id	sid	eid	entity	type
ejpam-6146	1	1	european journal	ORG
ejpam-6146	1	2	2025	DATE
ejpam-6146	1	3	18	CARDINAL
ejpam-6146	1	4	4	CARDINAL
ejpam-6146	1	5	6146	DATE
ejpam-6146	1	6	1307-5543	CARDINAL
ejpam-6146	1	7	new york	GPE
ejpam-6146	1	8	sameen ahmed khan1	PERSON
ejpam-6146	1	9	manisha m. kankarej2,∗	PERSON
ejpam-6146	1	10	mohammad nazrul islam khan3	PERSON
ejpam-6146	1	11	1	CARDINAL
ejpam-6146	1	12	dhofar university	ORG
ejpam-6146	1	13	salalah	ORG
ejpam-6146	1	14	oman 2 rochester institute of technology	ORG
ejpam-6146	1	15	dubai	GPE
ejpam-6146	1	16	uae 3	ORG
ejpam-6146	1	17	saudi arabia	GPE
ejpam-6146	2	1	two	CARDINAL
ejpam-6146	2	2	two	CARDINAL
ejpam-6146	3	1	two	CARDINAL
ejpam-6146	4	1	second	ORDINAL
ejpam-6146	6	1	2020	DATE
ejpam-6146	6	2	53d10	CARDINAL
ejpam-6146	6	3	53c25	CARDINAL
ejpam-6146	6	4	53c15	CARDINAL
ejpam-6146	6	5	58a30	CARDINAL
ejpam-6146	6	6	1	CARDINAL
ejpam-6146	9	1	babylonians	NORP
ejpam-6146	9	2	egyptians	NORP
ejpam-6146	9	3	indians	NORP
ejpam-6146	9	4	1	CARDINAL
ejpam-6146	14	1	6–9	CARDINAL
ejpam-6146	15	1	linear	ORG
ejpam-6146	15	2	10–15	CARDINAL
ejpam-6146	18	1	s. a. khan	PERSON
ejpam-6146	18	2	m. m. kankarej	PERSON
ejpam-6146	18	3	m.nazrul@qu.edu.sa	DATE
ejpam-6146	18	4	m. n. i. khan	PERSON
ejpam-6146	19	1	1	CARDINAL
ejpam-6146	19	2	2025	CARDINAL
ejpam-6146	20	1	s. a. khan	PERSON
ejpam-6146	20	2	m. m. kankarej	PERSON
ejpam-6146	20	3	m. n. i. khan	PERSON
ejpam-6146	21	1	j. pure	PERSON
ejpam-6146	21	2	18	CARDINAL
ejpam-6146	21	3	4	CARDINAL
ejpam-6146	21	4	2025	CARDINAL
ejpam-6146	21	5	6146 2	DATE
ejpam-6146	21	6	14	CARDINAL
ejpam-6146	21	7	16	CARDINAL
ejpam-6146	22	1	17	CARDINAL
ejpam-6146	23	1	18	CARDINAL
ejpam-6146	24	1	6	CARDINAL
ejpam-6146	24	2	7	DATE
ejpam-6146	24	3	9	CARDINAL
ejpam-6146	25	1	two	CARDINAL
ejpam-6146	26	1	first	ORDINAL
ejpam-6146	26	2	0	CARDINAL
ejpam-6146	27	1	second	ORDINAL
ejpam-6146	29	1	second	ORDINAL
ejpam-6146	32	1	2	CARDINAL
ejpam-6146	32	2	y′′	ORG
ejpam-6146	32	3	0	CARDINAL
ejpam-6146	32	4	second	ORDINAL
ejpam-6146	32	5	y′′ + p	ORG
ejpam-6146	33	1	r(x	WORK_OF_ART
ejpam-6146	33	2	1	CARDINAL
ejpam-6146	33	3	q(x	PERSON
ejpam-6146	33	4	r(x	PERSON
ejpam-6146	34	1	r(x	PERSON
ejpam-6146	34	2	0	CARDINAL
ejpam-6146	35	1	second	ORDINAL
ejpam-6146	36	1	second	ORDINAL
ejpam-6146	36	2	two	CARDINAL
ejpam-6146	37	1	two	CARDINAL
ejpam-6146	44	1	2	CARDINAL
ejpam-6146	44	2	zero	CARDINAL
ejpam-6146	44	3	two	CARDINAL
ejpam-6146	45	1	polish	NORP
ejpam-6146	45	2	maria hoënéwroński	PERSON
ejpam-6146	45	3	1776-1853	DATE
ejpam-6146	50	1	1	CARDINAL
ejpam-6146	51	1	s. a. khan	PERSON
ejpam-6146	51	2	m. m. kankarej	PERSON
ejpam-6146	51	3	m. n. i. khan	PERSON
