ap-4740	365	26	results	result	VERB
ap-4740	365	27	2a(2a+	2a(2a+	NUM
ap-4740	365	28	1)−a	1)−a	NUM
ap-4740	365	29	=	=	PUNCT
ap-4740	365	30	−4n(n−	−4n(n−	PROPN
ap-4740	365	31	1)−	1)−	PROPN
ap-4740	365	32	2n(4a+	2n(4a+	NUM
ap-4740	365	33	3	3	NUM
ap-4740	365	34	)	)	PUNCT
ap-4740	365	35	,	,	PUNCT
ap-4740	365	36	−4a2	−4a2	PROPN
ap-4740	366	1	+	+	CCONJ
ap-4740	366	2	8ab1	8ab1	NUM
ap-4740	366	3	+	+	CCONJ
ap-4740	366	4	4ap−	4ap−	NUM
ap-4740	366	5	2b1	2b1	NUM
ap-4740	366	6	−	−	NOUN
ap-4740	366	7	p−	p−	NOUN
ap-4740	366	8	ε	ε	NOUN
ap-4740	366	9	=	=	PUNCT
ap-4740	366	10	4n(n−	4n(n−	NUM
ap-4740	366	11	1	1	NUM
ap-4740	366	12	)	)	PUNCT
ap-4740	366	13	+	+	CCONJ
ap-4740	366	14	4n(2a−	4n(2a−	NUM
ap-4740	366	15	2b1	2b1	NUM
ap-4740	366	16	+	+	CCONJ
ap-4740	366	17	1−	1−	NUM
ap-4740	366	18	p)−	p)−	NOUN
ap-4740	366	19	8(n−	8(n−	NUM
ap-4740	366	20	1)m(1,0̇	1)m(1,0̇	NUM
ap-4740	366	21	)	)	PUNCT
ap-4740	366	22	−	−	ADP
ap-4740	366	23	2(4a+	2(4a+	NUM
ap-4740	366	24	3)m(1,0̇	3)m(1,0̇	NUM
ap-4740	366	25	)	)	PUNCT
ap-4740	366	26	,	,	PUNCT
ap-4740	366	27	b1	b1	NOUN
ap-4740	366	28	−	−	PROPN
ap-4740	366	29	4b1(2a−	4b1(2a−	NUM
ap-4740	366	30	b1	b1	PROPN
ap-4740	366	31	−	−	PROPN
ap-4740	366	32	1−	1−	NUM
ap-4740	366	33	p	p	NOUN
ap-4740	366	34	)	)	PUNCT
ap-4740	367	1	+	+	CCONJ
ap-4740	367	2	4b2(4a−	4b2(4a−	NUM
ap-4740	367	3	3	3	X
ap-4740	367	4	)	)	PUNCT
ap-4740	367	5	=	=	PUNCT
ap-4740	367	6	8n(b1	8n(b1	NOUN
ap-4740	367	7	−	−	PROPN
ap-4740	367	8	2b2	2b2	NUM
ap-4740	367	9	)	)	PUNCT
ap-4740	367	10	+	+	CCONJ
ap-4740	368	1	8(n−	8(n−	NUM
ap-4740	368	2	1)m(1,0̇	1)m(1,0̇	NUM
ap-4740	368	3	)	)	PUNCT
ap-4740	368	4	−	−	NOUN
ap-4740	368	5	8[(n−	8[(n−	NUM
ap-4740	368	6	1)m(2,0̇	1)m(2,0̇	NUM
ap-4740	368	7	)	)	PUNCT
ap-4740	369	1	+	+	NUM
ap-4740	369	2	m(12,0̇	m(12,0̇	NOUN
ap-4740	369	3	)	)	PUNCT
ap-4740	369	4	]	]	PUNCT
ap-4740	370	1	+	+	CCONJ
ap-4740	370	2	4(2a−	4(2a−	NUM
ap-4740	370	3	2b1	2b1	NUM
ap-4740	370	4	+	+	CCONJ
ap-4740	370	5	1−	1−	NUM
ap-4740	370	6	p)m(1,0̇	p)m(1,0̇	NOUN
ap-4740	370	7	)	)	PUNCT
ap-4740	370	8	−	−	ADP
ap-4740	370	9	2(4a+	2(4a+	NUM
ap-4740	370	10	3)m(2,0̇	3)m(2,0̇	NUM
ap-4740	370	11	)	)	PUNCT
ap-4740	370	12	.	.	PUNCT
ap-4740	371	1	(	(	PUNCT
ap-4740	371	2	5.12	5.12	NUM
ap-4740	371	3	)	)	PUNCT
ap-4740	371	4	in	in	ADP
ap-4740	371	5	both	both	DET
ap-4740	371	6	cases	case	NOUN
ap-4740	371	7	,	,	PUNCT
ap-4740	371	8	on	on	ADP
ap-4740	371	9	setting	set	VERB
ap-4740	371	10	n	n	X
ap-4740	371	11	=	=	SYM
ap-4740	371	12	0	0	PROPN
ap-4740	371	13	for	for	ADP
ap-4740	371	14	instance	instance	NOUN
ap-4740	371	15	,	,	PUNCT
ap-4740	371	16	we	we	PRON
ap-4740	371	17	get	get	VERB
ap-4740	371	18	that	that	SCONJ
ap-4740	371	19	the	the	DET
ap-4740	371	20	schrödinger	schrödinger	ADJ
ap-4740	371	21	equation	equation	NOUN
ap-4740	371	22	(	(	PUNCT
ap-4740	371	23	5.4	5.4	NUM
ap-4740	371	24	)	)	PUNCT
ap-4740	371	25	with	with	ADP
ap-4740	371	26	m	m	PROPN
ap-4740	371	27	=	=	SYM
ap-4740	371	28	2	2	NUM
ap-4740	371	29	,	,	PUNCT
ap-4740	371	30	a	a	PRON
ap-4740	371	31	=	=	SYM
ap-4740	371	32	2a(2a+	2a(2a+	NUM
ap-4740	371	33	1	1	NUM
ap-4740	371	34	)	)	PUNCT
ap-4740	371	35	,	,	PUNCT
ap-4740	371	36	b1	b1	NOUN
ap-4740	371	37	=	=	SYM
ap-4740	371	38	4b1(2a−	4b1(2a−	NUM
ap-4740	371	39	b1	b1	NOUN
ap-4740	371	40	−	−	PROPN
ap-4740	371	41	1−	1−	NUM
ap-4740	372	1	p)−	p)−	NOUN
ap-4740	372	2	4b2(4a−	4b2(4a−	NUM
ap-4740	372	3	3	3	NUM
ap-4740	372	4	)	)	PUNCT
ap-4740	372	5	,	,	PUNCT
ap-4740	372	6	(	(	PUNCT
ap-4740	372	7	5.13	5.13	NUM
ap-4740	372	8	)	)	PUNCT
ap-4740	372	9	and	and	CCONJ
ap-4740	372	10	b2	b2	NOUN
ap-4740	372	11	,	,	PUNCT
ap-4740	372	12	b3	b3	NOUN
ap-4740	372	13	,	,	PUNCT
ap-4740	372	14	b4	b4	NOUN
ap-4740	372	15	given	give	VERB
ap-4740	372	16	in	in	ADP
ap-4740	372	17	(	(	PUNCT
ap-4740	372	18	5.8	5.8	NUM
ap-4740	372	19	)	)	PUNCT
ap-4740	372	20	,	,	PUNCT
ap-4740	372	21	has	have	VERB
ap-4740	372	22	an	an	DET
ap-4740	372	23	eigenvalue	eigenvalue	PROPN
ap-4740	372	24	e0,p	e0,p	PROPN
ap-4740	372	25	=	=	SYM
ap-4740	372	26	λ(8ab1	λ(8ab1	PROPN
ap-4740	373	1	+	+	NUM
ap-4740	373	2	4ap+	4ap+	NOUN
ap-4740	373	3	2a−	2a−	NUM
ap-4740	373	4	2b1	2b1	NUM
ap-4740	373	5	−	−	NOUN
ap-4740	374	1	p	p	X
ap-4740	374	2	)	)	PUNCT
ap-4740	374	3	(	(	PUNCT
ap-4740	374	4	5.14	5.14	NUM
ap-4740	374	5	)	)	PUNCT
ap-4740	374	6	with	with	ADP
ap-4740	374	7	the	the	DET
ap-4740	374	8	corresponding	correspond	VERB
ap-4740	374	9	eigenfunction	eigenfunction	NOUN
ap-4740	374	10	ψ0,p(x	ψ0,p(x	NOUN
ap-4740	374	11	)	)	PUNCT
ap-4740	374	12	∝	∝	PROPN
ap-4740	374	13	xp(1	xp(1	PROPN
ap-4740	375	1	+	+	CCONJ
ap-4740	375	2	λx2)−ae−λ(b1	λx2)−ae−λ(b1	ADP
ap-4740	375	3	+	+	NOUN
ap-4740	375	4	2b2)x2−λ2b2x	2b2)x2−λ2b2x	NUM
ap-4740	375	5	4	4	NUM
ap-4740	375	6	.	.	PUNCT
ap-4740	376	1	(	(	PUNCT
ap-4740	376	2	5.15	5.15	NUM
ap-4740	376	3	)	)	PUNCT
ap-4740	376	4	the	the	DET
ap-4740	376	5	latter	latter	ADJ
ap-4740	376	6	is	be	AUX
ap-4740	376	7	normalizable	normalizable	ADJ
ap-4740	376	8	with	with	ADP
ap-4740	376	9	respect	respect	NOUN
ap-4740	376	10	to	to	ADP
ap-4740	376	11	the	the	DET
ap-4740	376	12	measure	measure	NOUN
ap-4740	376	13	dµ	dµ	ADP
ap-4740	376	14	provided	provide	VERB
ap-4740	376	15	b2	b2	PROPN
ap-4740	376	16	>	>	X
ap-4740	376	17	0	0	PUNCT
ap-4740	377	1	if	if	SCONJ
ap-4740	377	2	λ	λ	PROPN
ap-4740	377	3	>	>	X
ap-4740	377	4	0	0	NUM
ap-4740	377	5	or	or	CCONJ
ap-4740	377	6	a	a	DET
ap-4740	377	7	<	<	X
ap-4740	377	8	1	1	NUM
ap-4740	377	9	4	4	NUM
ap-4740	377	10	if	if	SCONJ
ap-4740	377	11	λ	λ	X
ap-4740	377	12	<	<	X
ap-4740	377	13	0	0	PUNCT
ap-4740	378	1	and	and	CCONJ
ap-4740	378	2	it	it	PRON
ap-4740	378	3	corresponds	correspond	VERB
ap-4740	378	4	to	to	ADP
ap-4740	378	5	a	a	DET
ap-4740	378	6	ground	ground	NOUN
ap-4740	378	7	state	state	NOUN
ap-4740	378	8	for	for	ADP
ap-4740	378	9	p	p	NOUN
ap-4740	378	10	=	=	NOUN
ap-4740	378	11	0	0	PROPN
ap-4740	378	12	and	and	CCONJ
ap-4740	378	13	to	to	ADP
ap-4740	378	14	a	a	DET
ap-4740	378	15	first	first	ADJ
ap-4740	378	16	excited	excited	ADJ
ap-4740	378	17	state	state	NOUN
ap-4740	378	18	for	for	ADP
ap-4740	378	19	p	p	NOUN
ap-4740	378	20	=	=	NOUN
ap-4740	378	21	1	1	X
ap-4740	378	22	.	.	PUNCT
ap-4740	379	1	furthermore	furthermore	ADV
ap-4740	379	2	,	,	PUNCT
ap-4740	379	3	for	for	ADP
ap-4740	379	4	n	n	NOUN
ap-4740	379	5	=	=	SYM
ap-4740	379	6	1	1	NUM
ap-4740	379	7	,	,	PUNCT
ap-4740	379	8	on	on	ADP
ap-4740	379	9	taking	take	VERB
ap-4740	379	10	into	into	ADP
ap-4740	379	11	account	account	NOUN
ap-4740	379	12	that	that	PRON
ap-4740	379	13	m(1,0̇	m(1,0̇	VERB
ap-4740	379	14	)	)	PUNCT
ap-4740	379	15	=	=	SYM
ap-4740	379	16	z1	z1	VERB
ap-4740	379	17	,	,	PUNCT
ap-4740	379	18	m(2,0̇	m(2,0̇	NOUN
ap-4740	379	19	)	)	PUNCT
ap-4740	379	20	=	=	SYM
ap-4740	379	21	z2	z2	PROPN
ap-4740	379	22	1	1	NUM
ap-4740	379	23	,	,	PUNCT
ap-4740	379	24	and	and	CCONJ
ap-4740	379	25	m(12,0̇	m(12,0̇	NOUN
ap-4740	379	26	)	)	PUNCT
ap-4740	379	27	=	=	SYM
ap-4740	379	28	0	0	NUM
ap-4740	379	29	in	in	ADP
ap-4740	379	30	terms	term	NOUN
ap-4740	379	31	of	of	ADP
ap-4740	379	32	the	the	DET
ap-4740	379	33	single	single	ADJ
ap-4740	379	34	root	root	NOUN
ap-4740	379	35	z1	z1	NOUN
ap-4740	379	36	of	of	ADP
ap-4740	379	37	y1(z	y1(z	PROPN
ap-4740	379	38	)	)	PUNCT
ap-4740	379	39	,	,	PUNCT
ap-4740	379	40	we	we	PRON
ap-4740	379	41	obtain	obtain	VERB
ap-4740	379	42	that	that	DET
ap-4740	379	43	equation	equation	NOUN
ap-4740	379	44	(	(	PUNCT
ap-4740	379	45	5.4	5.4	NUM
ap-4740	379	46	)	)	PUNCT
ap-4740	379	47	with	with	ADP
ap-4740	379	48	m	m	PROPN
ap-4740	379	49	=	=	SYM
ap-4740	379	50	2	2	NUM
ap-4740	379	51	,	,	PUNCT
ap-4740	379	52	a	a	PRON
ap-4740	379	53	=	=	X
ap-4740	379	54	(	(	PUNCT
ap-4740	379	55	2a+	2a+	NUM
ap-4740	379	56	2)(2a+	2)(2a+	NUM
ap-4740	379	57	3	3	NUM
ap-4740	379	58	)	)	PUNCT
ap-4740	379	59	,	,	PUNCT
ap-4740	379	60	b1	b1	NOUN
ap-4740	379	61	=	=	SYM
ap-4740	379	62	−2(4a+	−2(4a+	NOUN
ap-4740	379	63	3)z2	3)z2	NUM
ap-4740	379	64	1	1	NUM
ap-4740	379	65	+	+	NUM
ap-4740	379	66	4(2a−2b1	4(2a−2b1	NUM
ap-4740	379	67	+	+	CCONJ
ap-4740	379	68	1−p)z1	1−p)z1	NUM
ap-4740	379	69	+	+	CCONJ
ap-4740	379	70	4b1(2a−	4b1(2a−	NUM
ap-4740	379	71	b1	b1	NOUN
ap-4740	379	72	+	+	CCONJ
ap-4740	379	73	1−p)−4b2(4a+	1−p)−4b2(4a+	NUM
ap-4740	379	74	1	1	NUM
ap-4740	379	75	)	)	PUNCT
ap-4740	379	76	,	,	PUNCT
ap-4740	379	77	(	(	PUNCT
ap-4740	379	78	5.16	5.16	NUM
ap-4740	379	79	)	)	PUNCT