ejpam-6146	52	1	j. pure	PERSON
ejpam-6146	52	2	18	CARDINAL
ejpam-6146	52	3	4	CARDINAL
ejpam-6146	52	4	2025	CARDINAL
ejpam-6146	52	5	6146 3	DATE
ejpam-6146	52	6	14	CARDINAL
ejpam-6146	52	7	1	CARDINAL
ejpam-6146	52	8	q(x	PERSON
ejpam-6146	52	9	r(x	PERSON
ejpam-6146	53	1	x0	PERSON
ejpam-6146	53	2	y′′ + p	ORG
ejpam-6146	53	3	r(x	WORK_OF_ART
ejpam-6146	53	4	one	CARDINAL
ejpam-6146	53	5	only one	CARDINAL
ejpam-6146	53	6	y(x	ORG
ejpam-6146	55	1	two	CARDINAL
ejpam-6146	56	1	second	ORDINAL
ejpam-6146	56	2	0	CARDINAL
ejpam-6146	56	3	3	CARDINAL
ejpam-6146	57	1	0, y′1(0	PERCENT
ejpam-6146	57	2	1 and y2(0	DATE
ejpam-6146	57	3	1, y′2(0	DATE
ejpam-6146	60	1	1	CARDINAL
ejpam-6146	61	1	two	CARDINAL
ejpam-6146	61	2	0	CARDINAL
ejpam-6146	61	3	1	CARDINAL
ejpam-6146	61	4	c(0	NORP
ejpam-6146	62	1	1	CARDINAL
ejpam-6146	63	1	0	CARDINAL
ejpam-6146	66	1	3	CARDINAL
ejpam-6146	67	1	s′′(x	PERSON
ejpam-6146	68	1	s′′(x	PERSON
ejpam-6146	69	1	that s′′(x	TIME
ejpam-6146	70	1	zero	CARDINAL
ejpam-6146	77	1	x0	ORG
ejpam-6146	77	2	−1	DATE
ejpam-6146	79	1	2p	CARDINAL
ejpam-6146	79	2	first	ORDINAL
ejpam-6146	79	3	0	CARDINAL
ejpam-6146	80	1	one	CARDINAL
ejpam-6146	80	2	2p	CARDINAL
ejpam-6146	81	1	2p	CARDINAL
ejpam-6146	82	1	c(0	GPE
ejpam-6146	82	2	1	CARDINAL
ejpam-6146	82	3	0	CARDINAL
ejpam-6146	82	4	c(x	ORG
ejpam-6146	82	5	0	CARDINAL
ejpam-6146	82	6	1	CARDINAL
ejpam-6146	82	7	zero	CARDINAL
ejpam-6146	83	1	c(x	ORG
ejpam-6146	83	2	2p̃. later	DATE
ejpam-6146	83	3	p̃	ORG
ejpam-6146	84	1	c(x	ORG
ejpam-6146	84	2	p̃	ORG
ejpam-6146	85	1	3	CARDINAL
ejpam-6146	85	2	0 or	CARDINAL
ejpam-6146	86	1	0	CARDINAL
ejpam-6146	88	1	3	CARDINAL
ejpam-6146	89	1	c(x	ORG
ejpam-6146	90	1	3	CARDINAL
ejpam-6146	92	1	3	CARDINAL
ejpam-6146	93	1	0	CARDINAL
ejpam-6146	93	2	1	CARDINAL
ejpam-6146	93	3	c(0	NORP
ejpam-6146	93	4	1	CARDINAL
ejpam-6146	93	5	0	CARDINAL
ejpam-6146	93	6	1	CARDINAL
ejpam-6146	94	1	4	CARDINAL
ejpam-6146	94	2	s. a. khan	PERSON
ejpam-6146	94	3	m. m. kankarej	PERSON
ejpam-6146	94	4	m. n. i. khan	PERSON
ejpam-6146	95	1	j. pure	PERSON
ejpam-6146	95	2	18	CARDINAL
ejpam-6146	95	3	4	CARDINAL
ejpam-6146	95	4	2025	CARDINAL
ejpam-6146	95	5	6146 4	DATE
ejpam-6146	95	6	14	DATE
ejpam-6146	95	7	0	CARDINAL
ejpam-6146	98	1	5	CARDINAL
ejpam-6146	98	2	c(x	ORG
ejpam-6146	99	1	taylor	PERSON
ejpam-6146	99	2	f(x	ORG
ejpam-6146	99	3	f(x	ORG
ejpam-6146	101	1	+ 1 3	DATE
ejpam-6146	102	1	+ 1 n	QUANTITY
ejpam-6146	104	1	∞∑ k=0	PERSON
ejpam-6146	105	1	k)(a)(x−	NORP
ejpam-6146	105	2	6	CARDINAL
ejpam-6146	106	1	n)(a	GPE
ejpam-6146	106	2	brook taylor	PERSON
ejpam-6146	107	1	colin maclaurin	PERSON
ejpam-6146	107	2	1698-1746	DATE