ap-4740	379	80	and	and	CCONJ
ap-4740	379	81	b2	b2	NOUN
ap-4740	379	82	,	,	PUNCT
ap-4740	379	83	b3	b3	NOUN
ap-4740	379	84	,	,	PUNCT
ap-4740	379	85	b4	b4	NOUN
ap-4740	379	86	given	give	VERB
ap-4740	379	87	in	in	ADP
ap-4740	379	88	(	(	PUNCT
ap-4740	379	89	5.8	5.8	NUM
ap-4740	379	90	)	)	PUNCT
ap-4740	379	91	,	,	PUNCT
ap-4740	379	92	has	have	VERB
ap-4740	379	93	an	an	DET
ap-4740	379	94	eigenvalue	eigenvalue	ADJ
ap-4740	379	95	e1,p	e1,p	NOUN
ap-4740	379	96	=	=	SYM
ap-4740	379	97	λ[8ab1	λ[8ab1	PUNCT
ap-4740	380	1	+	+	PUNCT
ap-4740	380	2	4ap+	4ap+	NUM
ap-4740	380	3	2a+	2a+	NUM
ap-4740	380	4	6b1	6b1	NUM
ap-4740	380	5	+	+	CCONJ
ap-4740	380	6	3p+	3p+	NUM
ap-4740	380	7	2	2	NUM
ap-4740	380	8	+	+	NUM
ap-4740	380	9	2(4a+	2(4a+	NUM
ap-4740	380	10	3)z1	3)z1	NUM
ap-4740	380	11	]	]	PUNCT
ap-4740	380	12	(	(	PUNCT
ap-4740	380	13	5.17	5.17	NUM
ap-4740	380	14	)	)	PUNCT
ap-4740	380	15	with	with	ADP
ap-4740	380	16	the	the	DET
ap-4740	380	17	corresponding	correspond	VERB
ap-4740	380	18	eigenfunction	eigenfunction	NOUN
ap-4740	380	19	ψ1,p(x	ψ1,p(x	NOUN
ap-4740	380	20	)	)	PUNCT
ap-4740	380	21	∝	∝	PROPN
ap-4740	380	22	xp(1	xp(1	PROPN
ap-4740	380	23	+	+	CCONJ
ap-4740	380	24	λx2)−a−1[1−	λx2)−a−1[1−	PROPN
ap-4740	380	25	z1(1	z1(1	PROPN
ap-4740	380	26	+	+	PROPN
ap-4740	380	27	λx2)]e−λ(b1	λx2)]e−λ(b1	PROPN
ap-4740	380	28	+	+	NOUN
ap-4740	380	29	2b2)x2−λ2b2x	2b2)x2−λ2b2x	NUM
ap-4740	380	30	4	4	NUM
ap-4740	380	31	.	.	PUNCT
ap-4740	381	1	(	(	PUNCT
ap-4740	381	2	5.18	5.18	NUM
ap-4740	381	3	)	)	PUNCT
ap-4740	381	4	the	the	DET
ap-4740	381	5	normalizability	normalizability	NOUN
ap-4740	381	6	condition	condition	NOUN
ap-4740	381	7	is	be	AUX
ap-4740	381	8	now	now	ADV
ap-4740	381	9	b2	b2	VERB
ap-4740	381	10	>	>	X
ap-4740	381	11	0	0	PUNCT
ap-4740	382	1	if	if	SCONJ
ap-4740	382	2	λ	λ	PROPN
ap-4740	382	3	>	>	X
ap-4740	382	4	0	0	NUM
ap-4740	382	5	or	or	CCONJ
ap-4740	382	6	a	a	DET
ap-4740	382	7	<	<	X
ap-4740	382	8	−	−	PROPN
ap-4740	382	9	3	3	NUM
ap-4740	382	10	4	4	NUM
ap-4740	382	11	if	if	SCONJ
ap-4740	382	12	λ	λ	X
ap-4740	382	13	<	<	X
ap-4740	382	14	0	0	NUM
ap-4740	382	15	.	.	PUNCT
ap-4740	383	1	here	here	ADV
ap-4740	383	2	z1	z1	PROPN
ap-4740	383	3	is	be	AUX
ap-4740	383	4	a	a	DET
ap-4740	383	5	real	real	ADJ
ap-4740	383	6	solution	solution	NOUN
ap-4740	383	7	of	of	ADP
ap-4740	383	8	the	the	DET
ap-4740	383	9	cubic	cubic	ADJ
ap-4740	383	10	equation	equation	NOUN
ap-4740	383	11	(	(	PUNCT
ap-4740	383	12	4a+	4a+	NUM
ap-4740	383	13	3)z3	3)z3	NUM
ap-4740	383	14	1	1	NUM
ap-4740	383	15	−	−	NUM
ap-4740	383	16	2(2a−	2(2a−	NUM
ap-4740	383	17	2b1	2b1	NUM
ap-4740	384	1	+	+	CCONJ
ap-4740	384	2	1−	1−	NUM
ap-4740	384	3	p)z2	p)z2	NOUN
ap-4740	384	4	1	1	NUM
ap-4740	384	5	−	−	NOUN
ap-4740	384	6	4(b1	4(b1	NOUN
ap-4740	384	7	−	−	PROPN
ap-4740	384	8	2b2)z1	2b2)z1	NUM
ap-4740	384	9	−	−	NOUN
ap-4740	384	10	8b2	8b2	NUM
ap-4740	384	11	=	=	SYM
ap-4740	384	12	0	0	NUM
ap-4740	384	13	,	,	PUNCT
ap-4740	384	14	(	(	PUNCT
ap-4740	384	15	5.19	5.19	NUM
ap-4740	384	16	)	)	PUNCT
ap-4740	384	17	hence	hence	ADV
ap-4740	384	18	,	,	PUNCT
ap-4740	384	19	for	for	ADP
ap-4740	384	20	instance	instance	NOUN
ap-4740	384	21	,	,	PUNCT
ap-4740	384	22	z1	z1	PROPN
ap-4740	384	23	=	=	PUNCT
ap-4740	384	24	2(2a−	2(2a−	NUM
ap-4740	384	25	2b1	2b1	NUM
ap-4740	385	1	+	+	CCONJ
ap-4740	385	2	1−	1−	NUM
ap-4740	385	3	p	p	NOUN
ap-4740	385	4	)	)	PUNCT
ap-4740	385	5	3(4a+	3(4a+	NUM
ap-4740	385	6	3	3	NUM
ap-4740	385	7	)	)	PUNCT
ap-4740	386	1	+	+	CCONJ
ap-4740	386	2	(	(	PUNCT
ap-4740	386	3	−v2	−v2	NOUN
ap-4740	386	4	+	+	CCONJ
ap-4740	386	5	√(v	√(v	NOUN
ap-4740	386	6	2	2	NUM
ap-4740	386	7	)	)	SYM
ap-4740	386	8	2	2	NUM
ap-4740	387	1	+	+	CCONJ
ap-4740	387	2	(	(	PUNCT
ap-4740	387	3	u	u	NOUN
ap-4740	387	4	3	3	NUM
ap-4740	387	5	)	)	PUNCT
ap-4740	387	6	3	3	NUM
ap-4740	387	7	)	)	PUNCT
ap-4740	387	8	1/3	1/3	NOUN
ap-4740	387	9	+	+	CCONJ
ap-4740	387	10	(	(	PUNCT
ap-4740	387	11	−v2	−v2	PROPN
ap-4740	387	12	−	−	PROPN
ap-4740	387	13	√(v	√(v	NOUN
ap-4740	387	14	2	2	NUM
ap-4740	387	15	)	)	SYM
ap-4740	387	16	2	2	NUM
ap-4740	387	17	+	+	CCONJ
ap-4740	387	18	(	(	PUNCT
ap-4740	387	19	u	u	NOUN
ap-4740	387	20	3	3	NUM
ap-4740	387	21	)	)	PUNCT
ap-4740	387	22	3	3	NUM
ap-4740	387	23	)	)	PUNCT
ap-4740	387	24	1/3	1/3	NUM
ap-4740	387	25	,	,	PUNCT
ap-4740	387	26	u	u	NOUN
ap-4740	387	27	=	=	NOUN
ap-4740	387	28	4	4	NUM
ap-4740	387	29	4a+	4a+	NUM
ap-4740	387	30	3	3	NUM
ap-4740	387	31	(	(	PUNCT
ap-4740	387	32	−b1	−b1	PROPN
ap-4740	387	33	+	+	CCONJ
ap-4740	387	34	2b2	2b2	NUM
ap-4740	387	35	−	−	NOUN
ap-4740	387	36	(	(	PUNCT
ap-4740	387	37	2a−	2a−	PROPN
ap-4740	387	38	2b1	2b1	NUM
ap-4740	387	39	+	+	CCONJ
ap-4740	387	40	1−	1−	NUM
ap-4740	387	41	p)2	p)2	NOUN
ap-4740	387	42	3(4a+	3(4a+	NUM
ap-4740	387	43	3	3	NUM
ap-4740	387	44	)	)	PUNCT
ap-4740	387	45	)	)	PUNCT
ap-4740	387	46	,	,	PUNCT
ap-4740	387	47	v	v	X
ap-4740	387	48	=	=	SYM
ap-4740	387	49	−	−	PROPN
ap-4740	387	50	8	8	NUM
ap-4740	387	51	4a+	4a+	NUM
ap-4740	387	52	3	3	NUM
ap-4740	387	53	(	(	PUNCT
ap-4740	387	54	b2	b2	NOUN
ap-4740	387	55	+	+	CCONJ
ap-4740	387	56	2	2	NUM
ap-4740	387	57	27	27	NUM
ap-4740	387	58	(	(	PUNCT
ap-4740	387	59	2a−	2a−	NUM
ap-4740	387	60	2b1	2b1	NUM
ap-4740	387	61	+	+	CCONJ
ap-4740	387	62	1−	1−	NUM
ap-4740	387	63	p)3	p)3	NOUN
ap-4740	387	64	(	(	PUNCT
ap-4740	387	65	4a+	4a+	NUM
ap-4740	388	1	3)2	3)2	NUM
ap-4740	388	2	+	+	NUM
ap-4740	388	3	1	1	NUM
ap-4740	388	4	3	3	NUM
ap-4740	388	5	(	(	PUNCT
ap-4740	388	6	2a−	2a−	NUM
ap-4740	388	7	2b1	2b1	NUM
ap-4740	388	8	+	+	CCONJ
ap-4740	388	9	1−	1−	NUM
ap-4740	388	10	p)(b1	p)(b1	NOUN
ap-4740	388	11	−	−	NOUN
ap-4740	388	12	2b2	2b2	NUM
ap-4740	388	13	)	)	PUNCT
ap-4740	388	14	4a+	4a+	NUM
ap-4740	388	15	3	3	NUM
ap-4740	388	16	)	)	PUNCT
ap-4740	388	17	.	.	PUNCT
ap-4740	389	1	(	(	PUNCT
ap-4740	389	2	5.20	5.20	NUM
ap-4740	389	3	)	)	PUNCT
ap-4740	389	4	according	accord	VERB
ap-4740	389	5	to	to	ADP
ap-4740	389	6	its	its	PRON
ap-4740	389	7	value	value	NOUN
ap-4740	389	8	,	,	PUNCT
ap-4740	389	9	the	the	DET
ap-4740	389	10	wavefunction	wavefunction	NOUN
ap-4740	389	11	ψ1,p(x	ψ1,p(x	NOUN
ap-4740	389	12	)	)	PUNCT
ap-4740	389	13	may	may	AUX
ap-4740	389	14	correspond	correspond	VERB
ap-4740	389	15	to	to	ADP
ap-4740	389	16	a	a	DET
ap-4740	389	17	ground	ground	NOUN
ap-4740	389	18	or	or	CCONJ
ap-4740	389	19	second	second	ADV
ap-4740	389	20	-	-	PUNCT
ap-4740	389	21	excited	excited	ADJ
ap-4740	389	22	state	state	NOUN
ap-4740	389	23	for	for	ADP
ap-4740	389	24	p	p	NOUN
ap-4740	389	25	=	=	NOUN
ap-4740	389	26	0	0	PROPN
ap-4740	389	27	and	and	CCONJ
ap-4740	389	28	to	to	ADP
ap-4740	389	29	a	a	DET
ap-4740	389	30	firstor	firstor	NOUN
ap-4740	389	31	third	third	ADV
ap-4740	389	32	-	-	PUNCT
ap-4740	389	33	excited	excite	VERB
ap-4740	389	34	state	state	NOUN
ap-4740	389	35	for	for	ADP
ap-4740	389	36	p	p	NOUN
ap-4740	389	37	=	=	NOUN
ap-4740	389	38	1	1	NUM
ap-4740	389	39	.	.	NOUN
ap-4740	389	40	6	6	NUM
ap-4740	389	41	.	.	X
ap-4740	389	42	conclusion	conclusion	NOUN
ap-4740	389	43	in	in	ADP
ap-4740	389	44	the	the	DET
ap-4740	389	45	present	present	ADJ
ap-4740	389	46	paper	paper	NOUN
ap-4740	389	47	,	,	PUNCT
ap-4740	389	48	we	we	PRON
ap-4740	389	49	have	have	AUX
ap-4740	389	50	reconsidered	reconsider	VERB
ap-4740	389	51	the	the	DET
ap-4740	389	52	general	general	ADJ
ap-4740	389	53	conditions	condition	NOUN
ap-4740	389	54	that	that	PRON
ap-4740	389	55	have	have	VERB
ap-4740	389	56	to	to	PART
ap-4740	389	57	be	be	AUX
ap-4740	389	58	satisfied	satisfy	VERB
ap-4740	389	59	by	by	ADP
ap-4740	389	60	the	the	DET
ap-4740	389	61	coefficients	coefficient	NOUN
ap-4740	389	62	of	of	ADP
ap-4740	389	63	a	a	DET
ap-4740	389	64	second	second	ADJ
ap-4740	389	65	-	-	PUNCT
ap-4740	389	66	order	order	NOUN
ap-4740	389	67	differential	differential	ADJ
ap-4740	389	68	equation	equation	NOUN
ap-4740	389	69	with	with	ADP
ap-4740	389	70	at	at	ADP
ap-4740	389	71	most	most	ADJ
ap-4740	389	72	k	k	NOUN
ap-4740	389	73	+	+	CCONJ
ap-4740	389	74	1	1	NUM
ap-4740	389	75	singular	singular	ADJ
ap-4740	389	76	points	point	NOUN
ap-4740	389	77	in	in	ADP
ap-4740	389	78	order	order	NOUN
ap-4740	389	79	that	that	SCONJ
ap-4740	389	80	the	the	DET
ap-4740	389	81	equation	equation	NOUN
ap-4740	389	82	has	have	AUX
ap-4740	389	83	particular	particular	ADJ
ap-4740	389	84	solutions	solution	NOUN
ap-4740	389	85	that	that	PRON
ap-4740	389	86	are	be	AUX
ap-4740	389	87	nth	nth	ADJ
ap-4740	389	88	-	-	PUNCT
ap-4740	389	89	degree	degree	NOUN
ap-4740	389	90	polynomials	polynomial	NOUN
ap-4740	389	91	yn(z	yn(z	NOUN
ap-4740	389	92	)	)	PUNCT
ap-4740	389	93	and	and	CCONJ
ap-4740	389	94	we	we	PRON
ap-4740	389	95	have	have	AUX
ap-4740	389	96	expressed	express	VERB
ap-4740	389	97	them	they	PRON
ap-4740	389	98	in	in	ADP
ap-4740	389	99	terms	term	NOUN
ap-4740	389	100	of	of	ADP
ap-4740	389	101	symmetric	symmetric	ADJ
ap-4740	389	102	polynomials	polynomial	NOUN
ap-4740	389	103	in	in	ADP
ap-4740	389	104	the	the	DET
ap-4740	389	105	polynomial	polynomial	ADJ
ap-4740	389	106	solution	solution	NOUN
ap-4740	389	107	roots	root	NOUN
ap-4740	389	108	.	.	PUNCT
ap-4740	390	1	this	this	PRON
ap-4740	390	2	has	have	AUX
ap-4740	390	3	been	be	AUX
ap-4740	390	4	done	do	VERB
ap-4740	390	5	in	in	ADP
ap-4740	390	6	two	two	NUM
ap-4740	390	7	different	different	ADJ
ap-4740	390	8	ways	way	NOUN
ap-4740	390	9	.	.	PUNCT
ap-4740	391	1	125	125	NUM
ap-4740	391	2	christiane	christiane	NOUN
ap-4740	391	3	quesne	quesne	NOUN
ap-4740	391	4	acta	acta	PROPN
ap-4740	391	5	polytechnica	polytechnica	PROPN
ap-4740	391	6	in	in	ADP
ap-4740	391	7	the	the	DET
ap-4740	391	8	first	first	ADJ
ap-4740	391	9	one	one	NUM
ap-4740	392	1	,	,	PUNCT
ap-4740	392	2	we	we	PRON
ap-4740	392	3	have	have	AUX
ap-4740	392	4	shown	show	VERB
ap-4740	392	5	that	that	SCONJ
ap-4740	392	6	these	these	DET
ap-4740	392	7	conditions	condition	NOUN
ap-4740	392	8	involve	involve	VERB
ap-4740	392	9	k	k	X
ap-4740	392	10	−	−	NUM
ap-4740	392	11	2	2	NUM
ap-4740	392	12	integration	integration	NOUN
ap-4740	392	13	constants	constant	NOUN
ap-4740	392	14	,	,	PUNCT
ap-4740	392	15	which	which	PRON
ap-4740	392	16	satisfy	satisfy	VERB
ap-4740	392	17	a	a	DET
ap-4740	392	18	system	system	NOUN
ap-4740	392	19	of	of	ADP
ap-4740	392	20	linear	linear	ADJ
ap-4740	392	21	equations	equation	NOUN
ap-4740	392	22	whose	whose	DET
ap-4740	392	23	coefficients	coefficient	NOUN
ap-4740	392	24	can	can	AUX
ap-4740	392	25	be	be	AUX
ap-4740	392	26	expressed	express	VERB
ap-4740	392	27	in	in	ADP
ap-4740	392	28	terms	term	NOUN
ap-4740	392	29	of	of	ADP
ap-4740	392	30	elementary	elementary	ADJ
ap-4740	392	31	symmetric	symmetric	ADJ
ap-4740	392	32	polynomials	polynomial	NOUN
ap-4740	392	33	in	in	ADP
ap-4740	392	34	the	the	DET
ap-4740	392	35	polynomial	polynomial	ADJ
ap-4740	392	36	solution	solution	NOUN
ap-4740	392	37	roots	root	NOUN
ap-4740	392	38	whenever	whenever	SCONJ
ap-4740	392	39	such	such	ADJ
ap-4740	392	40	roots	root	NOUN
ap-4740	392	41	are	be	AUX
ap-4740	392	42	all	all	ADV
ap-4740	392	43	real	real	ADJ
ap-4740	392	44	and	and	CCONJ
ap-4740	392	45	distinct	distinct	ADJ
ap-4740	392	46	.	.	PUNCT
ap-4740	393	1	in	in	ADP
ap-4740	393	2	the	the	DET
ap-4740	393	3	second	second	ADJ
ap-4740	393	4	approach	approach	NOUN
ap-4740	393	5	,	,	PUNCT
ap-4740	393	6	we	we	PRON
ap-4740	393	7	have	have	AUX
ap-4740	393	8	considered	consider	VERB
ap-4740	393	9	the	the	DET
ap-4740	393	10	solution	solution	NOUN
ap-4740	393	11	of	of	ADP
ap-4740	393	12	the	the	DET
ap-4740	393	13	fba	fba	PROPN
ap-4740	393	14	method	method	NOUN
ap-4740	393	15	in	in	ADP
ap-4740	393	16	its	its	PRON
ap-4740	393	17	most	most	ADV
ap-4740	393	18	general	general	ADJ
ap-4740	393	19	form	form	NOUN
ap-4740	393	20	under	under	ADP
ap-4740	393	21	the	the	DET
ap-4740	393	22	same	same	ADJ
ap-4740	393	23	assumption	assumption	NOUN
ap-4740	393	24	.	.	PUNCT
ap-4740	394	1	comparing	compare	VERB
ap-4740	394	2	the	the	DET
ap-4740	394	3	outcomes	outcome	NOUN
ap-4740	394	4	of	of	ADP
ap-4740	394	5	both	both	DET
ap-4740	394	6	descriptions	description	NOUN
ap-4740	394	7	,	,	PUNCT
ap-4740	394	8	we	we	PRON
ap-4740	394	9	have	have	AUX
ap-4740	394	10	proved	prove	VERB
ap-4740	394	11	that	that	SCONJ
ap-4740	394	12	the	the	DET
ap-4740	394	13	above	above	ADV
ap-4740	394	14	-	-	PUNCT
ap-4740	394	15	mentioned	mention	VERB
ap-4740	394	16	k	k	NOUN
ap-4740	394	17	−	−	PROPN
ap-4740	394	18	2	2	NUM
ap-4740	394	19	integration	integration	NOUN
ap-4740	394	20	constants	constant	NOUN
ap-4740	394	21	can	can	AUX
ap-4740	394	22	be	be	AUX
ap-4740	394	23	expressed	express	VERB
ap-4740	394	24	as	as	ADP
ap-4740	394	25	linear	linear	ADJ
ap-4740	394	26	combinations	combination	NOUN
ap-4740	394	27	of	of	ADP
ap-4740	394	28	monomial	monomial	ADJ
ap-4740	394	29	symmetric	symmetric	ADJ
ap-4740	394	30	polynomials	polynomial	NOUN
ap-4740	394	31	in	in	ADP
ap-4740	394	32	the	the	DET
ap-4740	394	33	polynomial	polynomial	ADJ
ap-4740	394	34	solution	solution	NOUN
ap-4740	394	35	roots	root	NOUN
ap-4740	394	36	,	,	PUNCT
ap-4740	394	37	corresponding	correspond	VERB
ap-4740	394	38	to	to	ADP
ap-4740	394	39	partitions	partition	NOUN
ap-4740	394	40	into	into	ADP
ap-4740	394	41	no	no	DET
ap-4740	394	42	more	more	ADJ
ap-4740	394	43	than	than	ADP
ap-4740	394	44	two	two	NUM
ap-4740	394	45	parts	part	NOUN
ap-4740	394	46	.	.	PUNCT
ap-4740	395	1	as	as	ADV
ap-4740	395	2	far	far	ADV
ap-4740	395	3	as	as	SCONJ
ap-4740	395	4	the	the	DET
ap-4740	395	5	author	author	NOUN
ap-4740	395	6	knows	know	VERB
ap-4740	395	7	,	,	PUNCT
ap-4740	395	8	this	this	DET
ap-4740	395	9	property	property	NOUN
ap-4740	395	10	and	and	CCONJ
ap-4740	395	11	the	the	DET
ap-4740	395	12	general	general	ADJ
ap-4740	395	13	solution	solution	NOUN
ap-4740	395	14	of	of	ADP
ap-4740	395	15	the	the	DET
ap-4740	395	16	fba	fba	PROPN
ap-4740	395	17	method	method	NOUN
ap-4740	395	18	in	in	ADP
ap-4740	395	19	terms	term	NOUN
ap-4740	395	20	of	of	ADP
ap-4740	395	21	such	such	ADJ
ap-4740	395	22	symmetric	symmetric	ADJ
ap-4740	395	23	polynomials	polynomial	NOUN
ap-4740	395	24	are	be	AUX
ap-4740	395	25	new	new	ADJ
ap-4740	395	26	results	result	NOUN
ap-4740	395	27	.	.	PUNCT
ap-4740	396	1	in	in	ADP
ap-4740	396	2	addition	addition	NOUN
ap-4740	396	3	,	,	PUNCT
ap-4740	396	4	their	their	PRON
ap-4740	396	5	practical	practical	ADJ
ap-4740	396	6	usefulness	usefulness	NOUN
ap-4740	396	7	has	have	AUX
ap-4740	396	8	been	be	AUX
ap-4740	396	9	demonstrated	demonstrate	VERB
ap-4740	396	10	by	by	ADP
ap-4740	396	11	solving	solve	VERB
ap-4740	396	12	a	a	DET
ap-4740	396	13	qes	qes	NOUN
ap-4740	396	14	extension	extension	NOUN
ap-4740	396	15	of	of	ADP
ap-4740	396	16	the	the	DET
ap-4740	396	17	mathewslakshmanan	mathewslakshmanan	PROPN
ap-4740	396	18	nonlinear	nonlinear	PROPN
ap-4740	396	19	oscillator	oscillator	PROPN
ap-4740	396	20	,	,	PUNCT
ap-4740	396	21	corresponding	correspond	VERB
ap-4740	396	22	to	to	ADP
ap-4740	396	23	k	k	PROPN
ap-4740	396	24	=	=	PUNCT
ap-4740	396	25	4	4	NUM
ap-4740	396	26	.	.	NOUN
ap-4740	396	27	7	7	X
ap-4740	396	28	.	.	X
ap-4740	396	29	appendix	appendix	VERB
ap-4740	396	30	the	the	DET
ap-4740	396	31	purpose	purpose	NOUN
ap-4740	396	32	of	of	ADP
ap-4740	396	33	this	this	DET
ap-4740	396	34	appendix	appendix	NOUN
ap-4740	396	35	is	be	AUX
ap-4740	396	36	to	to	PART
ap-4740	396	37	solve	solve	VERB
ap-4740	396	38	equation	equation	NOUN
ap-4740	396	39	(	(	PUNCT
ap-4740	396	40	2.20	2.20	NUM
ap-4740	396	41	)	)	PUNCT
ap-4740	396	42	for	for	ADP
ap-4740	396	43	r	r	NOUN
ap-4740	396	44	=	=	SYM
ap-4740	396	45	3	3	NUM
ap-4740	396	46	,	,	PUNCT
ap-4740	396	47	4	4	NUM
ap-4740	396	48	,	,	PUNCT
ap-4740	396	49	5	5	NUM
ap-4740	396	50	and	and	CCONJ
ap-4740	396	51	to	to	PART
ap-4740	396	52	show	show	VERB
ap-4740	396	53	that	that	SCONJ
ap-4740	396	54	the	the	DET
ap-4740	396	55	resulting	result	VERB
ap-4740	396	56	expressions	expression	NOUN
ap-4740	396	57	of	of	ADP
ap-4740	396	58	c1,n	c1,n	PROPN
ap-4740	396	59	,	,	PUNCT
ap-4740	396	60	c2,n	c2,n	PROPN
ap-4740	396	61	,	,	PUNCT
ap-4740	396	62	and	and	CCONJ
ap-4740	396	63	c3,n	c3,n	PROPN
ap-4740	396	64	agree	agree	VERB
ap-4740	396	65	with	with	ADP
ap-4740	396	66	equation	equation	NOUN
ap-4740	396	67	(	(	PUNCT
ap-4740	396	68	2.22	2.22	NUM
ap-4740	396	69	)	)	PUNCT
ap-4740	396	70	.	.	PUNCT
ap-4740	397	1	for	for	ADP
ap-4740	397	2	r	r	NOUN
ap-4740	397	3	=	=	SYM
ap-4740	397	4	3	3	NUM
ap-4740	397	5	,	,	PUNCT
ap-4740	397	6	equation	equation	NOUN
ap-4740	397	7	(	(	PUNCT
ap-4740	397	8	2.20	2.20	NUM
ap-4740	397	9	)	)	PUNCT
ap-4740	397	10	directly	directly	ADV
ap-4740	397	11	leads	lead	VERB
ap-4740	397	12	to	to	ADP
ap-4740	397	13	c1,n	c1,n	PROPN
ap-4740	397	14	(	(	PUNCT
ap-4740	397	15	k	k	NOUN
ap-4740	397	16	−	−	PROPN
ap-4740	397	17	3	3	NUM