ejpam-6146	108	1	maclaurin series	GPE
ejpam-6146	108	2	zero	CARDINAL
ejpam-6146	108	3	0	CARDINAL
ejpam-6146	109	1	6	CARDINAL
ejpam-6146	110	1	taylor	PERSON
ejpam-6146	112	1	4	CARDINAL
ejpam-6146	112	2	c(x	ORG
ejpam-6146	113	1	c(2n)(x	GPE
ejpam-6146	114	1	0	CARDINAL
ejpam-6146	114	2	1	DATE
ejpam-6146	114	3	2	DATE
ejpam-6146	114	4	3	DATE
ejpam-6146	118	1	0	CARDINAL
ejpam-6146	119	1	taylor	PERSON
ejpam-6146	119	2	c(x	ORG
ejpam-6146	120	1	1 3	CARDINAL
ejpam-6146	122	1	x5 −	PERSON
ejpam-6146	124	1	∞∑ n=0	PERSON
ejpam-6146	124	2	(2n+ 1	CARDINAL
ejpam-6146	125	1	x2n+1	DATE
ejpam-6146	125	2	∀x	GPE
ejpam-6146	125	3	7	CARDINAL
ejpam-6146	127	1	x4 −	PERSON
ejpam-6146	128	1	∞∑ n=0	PERSON
ejpam-6146	128	2	2n	CARDINAL
ejpam-6146	129	1	∀x	GPE
ejpam-6146	130	1	c(x	ORG
ejpam-6146	130	2	taylor	PERSON
ejpam-6146	131	1	c(x	ORG
ejpam-6146	132	1	4	CARDINAL
ejpam-6146	133	1	[ s(x	PERSON
ejpam-6146	134	1	s. a. khan	PERSON
ejpam-6146	134	2	m. m. kankarej	PERSON
ejpam-6146	134	3	m. n. i. khan	PERSON
ejpam-6146	135	1	j. pure	PERSON
ejpam-6146	135	2	18	CARDINAL
ejpam-6146	135	3	4	CARDINAL
ejpam-6146	135	4	2025	CARDINAL
ejpam-6146	135	5	6146 5	DATE
ejpam-6146	135	6	14	CARDINAL
ejpam-6146	137	1	9	CARDINAL
ejpam-6146	137	2	1	CARDINAL
ejpam-6146	137	3	2	CARDINAL
ejpam-6146	140	1	10	CARDINAL
ejpam-6146	141	1	1 2	CARDINAL
ejpam-6146	142	1	+ 1 3	DATE
ejpam-6146	144	1	1 3	CARDINAL
ejpam-6146	145	1	x5 −	PERSON
ejpam-6146	148	1	0 1	CARDINAL
ejpam-6146	148	2	1 3	CARDINAL
ejpam-6146	150	1	x5 −	PERSON
ejpam-6146	151	1	1 0	CARDINAL
ejpam-6146	155	1	0 1	CARDINAL
ejpam-6146	156	1	11	CARDINAL
ejpam-6146	157	1	1 3	CARDINAL
ejpam-6146	159	1	x5 −	PERSON
ejpam-6146	163	1	12	CARDINAL
ejpam-6146	163	2	c(x	ORG
ejpam-6146	164	1	3	CARDINAL
ejpam-6146	166	1	1 2	CARDINAL
ejpam-6146	167	1	0	CARDINAL
ejpam-6146	168	1	c(0	NORP
ejpam-6146	169	1	1	CARDINAL
ejpam-6146	169	2	1	CARDINAL
ejpam-6146	170	1	1 .	CARDINAL
ejpam-6146	171	1	13	CARDINAL
ejpam-6146	171	2	two	CARDINAL
ejpam-6146	172	1	c(x	ORG
ejpam-6146	173	1	two	CARDINAL
ejpam-6146	173	2	c(x	ORG
ejpam-6146	175	1	13	CARDINAL
ejpam-6146	175	2	first	ORDINAL
ejpam-6146	175	3	1	CARDINAL
ejpam-6146	175	4	first	ORDINAL
ejpam-6146	175	5	zero	CARDINAL
ejpam-6146	175	6	c(x	ORG
ejpam-6146	177	1	p̃	ORG
ejpam-6146	177	2	zeros	CARDINAL
ejpam-6146	177	3	2p	CARDINAL
ejpam-6146	177	4	3p	CARDINAL
ejpam-6146	179	1	zeros	CARDINAL
ejpam-6146	179	2	c(x	ORG
ejpam-6146	179	3	5p/2	CARDINAL
ejpam-6146	181	1	s. a. khan	PERSON
ejpam-6146	181	2	m. m. kankarej	PERSON
ejpam-6146	181	3	m. n. i. khan	PERSON
ejpam-6146	182	1	j. pure	PERSON
ejpam-6146	182	2	18	CARDINAL
ejpam-6146	182	3	4	CARDINAL
ejpam-6146	182	4	2025	CARDINAL