ap-4740	397	18	)	)	PUNCT
ap-4740	397	19	!	!	PUNCT
ap-4740	398	1	=	=	NOUN
ap-4740	399	1	−[2(n−	−[2(n−	PRON
ap-4740	399	2	1)ak	1)ak	PROPN
ap-4740	400	1	+	+	NUM
ap-4740	400	2	bk−1]e1	bk−1]e1	NOUN
ap-4740	400	3	−	−	NOUN
ap-4740	400	4	2n(n−	2n(n−	NUM
ap-4740	400	5	1	1	NUM
ap-4740	400	6	)	)	PUNCT
ap-4740	400	7	k	k	NOUN
ap-4740	400	8	ak−1	ak−1	ADV
ap-4740	400	9	−	−	PROPN
ap-4740	400	10	n	n	CCONJ
ap-4740	400	11	k	k	PROPN
ap-4740	401	1	−	−	PROPN
ap-4740	401	2	1bk−2	1bk−2	PROPN
ap-4740	401	3	,	,	PUNCT
ap-4740	401	4	(	(	PUNCT
ap-4740	401	5	7.1	7.1	NUM
ap-4740	401	6	)	)	PUNCT
ap-4740	401	7	which	which	PRON
ap-4740	401	8	corresponds	correspond	VERB
ap-4740	401	9	to	to	ADP
ap-4740	401	10	equation	equation	NOUN
ap-4740	401	11	(	(	PUNCT
ap-4740	401	12	2.22	2.22	NUM
ap-4740	401	13	)	)	PUNCT
ap-4740	401	14	for	for	ADP
ap-4740	401	15	q	q	NOUN
ap-4740	401	16	=	=	SYM
ap-4740	401	17	1	1	NUM
ap-4740	401	18	because	because	SCONJ
ap-4740	401	19	e1	e1	NOUN
ap-4740	401	20	=	=	SYM
ap-4740	401	21	m(1,0̇	m(1,0̇	NOUN
ap-4740	401	22	)	)	PUNCT
ap-4740	401	23	.	.	PUNCT
ap-4740	402	1	for	for	ADP
ap-4740	402	2	r	r	NOUN
ap-4740	402	3	=	=	SYM
ap-4740	402	4	4	4	NUM
ap-4740	402	5	,	,	PUNCT
ap-4740	402	6	equation	equation	NOUN
ap-4740	402	7	(	(	PUNCT
ap-4740	402	8	2.20	2.20	NUM
ap-4740	402	9	)	)	PUNCT
ap-4740	402	10	becomes	become	VERB
ap-4740	402	11	c2,n	c2,n	PROPN
ap-4740	402	12	(	(	PUNCT
ap-4740	402	13	k	k	NOUN
ap-4740	403	1	−	−	PROPN
ap-4740	403	2	4	4	NUM
ap-4740	403	3	)	)	PUNCT
ap-4740	403	4	!	!	PUNCT
ap-4740	404	1	−	−	PROPN
ap-4740	405	1	c1,n	c1,n	PROPN
ap-4740	405	2	(	(	PUNCT
ap-4740	405	3	k	k	PROPN
ap-4740	405	4	−	−	PROPN
ap-4740	405	5	3)!e1	3)!e1	PROPN
ap-4740	405	6	=	=	SYM
ap-4740	405	7	2[(2n−	2[(2n−	NUM
ap-4740	405	8	3)ak	3)ak	NUM
ap-4740	405	9	+	+	NUM
ap-4740	405	10	bk−1]e2	bk−1]e2	NOUN
ap-4740	405	11	+	+	CCONJ
ap-4740	405	12	[	[	X
ap-4740	405	13	2	2	NUM
ap-4740	405	14	k	k	NOUN
ap-4740	405	15	(	(	PUNCT
ap-4740	405	16	n−	n−	NOUN
ap-4740	405	17	1)(n−	1)(n−	NUM
ap-4740	405	18	k)ak−1	k)ak−1	NOUN
ap-4740	405	19	+	+	CCONJ
ap-4740	405	20	1	1	NUM
ap-4740	405	21	k	k	NOUN
ap-4740	405	22	−	−	PROPN
ap-4740	406	1	1(n−	1(n−	NUM
ap-4740	407	1	k	k	PROPN
ap-4740	408	1	+	+	CCONJ
ap-4740	408	2	1)bk−2	1)bk−2	PROPN
ap-4740	408	3	]	]	PUNCT
ap-4740	408	4	e1	e1	PROPN
ap-4740	408	5	−	−	PROPN
ap-4740	408	6	2n(n−	2n(n−	NUM
ap-4740	408	7	1	1	NUM
ap-4740	408	8	)	)	PUNCT
ap-4740	408	9	k(k	k(k	NOUN
ap-4740	408	10	−	−	NOUN
ap-4740	408	11	1	1	NUM
ap-4740	408	12	)	)	PUNCT
ap-4740	408	13	(	(	PUNCT
ap-4740	408	14	2k	2k	NOUN
ap-4740	408	15	−	−	NUM
ap-4740	408	16	3)ak−2	3)ak−2	NUM
ap-4740	408	17	−	−	NUM
ap-4740	408	18	2n	2n	NUM
ap-4740	409	1	k	k	PRON
ap-4740	409	2	−	−	PROPN
ap-4740	409	3	1bk−3	1bk−3	NOUN
ap-4740	409	4	.	.	PUNCT
ap-4740	410	1	(	(	PUNCT
ap-4740	410	2	7.2	7.2	NUM
ap-4740	410	3	)	)	PUNCT
ap-4740	410	4	on	on	ADP
ap-4740	410	5	inserting	insert	VERB
ap-4740	410	6	(	(	PUNCT
ap-4740	410	7	7.1	7.1	NUM
ap-4740	410	8	)	)	PUNCT
ap-4740	410	9	in	in	ADP
ap-4740	410	10	(	(	PUNCT
ap-4740	410	11	7.2	7.2	NUM
ap-4740	410	12	)	)	PUNCT
ap-4740	410	13	and	and	CCONJ
ap-4740	410	14	using	use	VERB
ap-4740	410	15	the	the	DET
ap-4740	410	16	identities	identity	NOUN
ap-4740	410	17	e2	e2	PROPN
ap-4740	410	18	=	=	PUNCT
ap-4740	410	19	m(12,0̇	m(12,0̇	NOUN
ap-4740	410	20	)	)	PUNCT
ap-4740	410	21	,	,	PUNCT
ap-4740	410	22	e2	e2	PROPN
ap-4740	410	23	1	1	NUM
ap-4740	410	24	=	=	SYM
ap-4740	410	25	m(2,0̇	m(2,0̇	NOUN
ap-4740	410	26	)	)	PUNCT
ap-4740	411	1	+	+	CCONJ
ap-4740	411	2	2m(12,0̇	2m(12,0̇	NUM
ap-4740	411	3	)	)	PUNCT
ap-4740	411	4	,	,	PUNCT
ap-4740	411	5	we	we	PRON
ap-4740	411	6	get	get	VERB
ap-4740	411	7	c2,n	c2,n	VERB
ap-4740	411	8	(	(	PUNCT
ap-4740	411	9	k	k	NOUN
ap-4740	411	10	−	−	PROPN
ap-4740	411	11	4	4	NUM
ap-4740	411	12	)	)	PUNCT
ap-4740	411	13	!	!	PUNCT
ap-4740	412	1	=	=	NOUN
ap-4740	413	1	−[2(n−	−[2(n−	PRON
ap-4740	413	2	1)ak	1)ak	PROPN
ap-4740	413	3	+	+	CCONJ
ap-4740	413	4	bk−1]m(2,0̇	bk−1]m(2,0̇	NOUN
ap-4740	413	5	)	)	PUNCT
ap-4740	413	6	−	−	PROPN
ap-4740	414	1	[	[	X
ap-4740	414	2	2(n−	2(n−	NUM
ap-4740	414	3	1)ak−1	1)ak−1	NUM
ap-4740	414	4	+	+	NUM
ap-4740	414	5	bk−2]m(1,0̇	bk−2]m(1,0̇	NOUN
ap-4740	414	6	)	)	PUNCT
ap-4740	414	7	−	−	NUM
ap-4740	414	8	2akm(12,0̇	2akm(12,0̇	NUM
ap-4740	414	9	)	)	PUNCT
ap-4740	414	10	−	−	PROPN
ap-4740	414	11	2n(n−	2n(n−	NUM
ap-4740	414	12	1	1	NUM
ap-4740	414	13	)	)	PUNCT
ap-4740	414	14	k(k	k(k	NOUN
ap-4740	414	15	−	−	NOUN
ap-4740	414	16	1	1	NUM
ap-4740	414	17	)	)	PUNCT
ap-4740	414	18	(	(	PUNCT
ap-4740	414	19	2k	2k	NOUN
ap-4740	414	20	−	−	NUM
ap-4740	414	21	3)ak−2	3)ak−2	NUM
ap-4740	414	22	−	−	NUM
ap-4740	414	23	2n	2n	NUM
ap-4740	415	1	k	k	PRON
ap-4740	415	2	−	−	PROPN
ap-4740	415	3	1bk−3	1bk−3	NOUN
ap-4740	415	4	,	,	PUNCT
ap-4740	415	5	(	(	PUNCT
ap-4740	415	6	7.3	7.3	NUM
ap-4740	415	7	)	)	PUNCT
ap-4740	415	8	which	which	PRON
ap-4740	415	9	agrees	agree	VERB
ap-4740	415	10	with	with	ADP
ap-4740	415	11	equation	equation	NOUN
ap-4740	415	12	(	(	PUNCT
ap-4740	415	13	2.22	2.22	NUM
ap-4740	415	14	)	)	PUNCT
ap-4740	415	15	for	for	ADP
ap-4740	415	16	q	q	NOUN
ap-4740	415	17	=	=	SYM
ap-4740	415	18	2	2	X
ap-4740	415	19	.	.	PUNCT
ap-4740	415	20	on	on	ADP
ap-4740	415	21	setting	set	VERB
ap-4740	415	22	now	now	ADV
ap-4740	415	23	r	r	NOUN
ap-4740	415	24	=	=	SYM
ap-4740	415	25	5	5	NUM
ap-4740	415	26	in	in	ADP
ap-4740	415	27	equation	equation	NOUN
ap-4740	415	28	(	(	PUNCT
ap-4740	415	29	2.20	2.20	NUM
ap-4740	415	30	)	)	PUNCT
ap-4740	415	31	,	,	PUNCT
ap-4740	415	32	we	we	PRON
ap-4740	415	33	obtain	obtain	VERB
ap-4740	415	34	c3,n	c3,n	PROPN
ap-4740	415	35	(	(	PUNCT
ap-4740	415	36	k	k	PROPN
ap-4740	415	37	−	−	PROPN
ap-4740	415	38	5	5	NUM
ap-4740	415	39	)	)	PUNCT
ap-4740	415	40	!	!	PUNCT
ap-4740	416	1	−	−	PROPN
ap-4740	417	1	c2,n	c2,n	PROPN
ap-4740	417	2	(	(	PUNCT
ap-4740	417	3	k	k	NOUN
ap-4740	417	4	−	−	PROPN
ap-4740	417	5	4)!e1	4)!e1	NUM
ap-4740	418	1	+	+	NUM
ap-4740	418	2	c1,n	c1,n	PROPN
ap-4740	418	3	(	(	PUNCT
ap-4740	418	4	k	k	NOUN
ap-4740	418	5	−	−	PROPN
ap-4740	418	6	3)!e2	3)!e2	NUM
ap-4740	418	7	=	=	SYM
ap-4740	418	8	−3[2(n−	−3[2(n−	PROPN
ap-4740	418	9	2)ak	2)ak	PROPN
ap-4740	418	10	+	+	CCONJ
ap-4740	418	11	bk−1]e3	bk−1]e3	PROPN
ap-4740	418	12	−	−	PROPN
ap-4740	418	13	{	{	PUNCT
ap-4740	418	14	2	2	NUM
ap-4740	418	15	k	k	NOUN
ap-4740	418	16	[	[	X
ap-4740	418	17	n2	n2	ADJ
ap-4740	418	18	−	−	PROPN
ap-4740	418	19	(	(	PUNCT
ap-4740	418	20	2k	2k	NUM
ap-4740	418	21	+	+	CCONJ
ap-4740	418	22	1)n+	1)n+	NUM
ap-4740	418	23	3k]ak−1	3k]ak−1	NUM
ap-4740	418	24	+	+	NUM
ap-4740	418	25	1	1	NUM
ap-4740	418	26	k	k	NOUN
ap-4740	418	27	−	−	PROPN
ap-4740	418	28	1(n−	1(n−	NUM
ap-4740	418	29	2k	2k	NOUN
ap-4740	418	30	+	+	CCONJ
ap-4740	418	31	2)bk−2	2)bk−2	NUM
ap-4740	418	32	}	}	PUNCT
ap-4740	418	33	e2	e2	NOUN
ap-4740	418	34	+	+	CCONJ
ap-4740	418	35	{	{	PUNCT
ap-4740	418	36	2	2	NUM
ap-4740	418	37	k(k	k(k	NOUN
ap-4740	418	38	−	−	PROPN
ap-4740	418	39	1)(n−	1)(n−	NUM
ap-4740	418	40	1)[(2k	1)[(2k	NUM
ap-4740	418	41	−	−	PROPN
ap-4740	418	42	3)n−	3)n−	NUM
ap-4740	418	43	k(k	k(k	ADJ
ap-4740	418	44	−	−	PROPN
ap-4740	419	1	1)]ak−2	1)]ak−2	PROPN
ap-4740	420	1	+	+	NOUN
ap-4740	420	2	1	1	NUM
ap-4740	420	3	k	k	NOUN
ap-4740	420	4	−	−	PROPN
ap-4740	421	1	1(2n−	1(2n−	NUM
ap-4740	421	2	k	k	PROPN
ap-4740	421	3	+	+	CCONJ
ap-4740	421	4	1)bk−3	1)bk−3	PROPN
ap-4740	421	5	}	}	PUNCT
ap-4740	421	6	e1	e1	VERB
ap-4740	421	7	−	−	PROPN
ap-4740	421	8	6n(n−	6n(n−	NUM
ap-4740	421	9	1	1	NUM
ap-4740	421	10	)	)	PUNCT
ap-4740	421	11	k(k	k(k	NOUN
ap-4740	421	12	−	−	NOUN
ap-4740	421	13	1	1	NUM
ap-4740	421	14	)	)	PUNCT
ap-4740	421	15	(	(	PUNCT
ap-4740	421	16	k	k	NOUN
ap-4740	421	17	−	−	PROPN
ap-4740	421	18	2)ak−3	2)ak−3	PROPN
ap-4740	421	19	−	−	NOUN
ap-4740	421	20	3n	3n	NUM
ap-4740	422	1	k	k	NOUN
ap-4740	422	2	−	−	PROPN
ap-4740	422	3	1bk−4	1bk−4	NUM
ap-4740	422	4	.	.	PUNCT
ap-4740	423	1	(	(	PUNCT
ap-4740	423	2	7.4	7.4	NUM
ap-4740	423	3	)	)	PUNCT
ap-4740	423	4	here	here	ADV
ap-4740	423	5	,	,	PUNCT
ap-4740	423	6	let	let	VERB
ap-4740	423	7	us	we	PRON
ap-4740	423	8	employ	employ	VERB
ap-4740	423	9	equations	equation	NOUN
ap-4740	423	10	(	(	PUNCT
ap-4740	423	11	7.1	7.1	NUM
ap-4740	423	12	)	)	PUNCT
ap-4740	423	13	and	and	CCONJ
ap-4740	423	14	(	(	PUNCT
ap-4740	423	15	7.3	7.3	NUM
ap-4740	423	16	)	)	PUNCT
ap-4740	423	17	,	,	PUNCT
ap-4740	423	18	as	as	ADV
ap-4740	423	19	well	well	ADV
ap-4740	423	20	as	as	ADP
ap-4740	423	21	the	the	DET
ap-4740	423	22	identities	identity	NOUN
ap-4740	423	23	e3	e3	VERB
ap-4740	423	24	=	=	NOUN
ap-4740	423	25	m(13,0̇	m(13,0̇	NOUN
ap-4740	423	26	)	)	PUNCT
ap-4740	423	27	,	,	PUNCT
ap-4740	423	28	m(2,0̇)m(1,0̇	m(2,0̇)m(1,0̇	NOUN
ap-4740	423	29	)	)	PUNCT
ap-4740	423	30	=	=	SYM
ap-4740	423	31	m(3,0̇	m(3,0̇	NOUN
ap-4740	423	32	)	)	PUNCT
ap-4740	424	1	+	+	CCONJ
ap-4740	424	2	m(2,1,0̇	m(2,1,0̇	NOUN
ap-4740	424	3	)	)	PUNCT
ap-4740	424	4	,	,	PUNCT
ap-4740	424	5	and	and	CCONJ
ap-4740	424	6	m(12,0̇)m(1,0̇	m(12,0̇)m(1,0̇	NOUN
ap-4740	424	7	)	)	PUNCT
ap-4740	424	8	=	=	SYM
ap-4740	424	9	m(2,1,0̇	m(2,1,0̇	NOUN
ap-4740	424	10	)	)	PUNCT
ap-4740	425	1	+	+	CCONJ
ap-4740	425	2	3m(13,0̇	3m(13,0̇	NUM
ap-4740	425	3	)	)	PUNCT
ap-4740	425	4	.	.	PUNCT
ap-4740	426	1	for	for	ADP
ap-4740	426	2	the	the	DET
ap-4740	426	3	coefficient	coefficient	NOUN
ap-4740	426	4	of	of	ADP
ap-4740	426	5	m(13,0̇	m(13,0̇	NOUN
ap-4740	426	6	)	)	PUNCT
ap-4740	426	7	in	in	ADP
ap-4740	426	8	c3,n/(k	c3,n/(k	ADP
ap-4740	426	9	−	−	PROPN
ap-4740	426	10	5	5	NUM
ap-4740	426	11	)	)	PUNCT
ap-4740	426	12	!	!	PUNCT
ap-4740	426	13	,	,	PUNCT
ap-4740	426	14	we	we	PRON
ap-4740	426	15	obtain	obtain	VERB
ap-4740	426	16	−3[2(n−	−3[2(n−	PRON
ap-4740	426	17	2)ak	2)ak	PROPN
ap-4740	427	1	+	+	CCONJ
ap-4740	427	2	bk−1	bk−1	NOUN
ap-4740	427	3	]	]	PUNCT
ap-4740	427	4	from	from	ADP
ap-4740	427	5	the	the	DET
ap-4740	427	6	right	right	ADJ
ap-4740	427	7	-	-	PUNCT
ap-4740	427	8	hand	hand	NOUN
ap-4740	427	9	side	side	NOUN
ap-4740	427	10	of	of	ADP
ap-4740	427	11	(	(	PUNCT
ap-4740	427	12	7.4	7.4	NUM
ap-4740	427	13	)	)	PUNCT
ap-4740	427	14	,	,	PUNCT
ap-4740	427	15	−6ak	−6ak	NOUN
ap-4740	427	16	from	from	ADP
ap-4740	427	17	c2,ne1/(k	c2,ne1/(k	NOUN
ap-4740	427	18	−	−	PROPN
ap-4740	427	19	4	4	NUM
ap-4740	427	20	)	)	PUNCT
ap-4740	427	21	!	!	PUNCT
ap-4740	427	22	,	,	PUNCT
ap-4740	427	23	and	and	CCONJ
ap-4740	427	24	3[2(n−	3[2(n−	NUM
ap-4740	427	25	1)ak	1)ak	PROPN
ap-4740	428	1	+	+	CCONJ
ap-4740	428	2	bk−1	bk−1	NOUN
ap-4740	428	3	]	]	PUNCT
ap-4740	428	4	from	from	ADP
ap-4740	428	5	−c1,ne2/(k−	−c1,ne2/(k−	DET
ap-4740	428	6	3	3	NUM
ap-4740	428	7	)	)	PUNCT
ap-4740	428	8	!	!	PUNCT
ap-4740	428	9	,	,	PUNCT
ap-4740	428	10	respectively	respectively	ADV
ap-4740	428	11	.	.	PUNCT
ap-4740	429	1	we	we	PRON
ap-4740	429	2	conclude	conclude	VERB
ap-4740	429	3	that	that	SCONJ
ap-4740	429	4	m(13,0̇	m(13,0̇	NOUN
ap-4740	429	5	)	)	PUNCT
ap-4740	429	6	does	do	AUX
ap-4740	429	7	not	not	PART
ap-4740	429	8	occur	occur	VERB
ap-4740	429	9	in	in	ADP
ap-4740	429	10	c3,n/(k−	c3,n/(k−	NOUN
ap-4740	429	11	5	5	NUM
ap-4740	429	12	)	)	PUNCT
ap-4740	429	13	!	!	PUNCT
ap-4740	429	14	,	,	PUNCT
ap-4740	429	15	which	which	PRON
ap-4740	429	16	is	be	AUX
ap-4740	429	17	given	give	VERB
ap-4740	429	18	by	by	ADP
ap-4740	429	19	c3,n	c3,n	PROPN
ap-4740	429	20	(	(	PUNCT
ap-4740	429	21	k	k	PROPN
ap-4740	429	22	−	−	PROPN
ap-4740	429	23	5	5	NUM
ap-4740	429	24	)	)	PUNCT
ap-4740	429	25	!	!	PUNCT
ap-4740	430	1	=	=	NOUN
ap-4740	431	1	−[2(n−	−[2(n−	PRON
ap-4740	431	2	1)ak	1)ak	PROPN
ap-4740	432	1	+	+	CCONJ
ap-4740	432	2	bk−1]m(3,0̇	bk−1]m(3,0̇	NOUN
ap-4740	432	3	)	)	PUNCT
ap-4740	432	4	−	−	PUNCT
ap-4740	433	1	[	[	X
ap-4740	433	2	2(n−	2(n−	NUM
ap-4740	433	3	1)ak−1	1)ak−1	NUM
ap-4740	433	4	+	+	NUM
ap-4740	433	5	bk−2]m(2,0̇	bk−2]m(2,0̇	NOUN
ap-4740	433	6	)	)	PUNCT
ap-4740	433	7	−	−	PROPN
ap-4740	434	1	[	[	X
ap-4740	434	2	2(n−	2(n−	NUM
ap-4740	434	3	1)ak−2	1)ak−2	NUM
ap-4740	435	1	+	+	CCONJ
ap-4740	435	2	bk−3]m(1,0̇	bk−3]m(1,0̇	NOUN
ap-4740	435	3	)	)	PUNCT
ap-4740	436	1	−	−	NOUN
ap-4740	436	2	2akm(2,1,0̇	2akm(2,1,0̇	NUM
ap-4740	436	3	)	)	PUNCT
ap-4740	437	1	−	−	ADP
ap-4740	437	2	2ak−1m(12,0̇	2ak−1m(12,0̇	NUM
ap-4740	437	3	)	)	PUNCT
ap-4740	437	4	−	−	NOUN
ap-4740	437	5	6n(n−	6n(n−	NUM
ap-4740	437	6	1	1	NUM
ap-4740	437	7	)	)	PUNCT
ap-4740	437	8	k(k	k(k	NOUN
ap-4740	437	9	−	−	NOUN
ap-4740	437	10	1	1	NUM
ap-4740	437	11	)	)	PUNCT
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ap-4740	437	14	−	−	PROPN
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ap-4740	437	19	−	−	PROPN
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ap-4740	437	21	,	,	PUNCT
ap-4740	437	22	(	(	PUNCT
ap-4740	437	23	7.5	7.5	NUM
ap-4740	437	24	)	)	PUNCT
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ap-4740	437	26	agreement	agreement	NOUN
ap-4740	437	27	with	with	ADP
ap-4740	437	28	equation	equation	NOUN
ap-4740	437	29	(	(	PUNCT
ap-4740	437	30	2.22	2.22	NUM
ap-4740	437	31	)	)	PUNCT
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ap-4740	437	34	=	=	SYM
ap-4740	437	35	3	3	NUM
ap-4740	437	36	.	.	NOUN
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ap-4740	437	39	.	.	PUNCT
ap-4740	438	1	58	58	NUM
ap-4740	438	2	no	no	INTJ
ap-4740	438	3	.	.	PUNCT
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ap-4740	439	3	-	-	ADJ
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ap-4740	439	6	schrödinger	schrödinger	ADJ
ap-4740	439	7	equations	equation	NOUN
ap-4740	439	8	references	reference	NOUN
ap-4740	439	9	[	[	X
ap-4740	439	10	1	1	NUM
ap-4740	439	11	]	]	X
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ap-4740	439	14	,	,	PUNCT
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ap-4740	439	17	,	,	PUNCT
ap-4740	439	18	u.	u.	PROPN
ap-4740	439	19	sukhatme	sukhatme	PROPN
ap-4740	439	20	.	.	PUNCT
ap-4740	440	1	supersymmetry	supersymmetry	NOUN
ap-4740	440	2	and	and	CCONJ
ap-4740	440	3	quantum	quantum	NOUN
ap-4740	440	4	mechanics	mechanic	NOUN
ap-4740	440	5	,	,	PUNCT
ap-4740	440	6	phys	phy	NOUN
ap-4740	440	7	.	.	PUNCT
ap-4740	441	1	rep	rep	PROPN
ap-4740	441	2	.	.	PROPN
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ap-4740	441	4	,	,	PUNCT
ap-4740	441	5	1995	1995	NUM
ap-4740	441	6	.	.	PUNCT
ap-4740	442	1	doi:10.1016/0370	doi:10.1016/0370	NOUN
ap-4740	442	2	-	-	PUNCT
ap-4740	442	3	1573(94)00080	1573(94)00080	NUM
ap-4740	442	4	-	-	PUNCT
ap-4740	442	5	m.	m.	NOUN
ap-4740	442	6	[	[	X
ap-4740	442	7	2	2	NUM
ap-4740	442	8	]	]	X
ap-4740	442	9	d.	d.	PROPN
ap-4740	442	10	gómez	gómez	PROPN
ap-4740	442	11	-	-	PUNCT
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ap-4740	442	13	,	,	PUNCT
ap-4740	442	14	y.	y.	PROPN
ap-4740	442	15	grandati	grandati	PROPN
ap-4740	442	16	,	,	PUNCT
ap-4740	442	17	r.	r.	PROPN
ap-4740	442	18	milson	milson	PROPN
ap-4740	442	19	.	.	PUNCT
ap-4740	443	1	extended	extend	VERB
ap-4740	443	2	krein	krein	PROPN
ap-4740	443	3	-	-	PUNCT
ap-4740	443	4	adler	adler	PROPN
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ap-4740	443	6	for	for	ADP
ap-4740	443	7	the	the	DET
ap-4740	443	8	translationally	translationally	ADJ
ap-4740	443	9	shape	shape	NOUN
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ap-4740	443	12	,	,	PUNCT
ap-4740	443	13	j.	j.	PROPN
ap-4740	443	14	math	math	PROPN
ap-4740	443	15	.	.	PUNCT
ap-4740	444	1	phys	phy	NOUN
ap-4740	444	2	.	.	PUNCT
ap-4740	445	1	55:043510	55:043510	NUM
ap-4740	445	2	,	,	PUNCT
ap-4740	445	3	30	30	NUM
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ap-4740	445	5	,	,	PUNCT
ap-4740	445	6	2014	2014	NUM
ap-4740	445	7	.	.	PUNCT
ap-4740	446	1	doi:10.1063/1.4871443	doi:10.1063/1.4871443	PROPN
ap-4740	446	2	.	.	PUNCT
ap-4740	447	1	[	[	X
ap-4740	447	2	3	3	X
ap-4740	447	3	]	]	X
ap-4740	447	4	g.	g.	PROPN
ap-4740	447	5	szegö	szegö	PROPN
ap-4740	447	6	.	.	PUNCT
ap-4740	448	1	orthogonal	orthogonal	ADJ
ap-4740	448	2	polynomials	polynomial	NOUN
ap-4740	448	3	,	,	PUNCT
ap-4740	448	4	american	american	PROPN
ap-4740	448	5	mathematical	mathematical	ADJ
ap-4740	448	6	society	society	NOUN
ap-4740	448	7	,	,	PUNCT
ap-4740	448	8	new	new	PROPN
ap-4740	448	9	york	york	PROPN
ap-4740	448	10	,	,	PUNCT
ap-4740	448	11	1939	1939	NUM
ap-4740	448	12	.	.	PUNCT
ap-4740	449	1	doi:10.1090	doi:10.1090	NOUN
ap-4740	449	2	/	/	SYM
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ap-4740	449	4	.	.	PUNCT
ap-4740	450	1	[	[	X
ap-4740	450	2	4	4	NUM
ap-4740	450	3	]	]	X
ap-4740	450	4	a.	a.	NOUN
ap-4740	450	5	v.	v.	PROPN
ap-4740	450	6	turbiner	turbiner	PROPN
ap-4740	450	7	,	,	PUNCT
ap-4740	450	8	a.	a.	NOUN
ap-4740	450	9	g.	g.	PROPN
ap-4740	450	10	ushveridze	ushveridze	PROPN
ap-4740	450	11	.	.	PUNCT
ap-4740	451	1	spectral	spectral	ADJ
ap-4740	451	2	singularities	singularity	NOUN
ap-4740	451	3	and	and	CCONJ
ap-4740	451	4	quasi	quasi	ADJ
ap-4740	451	5	-	-	ADJ
ap-4740	451	6	exactly	exactly	ADV
ap-4740	451	7	solvable	solvable	ADJ
ap-4740	451	8	quantal	quantal	ADJ
ap-4740	451	9	problem	problem	NOUN
ap-4740	451	10	,	,	PUNCT
ap-4740	451	11	phys	phy	NOUN
ap-4740	451	12	.	.	PUNCT
ap-4740	452	1	lett	lett	PROPN
ap-4740	452	2	.	.	PUNCT
ap-4740	453	1	a126:181–183	a126:181–183	PROPN
ap-4740	453	2	,	,	PUNCT
ap-4740	453	3	1987	1987	NUM
ap-4740	453	4	.	.	PUNCT
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ap-4740	454	2	-	-	PUNCT
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ap-4740	454	4	-	-	PUNCT
ap-4740	454	5	7	7	NUM
ap-4740	454	6	.	.	PUNCT
ap-4740	455	1	[	[	X
ap-4740	455	2	5	5	NUM
ap-4740	455	3	]	]	PUNCT
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ap-4740	455	5	v.	v.	PROPN
ap-4740	455	6	turbiner	turbiner	NOUN
ap-4740	455	7	.	.	PUNCT
ap-4740	456	1	quasi	quasi	ADJ
ap-4740	456	2	-	-	ADJ
ap-4740	456	3	exactly	exactly	ADV
ap-4740	456	4	-	-	PUNCT
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ap-4740	456	6	problems	problem	NOUN
ap-4740	456	7	and	and	CCONJ
ap-4740	456	8	sl(2	sl(2	PROPN
ap-4740	456	9	)	)	PUNCT
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ap-4740	456	11	,	,	PUNCT
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ap-4740	456	13	.	.	PUNCT
ap-4740	456	14	math	math	NOUN
ap-4740	456	15	.	.	PUNCT
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ap-4740	457	2	.	.	PUNCT
ap-4740	458	1	118:467–474	118:467–474	NUM
ap-4740	458	2	,	,	PUNCT
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ap-4740	458	4	.	.	PUNCT
ap-4740	459	1	doi:10.1007	doi:10.1007	VERB
ap-4740	459	2	/	/	SYM
ap-4740	459	3	bf01466727	bf01466727	ADJ
ap-4740	459	4	.	.	PUNCT
ap-4740	460	1	[	[	X
ap-4740	460	2	6	6	NUM
ap-4740	460	3	]	]	PUNCT
ap-4740	460	4	a.	a.	NOUN
ap-4740	460	5	g.	g.	PROPN
ap-4740	460	6	ushveridze	ushveridze	PROPN
ap-4740	460	7	.	.	PUNCT
ap-4740	461	1	quasi	quasi	ADJ
ap-4740	461	2	-	-	ADJ
ap-4740	461	3	exactly	exactly	ADV
ap-4740	461	4	solvable	solvable	ADJ
ap-4740	461	5	models	model	NOUN
ap-4740	461	6	in	in	ADP
ap-4740	461	7	quantum	quantum	ADJ
ap-4740	461	8	mechanics	mechanic	NOUN
ap-4740	461	9	,	,	PUNCT
ap-4740	461	10	iop	iop	PROPN
ap-4740	461	11	,	,	PUNCT
ap-4740	461	12	bristol	bristol	PROPN
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ap-4740	461	15	.	.	PUNCT
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ap-4740	462	2	.	.	PUNCT
ap-4740	463	1	[	[	X
ap-4740	463	2	7	7	X
ap-4740	463	3	]	]	PUNCT
ap-4740	463	4	a.	a.	PROPN
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ap-4740	463	6	-	-	PUNCT
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ap-4740	463	8	,	,	PUNCT
ap-4740	463	9	n.	n.	PROPN
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ap-4740	463	15	.	.	PUNCT
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ap-4740	464	2	of	of	ADP
ap-4740	464	3	one	one	NUM
ap-4740	464	4	-	-	PUNCT
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ap-4740	464	6	quasi	quasi	ADJ
ap-4740	464	7	-	-	ADJ
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ap-4740	464	10	schrödinger	schrödinger	ADJ
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ap-4740	464	12	,	,	PUNCT
ap-4740	464	13	commun	commun	PROPN
ap-4740	464	14	.	.	PUNCT
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ap-4740	464	16	.	.	PUNCT
ap-4740	465	1	phys	phy	NOUN
ap-4740	465	2	.	.	PUNCT
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ap-4740	466	2	,	,	PUNCT
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ap-4740	466	4	.	.	PUNCT
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ap-4740	467	2	/	/	SYM
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ap-4740	467	4	.	.	PUNCT
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ap-4740	468	2	8	8	NUM
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ap-4740	468	5	v.	v.	PROPN
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ap-4740	468	7	.	.	PUNCT
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ap-4740	469	2	-	-	PUNCT
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ap-4740	470	2	.	.	PROPN
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ap-4740	470	4	,	,	PUNCT
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ap-4740	470	6	.	.	PUNCT
ap-4740	471	1	doi:10.1016	doi:10.1016	PROPN
ap-4740	471	2	/	/	SYM
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ap-4740	471	4	.	.	PUNCT
ap-4740	472	1	[	[	X
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ap-4740	472	3	]	]	PUNCT
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ap-4740	472	6	,	,	PUNCT
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ap-4740	472	18	.	.	PUNCT
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ap-4740	473	3	]	]	X
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ap-4740	473	8	i.	i.	PROPN
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ap-4740	473	11	n.	n.	PROPN
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ap-4740	473	13	,	,	PUNCT
ap-4740	473	14	e.	e.	PROPN
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ap-4740	473	16	.	.	PUNCT
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ap-4740	474	2	applications	application	NOUN
ap-4740	474	3	of	of	ADP
ap-4740	474	4	second	second	ADJ
ap-4740	474	5	-	-	PUNCT
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ap-4740	474	14	,	,	PUNCT
ap-4740	474	15	j.	j.	PROPN
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ap-4740	474	17	.	.	PUNCT
ap-4740	475	1	a	a	DET
ap-4740	475	2	:	:	PUNCT
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ap-4740	475	4	.	.	PUNCT
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ap-4740	476	2	.	.	PUNCT
ap-4740	477	1	43:415206	43:415206	NUM
ap-4740	477	2	,	,	PUNCT
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ap-4740	477	5	,	,	PUNCT
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ap-4740	477	7	.	.	PUNCT
ap-4740	478	1	doi:10.1088/1751	doi:10.1088/1751	NOUN
ap-4740	478	2	-	-	PUNCT
ap-4740	478	3	8113/43/41/415206	8113/43/41/415206	NUM
ap-4740	478	4	.	.	PUNCT
ap-4740	479	1	[	[	X
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ap-4740	479	9	d’onde	d’onde	PROPN
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ap-4740	479	11	bethe	bethe	PROPN
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ap-4740	479	14	,	,	PUNCT
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ap-4740	479	16	,	,	PUNCT
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ap-4740	479	18	.	.	PUNCT
ap-4740	480	1	[	[	X
ap-4740	480	2	12	12	NUM
ap-4740	480	3	]	]	PUNCT
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ap-4740	480	5	.	.	PUNCT
ap-4740	481	1	ho	ho	PROPN
ap-4740	481	2	.	.	PROPN
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ap-4740	481	4	approach	approach	NOUN
ap-4740	481	5	to	to	ADP
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ap-4740	481	7	and	and	CCONJ
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ap-4740	481	9	-	-	ADJ
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ap-4740	481	12	,	,	PUNCT
ap-4740	481	13	ann	ann	PROPN
ap-4740	481	14	.	.	PUNCT
ap-4740	482	1	phys	phys	PROPN
ap-4740	482	2	.	.	PUNCT
ap-4740	483	1	(	(	PUNCT
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ap-4740	483	3	)	)	PUNCT
ap-4740	483	4	323:2241–2252	323:2241–2252	NUM
ap-4740	483	5	,	,	PUNCT
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ap-4740	483	7	.	.	PUNCT
ap-4740	484	1	doi:10.1016	doi:10.1016	PROPN
ap-4740	484	2	/	/	SYM
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ap-4740	484	4	.	.	PUNCT
ap-4740	485	1	[	[	X
ap-4740	485	2	13	13	NUM
ap-4740	485	3	]	]	PUNCT
ap-4740	485	4	y.-z	y.-z	NOUN
ap-4740	485	5	.	.	PUNCT
ap-4740	486	1	zhang	zhang	PROPN
ap-4740	486	2	.	.	PUNCT
ap-4740	487	1	exact	exact	ADJ
ap-4740	487	2	polynomial	polynomial	ADJ
ap-4740	487	3	solutions	solution	NOUN
ap-4740	487	4	of	of	ADP
ap-4740	487	5	second	second	ADJ
ap-4740	487	6	order	order	NOUN
ap-4740	487	7	differential	differential	ADJ
ap-4740	487	8	equations	equation	NOUN
ap-4740	487	9	and	and	CCONJ
ap-4740	487	10	their	their	PRON
ap-4740	487	11	applications	application	NOUN
ap-4740	487	12	,	,	PUNCT
ap-4740	487	13	j.	j.	PROPN
ap-4740	487	14	phys	phys	PROPN
ap-4740	487	15	.	.	PUNCT
ap-4740	488	1	a	a	DET
ap-4740	488	2	:	:	PUNCT
ap-4740	488	3	math	math	NOUN
ap-4740	488	4	.	.	PUNCT
ap-4740	489	1	theor	theor	PROPN
ap-4740	489	2	.	.	PUNCT
ap-4740	490	1	45:065206	45:065206	NUM
ap-4740	490	2	,	,	PUNCT
ap-4740	490	3	20	20	NUM
ap-4740	490	4	pages	page	NOUN
ap-4740	490	5	,	,	PUNCT
ap-4740	490	6	2012	2012	NUM
ap-4740	490	7	.	.	PUNCT
ap-4740	491	1	doi:10.1088/1751	doi:10.1088/1751	NOUN
ap-4740	491	2	-	-	PUNCT
ap-4740	491	3	8113/45/6/065206	8113/45/6/065206	NUM
ap-4740	491	4	.	.	PUNCT
ap-4740	492	1	[	[	X
ap-4740	492	2	14	14	NUM
ap-4740	492	3	]	]	X
ap-4740	492	4	d.	d.	PROPN
ap-4740	492	5	agboola	agboola	PROPN
ap-4740	492	6	,	,	PUNCT
ap-4740	492	7	y.-z	y.-z	PROPN
ap-4740	492	8	.	.	PUNCT
ap-4740	493	1	zhang	zhang	PROPN
ap-4740	493	2	.	.	PUNCT
ap-4740	494	1	exact	exact	ADJ
ap-4740	494	2	solutions	solution	NOUN
ap-4740	494	3	of	of	ADP
ap-4740	494	4	the	the	DET
ap-4740	494	5	schrödinger	schrödinger	ADJ
ap-4740	494	6	equation	equation	NOUN
ap-4740	494	7	with	with	ADP
ap-4740	494	8	spherically	spherically	PROPN
ap-4740	494	9	symmetric	symmetric	ADJ
ap-4740	494	10	octic	octic	ADJ
ap-4740	494	11	potential	potential	NOUN
ap-4740	494	12	,	,	PUNCT
ap-4740	494	13	mod	mod	PROPN
ap-4740	494	14	.	.	PUNCT
ap-4740	495	1	phys	phys	PROPN
ap-4740	495	2	.	.	PUNCT
ap-4740	496	1	lett	lett	PROPN
ap-4740	496	2	.	.	PUNCT
ap-4740	497	1	a27:1250112	a27:1250112	PROPN
ap-4740	497	2	,	,	PUNCT
ap-4740	497	3	8	8	NUM
ap-4740	497	4	pages	page	NOUN
ap-4740	497	5	,	,	PUNCT
ap-4740	497	6	2012	2012	NUM
ap-4740	497	7	.	.	PUNCT
ap-4740	498	1	doi:10.1142	doi:10.1142	NOUN
ap-4740	498	2	/	/	SYM
ap-4740	498	3	s021773231250112x	s021773231250112x	NOUN
ap-4740	498	4	.	.	PUNCT
ap-4740	499	1	[	[	X
ap-4740	499	2	15	15	NUM
ap-4740	499	3	]	]	X
ap-4740	499	4	d.	d.	PROPN
ap-4740	499	5	agboola	agboola	PROPN
ap-4740	499	6	,	,	PUNCT
ap-4740	499	7	y.-z	y.-z	PROPN
ap-4740	499	8	.	.	PUNCT
ap-4740	500	1	zhang	zhang	PROPN
ap-4740	500	2	.	.	PUNCT
ap-4740	501	1	novel	novel	PROPN
ap-4740	501	2	quasi	quasi	ADJ
ap-4740	501	3	-	-	ADJ
ap-4740	501	4	exactly	exactly	ADV
ap-4740	501	5	solvable	solvable	ADJ
ap-4740	501	6	models	model	NOUN
ap-4740	501	7	with	with	ADP
ap-4740	501	8	anharmonic	anharmonic	ADJ
ap-4740	501	9	singular	singular	NOUN
ap-4740	501	10	potentials	potential	NOUN
ap-4740	501	11	,	,	PUNCT
ap-4740	501	12	ann	ann	PROPN
ap-4740	501	13	.	.	PUNCT
ap-4740	501	14	phys	phys	PROPN
ap-4740	501	15	.	.	PUNCT
ap-4740	502	1	(	(	PUNCT
ap-4740	502	2	ny	ny	NOUN
ap-4740	502	3	)	)	PUNCT
ap-4740	502	4	330:246–262	330:246–262	NUM
ap-4740	502	5	,	,	PUNCT
ap-4740	502	6	2013	2013	NUM
ap-4740	502	7	.	.	PUNCT
ap-4740	503	1	doi:10.1016	doi:10.1016	PROPN
ap-4740	503	2	/	/	SYM
ap-4740	503	3	j.aop.2012.11.013	j.aop.2012.11.013	PROPN
ap-4740	503	4	.	.	PUNCT
ap-4740	504	1	[	[	X
ap-4740	504	2	16	16	NUM
ap-4740	504	3	]	]	X
ap-4740	504	4	d.	d.	PROPN
ap-4740	504	5	agboola	agboola	PROPN
ap-4740	504	6	,	,	PUNCT
ap-4740	504	7	j.	j.	PROPN
ap-4740	504	8	links	links	PROPN
ap-4740	504	9	,	,	PUNCT
ap-4740	504	10	i.	i.	PROPN
ap-4740	504	11	marquette	marquette	PROPN
ap-4740	504	12	,	,	PUNCT
ap-4740	504	13	y.-z	y.-z	PROPN
ap-4740	504	14	.	.	PUNCT
ap-4740	505	1	zhang	zhang	PROPN
ap-4740	505	2	.	.	PUNCT
ap-4740	506	1	new	new	ADJ
ap-4740	506	2	quasi	quasi	ADJ
ap-4740	506	3	-	-	ADJ
ap-4740	506	4	exactly	exactly	ADV
ap-4740	506	5	solvable	solvable	ADJ
ap-4740	506	6	class	class	NOUN
ap-4740	506	7	of	of	ADP
ap-4740	506	8	generalized	generalized	ADJ
ap-4740	506	9	isotonic	isotonic	ADJ
ap-4740	506	10	oscillators	oscillator	NOUN
ap-4740	506	11	,	,	PUNCT
ap-4740	506	12	j.	j.	PROPN
ap-4740	506	13	phys	phys	PROPN
ap-4740	506	14	.	.	PUNCT
ap-4740	507	1	a	a	DET
ap-4740	507	2	:	:	PUNCT
ap-4740	507	3	math	math	NOUN
ap-4740	507	4	.	.	PUNCT
ap-4740	508	1	theor	theor	PROPN
ap-4740	508	2	.	.	PUNCT
ap-4740	509	1	47:395305	47:395305	NUM
ap-4740	509	2	,	,	PUNCT
ap-4740	509	3	17	17	NUM
ap-4740	509	4	pages	page	NOUN
ap-4740	509	5	,	,	PUNCT
ap-4740	509	6	2014	2014	NUM
ap-4740	509	7	.	.	PUNCT
ap-4740	510	1	doi:10.1088/1751	doi:10.1088/1751	ADV
ap-4740	510	2	-	-	PUNCT
ap-4740	510	3	8113/47/39/395305	8113/47/39/395305	ADJ
ap-4740	510	4	.	.	PUNCT
ap-4740	511	1	[	[	X
ap-4740	511	2	17	17	NUM
ap-4740	511	3	]	]	PUNCT
ap-4740	511	4	c.	c.	NOUN
ap-4740	511	5	quesne	quesne	NOUN
ap-4740	511	6	.	.	PUNCT
ap-4740	512	1	families	family	NOUN
ap-4740	512	2	of	of	ADP
ap-4740	512	3	quasi	quasi	ADJ
ap-4740	512	4	-	-	ADJ
ap-4740	512	5	exactly	exactly	ADV
ap-4740	512	6	solvable	solvable	ADJ
ap-4740	512	7	extensions	extension	NOUN
ap-4740	512	8	of	of	ADP
ap-4740	512	9	the	the	DET
ap-4740	512	10	quantum	quantum	NOUN
ap-4740	512	11	oscillator	oscillator	NOUN
ap-4740	512	12	in	in	ADP
ap-4740	512	13	curved	curved	ADJ
ap-4740	512	14	spaces	space	NOUN
ap-4740	512	15	,	,	PUNCT
ap-4740	512	16	j.	j.	PROPN
ap-4740	512	17	math	math	PROPN
ap-4740	512	18	.	.	PUNCT
ap-4740	513	1	phys	phy	NOUN
ap-4740	513	2	.	.	PUNCT
ap-4740	514	1	58:052104	58:052104	NUM
ap-4740	514	2	,	,	PUNCT
ap-4740	514	3	19	19	NUM
ap-4740	514	4	pages	page	NOUN
ap-4740	514	5	,	,	PUNCT
ap-4740	514	6	2017	2017	NUM
ap-4740	514	7	.	.	PUNCT
ap-4740	515	1	doi:10.1063/1.4983563	doi:10.1063/1.4983563	ADV
ap-4740	515	2	.	.	PUNCT
ap-4740	516	1	[	[	X
ap-4740	516	2	18	18	NUM
ap-4740	516	3	]	]	X
ap-4740	516	4	e.	e.	PROPN
ap-4740	516	5	heine	heine	PROPN
ap-4740	516	6	.	.	PUNCT
ap-4740	516	7	handbuch	handbuch	PROPN
ap-4740	516	8	der	der	PROPN
ap-4740	516	9	kugelfunctionen	kugelfunctionen	PROPN
ap-4740	516	10	,	,	PUNCT
ap-4740	516	11	vol	vol	NOUN
ap-4740	516	12	.	.	PROPN
ap-4740	516	13	1	1	NUM
ap-4740	516	14	,	,	PUNCT
ap-4740	516	15	pp	pp	ADJ
ap-4740	516	16	.	.	PUNCT
ap-4740	517	1	472–479	472–479	NUM
ap-4740	517	2	,	,	PUNCT
ap-4740	517	3	g.	g.	PROPN
ap-4740	517	4	reimer	reimer	PROPN
ap-4740	517	5	,	,	PUNCT
ap-4740	517	6	berlin	berlin	PROPN
ap-4740	517	7	,	,	PUNCT
ap-4740	517	8	1878	1878	NUM
ap-4740	517	9	.	.	PUNCT
ap-4740	518	1	[	[	X
ap-4740	518	2	19	19	NUM
ap-4740	518	3	]	]	PUNCT
ap-4740	518	4	t.	t.	PROPN
ap-4740	518	5	j.	j.	PROPN
ap-4740	518	6	stieltjes	stieltjes	PROPN
ap-4740	518	7	.	.	PUNCT
ap-4740	519	1	sur	sur	PROPN
ap-4740	519	2	certains	certains	PROPN
ap-4740	519	3	polynômes	polynôme	NOUN
ap-4740	519	4	qui	qui	X
ap-4740	519	5	vérifient	vérifient	PROPN
ap-4740	519	6	une	une	PROPN
ap-4740	519	7	équation	équation	PROPN
ap-4740	519	8	differentielle	differentielle	NOUN
ap-4740	519	9	linéaire	linéaire	PROPN
ap-4740	519	10	du	du	PROPN
ap-4740	519	11	second	second	PROPN
ap-4740	519	12	ordre	ordre	PROPN
ap-4740	519	13	et	et	PROPN
ap-4740	519	14	sur	sur	PROPN
ap-4740	519	15	la	la	PROPN
ap-4740	519	16	théorie	théorie	PROPN
ap-4740	519	17	des	des	PROPN
ap-4740	519	18	fonctions	fonctions	PROPN
ap-4740	519	19	de	de	X
ap-4740	519	20	lamé	lamé	NOUN
ap-4740	519	21	,	,	PUNCT
ap-4740	519	22	acta	acta	PROPN
ap-4740	519	23	math	math	PROPN
ap-4740	519	24	.	.	PUNCT
ap-4740	520	1	6:321–326	6:321–326	NUM
ap-4740	520	2	,	,	PUNCT
ap-4740	520	3	1885	1885	NUM
ap-4740	520	4	.	.	PUNCT
ap-4740	521	1	[	[	X
ap-4740	521	2	20	20	NUM
ap-4740	521	3	]	]	X
ap-4740	521	4	c.	c.	NOUN
ap-4740	521	5	quesne	quesne	NOUN
ap-4740	521	6	,	,	PUNCT
ap-4740	521	7	v.	v.	ADP
ap-4740	521	8	m.	m.	NOUN
ap-4740	521	9	tkachuk	tkachuk	NOUN
ap-4740	521	10	.	.	PUNCT
ap-4740	522	1	deformed	deform	VERB
ap-4740	522	2	algebras	algebra	NOUN
ap-4740	522	3	,	,	PUNCT
ap-4740	522	4	position	position	NOUN
ap-4740	522	5	-	-	PUNCT
ap-4740	522	6	dependent	dependent	ADJ
ap-4740	522	7	effective	effective	ADJ
ap-4740	522	8	masses	masse	NOUN
ap-4740	522	9	and	and	CCONJ
ap-4740	522	10	curved	curved	ADJ
ap-4740	522	11	spaces	space	NOUN
ap-4740	522	12	:	:	PUNCT
ap-4740	522	13	an	an	DET
ap-4740	522	14	exactly	exactly	ADV
ap-4740	522	15	solvable	solvable	ADJ
ap-4740	522	16	coulomb	coulomb	NOUN
ap-4740	522	17	problem	problem	NOUN
ap-4740	522	18	,	,	PUNCT
ap-4740	522	19	j.	j.	PROPN
ap-4740	522	20	phys	phys	PROPN
ap-4740	522	21	.	.	PUNCT
ap-4740	523	1	a	a	DET
ap-4740	523	2	:	:	PUNCT
ap-4740	523	3	math	math	NOUN
ap-4740	523	4	.	.	PUNCT
ap-4740	524	1	gen	gen	PROPN
ap-4740	524	2	.	.	PROPN
ap-4740	524	3	37:4267–4281	37:4267–4281	NUM
ap-4740	524	4	,	,	PUNCT
ap-4740	524	5	2004	2004	NUM
ap-4740	524	6	.	.	PUNCT
ap-4740	525	1	doi:10.1088/0305	doi:10.1088/0305	ADJ
ap-4740	525	2	-	-	PUNCT
ap-4740	525	3	4470/37/14/006	4470/37/14/006	NOUN
ap-4740	525	4	.	.	PUNCT
ap-4740	526	1	[	[	X
ap-4740	526	2	21	21	NUM
ap-4740	526	3	]	]	X
ap-4740	526	4	h.	h.	PROPN
ap-4740	526	5	karayer	karayer	PROPN
ap-4740	526	6	,	,	PUNCT
ap-4740	526	7	d.	d.	PROPN
ap-4740	526	8	demirhan	demirhan	PROPN
ap-4740	526	9	,	,	PUNCT
ap-4740	526	10	f.	f.	PROPN
ap-4740	526	11	büyükkılıç	büyükkılıç	PROPN
ap-4740	526	12	.	.	PUNCT
ap-4740	527	1	extension	extension	NOUN
ap-4740	527	2	of	of	ADP
ap-4740	527	3	nikiforov	nikiforov	NOUN
ap-4740	527	4	-	-	PUNCT
ap-4740	527	5	uvarov	uvarov	ADJ
ap-4740	527	6	method	method	NOUN
ap-4740	527	7	for	for	ADP
ap-4740	527	8	the	the	DET
ap-4740	527	9	solution	solution	NOUN
ap-4740	527	10	of	of	ADP
ap-4740	527	11	heun	heun	ADJ
ap-4740	527	12	equation	equation	NOUN
ap-4740	527	13	,	,	PUNCT
ap-4740	527	14	j.	j.	PROPN
ap-4740	527	15	math	math	PROPN
ap-4740	527	16	.	.	PUNCT
ap-4740	528	1	phys	phy	NOUN
ap-4740	528	2	.	.	PUNCT
ap-4740	529	1	56:063504	56:063504	NUM
ap-4740	529	2	,	,	PUNCT
ap-4740	529	3	14	14	NUM
ap-4740	529	4	pages	page	NOUN
ap-4740	529	5	,	,	PUNCT
ap-4740	529	6	2015	2015	NUM
ap-4740	529	7	.	.	PUNCT
ap-4740	530	1	doi:10.1063/1.4922601	doi:10.1063/1.4922601	PROPN
ap-4740	530	2	.	.	PUNCT
ap-4740	531	1	[	[	X
ap-4740	531	2	22	22	NUM
ap-4740	531	3	]	]	X
ap-4740	531	4	d.	d.	PROPN
ap-4740	531	5	e.	e.	PROPN
ap-4740	531	6	littlewood	littlewood	PROPN
ap-4740	531	7	.	.	PUNCT
ap-4740	532	1	a	a	DET
ap-4740	532	2	university	university	NOUN
ap-4740	532	3	algebra	algebra	NOUN
ap-4740	532	4	:	:	PUNCT
ap-4740	532	5	an	an	DET
ap-4740	532	6	introduction	introduction	NOUN
ap-4740	532	7	to	to	ADP
ap-4740	532	8	classic	classic	ADJ
ap-4740	532	9	and	and	CCONJ
ap-4740	532	10	modern	modern	ADJ
ap-4740	532	11	algebra	algebra	PROPN
ap-4740	532	12	,	,	PUNCT
ap-4740	532	13	dover	dover	PROPN
ap-4740	532	14	,	,	PUNCT
ap-4740	532	15	new	new	PROPN
ap-4740	532	16	york	york	PROPN
ap-4740	532	17	,	,	PUNCT
ap-4740	532	18	1971	1971	NUM
ap-4740	532	19	.	.	PUNCT
ap-4740	533	1	[	[	X
ap-4740	533	2	23	23	NUM
ap-4740	533	3	]	]	X
ap-4740	533	4	p.	p.	NOUN
ap-4740	533	5	m.	m.	NOUN
ap-4740	533	6	mathews	mathews	PROPN
ap-4740	533	7	,	,	PUNCT
ap-4740	533	8	m.	m.	NOUN
ap-4740	533	9	lakshmanan	lakshmanan	PROPN
ap-4740	533	10	.	.	PUNCT
ap-4740	534	1	on	on	ADP
ap-4740	534	2	a	a	DET
ap-4740	534	3	unique	unique	ADJ
ap-4740	534	4	nonlinear	nonlinear	ADJ
ap-4740	534	5	oscillator	oscillator	NOUN
ap-4740	534	6	,	,	PUNCT
ap-4740	534	7	quart	quart	NOUN
ap-4740	534	8	.	.	PUNCT
ap-4740	535	1	appl	appl	PROPN
ap-4740	535	2	.	.	PROPN
ap-4740	535	3	math	math	NOUN
ap-4740	535	4	.	.	PUNCT
ap-4740	536	1	32:215–218	32:215–218	NUM
ap-4740	536	2	,	,	PUNCT
ap-4740	536	3	1974	1974	NUM
ap-4740	536	4	.	.	PUNCT
ap-4740	537	1	doi:10.1090	doi:10.1090	NOUN
ap-4740	537	2	/	/	SYM
ap-4740	537	3	qam/430422	qam/430422	NOUN
ap-4740	537	4	.	.	PUNCT
ap-4740	538	1	[	[	X
ap-4740	538	2	24	24	NUM
ap-4740	538	3	]	]	PUNCT
ap-4740	538	4	j.	j.	PROPN
ap-4740	538	5	f.	f.	PROPN
ap-4740	538	6	cariñena	cariñena	PROPN
ap-4740	538	7	,	,	PUNCT
ap-4740	538	8	m.	m.	PROPN
ap-4740	538	9	f.	f.	PROPN
ap-4740	538	10	rañada	rañada	PROPN
ap-4740	538	11	,	,	PUNCT
ap-4740	538	12	m.	m.	NOUN
ap-4740	538	13	santander	santander	NOUN
ap-4740	538	14	.	.	PUNCT
ap-4740	539	1	one	one	NUM
ap-4740	539	2	-	-	PUNCT
ap-4740	539	3	dimensional	dimensional	ADJ
ap-4740	539	4	model	model	NOUN
ap-4740	539	5	of	of	ADP
ap-4740	539	6	a	a	DET
ap-4740	539	7	quantum	quantum	ADJ
ap-4740	539	8	nonlinear	nonlinear	ADJ
ap-4740	539	9	harmonic	harmonic	ADJ
ap-4740	539	10	oscillator	oscillator	NOUN
ap-4740	539	11	,	,	PUNCT
ap-4740	539	12	rep	rep	PROPN
ap-4740	539	13	.	.	PROPN
ap-4740	539	14	math	math	NOUN
ap-4740	539	15	.	.	PUNCT
ap-4740	540	1	phys	phy	NOUN
ap-4740	540	2	.	.	PUNCT
ap-4740	541	1	54:285–293	54:285–293	NUM
ap-4740	541	2	,	,	PUNCT
ap-4740	541	3	2004	2004	NUM
ap-4740	541	4	.	.	PUNCT
ap-4740	542	1	doi:10.1016	doi:10.1016	PROPN
ap-4740	542	2	/	/	SYM
ap-4740	542	3	s0034	s0034	PROPN
ap-4740	542	4	-	-	PUNCT
ap-4740	542	5	4877(04)80020	4877(04)80020	NUM
ap-4740	542	6	-	-	PUNCT
ap-4740	542	7	x.	x.	NOUN
ap-4740	543	1	[	[	X
ap-4740	543	2	25	25	NUM
ap-4740	543	3	]	]	PUNCT
ap-4740	543	4	j.	j.	PROPN
ap-4740	543	5	f.	f.	PROPN
ap-4740	543	6	cariñena	cariñena	PROPN
ap-4740	543	7	,	,	PUNCT
ap-4740	543	8	m.	m.	PROPN
ap-4740	543	9	f.	f.	PROPN
ap-4740	543	10	rañada	rañada	PROPN
ap-4740	543	11	,	,	PUNCT
ap-4740	543	12	m.	m.	NOUN
ap-4740	543	13	santander	santander	NOUN
ap-4740	543	14	.	.	PUNCT
ap-4740	544	1	a	a	DET
ap-4740	544	2	quantum	quantum	NOUN
ap-4740	544	3	exactly	exactly	ADV
ap-4740	544	4	solvable	solvable	ADJ
ap-4740	544	5	non	non	ADJ
ap-4740	544	6	-	-	ADJ
ap-4740	544	7	linear	linear	ADJ
ap-4740	544	8	oscillator	oscillator	NOUN
ap-4740	544	9	with	with	ADP
ap-4740	544	10	quasi	quasi	ADJ
ap-4740	544	11	-	-	ADJ
ap-4740	544	12	harmonic	harmonic	ADJ
ap-4740	544	13	behaviour	behaviour	NOUN
ap-4740	544	14	,	,	PUNCT
ap-4740	544	15	ann	ann	PROPN
ap-4740	544	16	.	.	PUNCT
ap-4740	545	1	phys	phys	PROPN
ap-4740	545	2	.	.	PUNCT
ap-4740	546	1	(	(	PUNCT
ap-4740	546	2	ny	ny	NOUN
ap-4740	546	3	)	)	PUNCT
ap-4740	546	4	322:434–459	322:434–459	NUM
ap-4740	546	5	,	,	PUNCT
ap-4740	546	6	2007	2007	NUM
ap-4740	546	7	.	.	PUNCT
ap-4740	547	1	doi:10.1016	doi:10.1016	PROPN
ap-4740	547	2	/	/	SYM
ap-4740	547	3	j.aop.2006.03.005	j.aop.2006.03.005	PROPN
ap-4740	547	4	.	.	PUNCT
ap-4740	548	1	[	[	X
ap-4740	548	2	26	26	NUM
ap-4740	548	3	]	]	X
ap-4740	548	4	a.	a.	NOUN
ap-4740	548	5	schulze	schulze	PROPN
ap-4740	548	6	-	-	PUNCT
ap-4740	548	7	halberg	halberg	PROPN
ap-4740	548	8	,	,	PUNCT
ap-4740	548	9	j.	j.	PROPN
ap-4740	548	10	r.	r.	PROPN
ap-4740	548	11	morris	morris	PROPN
ap-4740	548	12	.	.	PROPN
ap-4740	549	1	special	special	ADJ
ap-4740	549	2	function	function	NOUN
ap-4740	549	3	solutions	solution	NOUN
ap-4740	549	4	of	of	ADP
ap-4740	549	5	a	a	DET
ap-4740	549	6	spectral	spectral	ADJ
ap-4740	549	7	problem	problem	NOUN
ap-4740	549	8	for	for	ADP
ap-4740	549	9	a	a	DET
ap-4740	549	10	nonlinear	nonlinear	ADJ
ap-4740	549	11	quantum	quantum	ADJ
ap-4740	549	12	oscillator	oscillator	NOUN
ap-4740	549	13	,	,	PUNCT
ap-4740	549	14	j.	j.	PROPN
ap-4740	549	15	phys	phys	PROPN
ap-4740	549	16	.	.	PUNCT
ap-4740	550	1	a	a	DET
ap-4740	550	2	:	:	PUNCT
ap-4740	550	3	math	math	NOUN
ap-4740	550	4	.	.	PUNCT
ap-4740	551	1	theor	theor	PROPN
ap-4740	551	2	.	.	PUNCT
ap-4740	552	1	45:305301	45:305301	NUM
ap-4740	552	2	,	,	PUNCT
ap-4740	552	3	9	9	NUM
ap-4740	552	4	pages	page	NOUN
ap-4740	552	5	,	,	PUNCT
ap-4740	552	6	2012	2012	NUM
ap-4740	552	7	.	.	PUNCT
ap-4740	553	1	doi:10.1088/1751	doi:10.1088/1751	ADV
ap-4740	553	2	-	-	PUNCT
ap-4740	553	3	8113/45/30/305301	8113/45/30/305301	PROPN
ap-4740	553	4	.	.	PUNCT
ap-4740	554	1	127	127	NUM
ap-4740	554	2	acta	acta	PROPN
ap-4740	554	3	polytechnica	polytechnica	PROPN
ap-4740	554	4	58(2):118–127	58(2):118–127	PROPN
ap-4740	554	5	,	,	PUNCT
ap-4740	554	6	2018	2018	NUM
ap-4740	554	7	1	1	NUM
ap-4740	554	8	introduction	introduction	NOUN
ap-4740	554	9	2	2	NUM
ap-4740	554	10	second	second	ADJ
ap-4740	554	11	-	-	PUNCT
ap-4740	554	12	order	order	NOUN
ap-4740	554	13	differential	differential	ADJ
ap-4740	554	14	equations	equation	NOUN
ap-4740	554	15	with	with	ADP
ap-4740	554	16	polynomial	polynomial	ADJ
ap-4740	554	17	solutions	solution	NOUN
ap-4740	554	18	and	and	CCONJ
ap-4740	554	19	integration	integration	NOUN
ap-4740	554	20	constants	constant	VERB
ap-4740	554	21	3	3	NUM
ap-4740	554	22	functional	functional	ADJ
ap-4740	554	23	bethe	bethe	ADJ
ap-4740	554	24	ansatz	ansatz	ADJ
ap-4740	554	25	method	method	NOUN
ap-4740	554	26	4	4	NUM
ap-4740	554	27	comparison	comparison	NOUN
ap-4740	554	28	between	between	ADP
ap-4740	554	29	the	the	DET
ap-4740	554	30	two	two	NUM
ap-4740	554	31	approaches	approach	NOUN
ap-4740	554	32	5	5	NUM
ap-4740	554	33	example	example	NOUN
ap-4740	554	34	:	:	PUNCT
ap-4740	554	35	qes	qes	NOUN
ap-4740	554	36	extension	extension	NOUN
ap-4740	554	37	of	of	ADP
ap-4740	554	38	the	the	DET
ap-4740	554	39	mathews	mathews	NOUN
ap-4740	554	40	-	-	PUNCT
ap-4740	554	41	lakshmanan	lakshmanan	PROPN
ap-4740	554	42	nonlinear	nonlinear	ADJ
ap-4740	554	43	oscillator	oscillator	NOUN
ap-4740	554	44	6	6	NUM
ap-4740	554	45	conclusion	conclusion	NOUN
ap-4740	554	46	7	7	NUM
ap-4740	554	47	appendix	appendix	ADJ
ap-4740	554	48	references	reference	NOUN