ejpam-6146	182	5	6	CARDINAL
ejpam-6146	182	6	14	CARDINAL
ejpam-6146	182	7	two	CARDINAL
ejpam-6146	182	8	zeros	CARDINAL
ejpam-6146	182	9	one zero	CARDINAL
ejpam-6146	182	10	c(x	ORG
ejpam-6146	182	11	two	CARDINAL
ejpam-6146	182	12	zeros	CARDINAL
ejpam-6146	182	13	one zero	CARDINAL
ejpam-6146	183	1	c(x	ORG
ejpam-6146	186	1	−1	DATE
ejpam-6146	187	1	14	CARDINAL
ejpam-6146	187	2	zero	CARDINAL
ejpam-6146	187	3	two	CARDINAL
ejpam-6146	187	4	c(x	ORG
ejpam-6146	190	1	3	CARDINAL
ejpam-6146	194	1	c1 = rc(a	PERSON
ejpam-6146	195	1	s(x)s(a	PERSON
ejpam-6146	196	1	15	CARDINAL
ejpam-6146	197	1	15	CARDINAL
ejpam-6146	200	1	16	CARDINAL
ejpam-6146	200	2	13	CARDINAL
ejpam-6146	200	3	1	CARDINAL
ejpam-6146	201	1	two	CARDINAL
ejpam-6146	201	2	c(x	ORG
ejpam-6146	203	1	two	CARDINAL
ejpam-6146	204	1	3	CARDINAL
ejpam-6146	205	1	17	CARDINAL
ejpam-6146	205	2	two	CARDINAL
ejpam-6146	206	1	two	CARDINAL
ejpam-6146	207	1	sinx	ORG
ejpam-6146	207	2	cosx	ORG
ejpam-6146	207	3	second	ORDINAL
ejpam-6146	207	4	0	CARDINAL
ejpam-6146	209	1	s. a. khan	PERSON
ejpam-6146	209	2	m. m. kankarej	PERSON
ejpam-6146	209	3	m. n. i. khan	PERSON
ejpam-6146	210	1	j. pure	PERSON
ejpam-6146	210	2	18	CARDINAL
ejpam-6146	210	3	4	CARDINAL
ejpam-6146	210	4	2025	CARDINAL
ejpam-6146	210	5	6146 7	DATE
ejpam-6146	211	1	2π	CARDINAL
ejpam-6146	211	2	sin(x	GPE
ejpam-6146	211	3	1	CARDINAL
ejpam-6146	213	1	two	CARDINAL
ejpam-6146	214	1	zeros	CARDINAL
ejpam-6146	214	2	two	CARDINAL
ejpam-6146	215	1	two	CARDINAL
ejpam-6146	215	2	zeros	CARDINAL
ejpam-6146	215	3	one	CARDINAL
ejpam-6146	215	4	one zero	CARDINAL
ejpam-6146	216	1	zeros	CARDINAL
ejpam-6146	216	2	second	ORDINAL
ejpam-6146	221	1	0	CARDINAL
ejpam-6146	222	1	3	CARDINAL
ejpam-6146	224	1	isaac newton	PERSON
ejpam-6146	224	2	1642-1727	DATE
ejpam-6146	224	3	gottfried wilhelm von leibniz	PERSON
ejpam-6146	224	4	1646-1716	DATE
ejpam-6146	226	1	joseph liouville	PERSON
ejpam-6146	226	2	1809-1882	DATE
ejpam-6146	227	1	six	CARDINAL
ejpam-6146	227	2	six	CARDINAL
ejpam-6146	227	3	six	CARDINAL
ejpam-6146	230	1	6–9	CARDINAL
ejpam-6146	231	1	early 19th century	DATE
ejpam-6146	231	2	jules henri poincaré	PERSON
ejpam-6146	231	3	1854-1912	DATE
ejpam-6146	231	4	aleksandr mikhailovich	PERSON
ejpam-6146	231	5	lyapunov	DATE
ejpam-6146	231	6	1857-1918	DATE
ejpam-6146	232	1	poincaré	PERSON
ejpam-6146	232	2	19	CARDINAL
ejpam-6146	234	1	s. a. khan	PERSON
ejpam-6146	234	2	m. m. kankarej	PERSON
ejpam-6146	234	3	m. n. i. khan	PERSON
ejpam-6146	235	1	j. pure	PERSON
ejpam-6146	235	2	18	CARDINAL
ejpam-6146	235	3	4	CARDINAL
ejpam-6146	235	4	2025	CARDINAL
ejpam-6146	235	5	6146 8	DATE
ejpam-6146	235	6	14	CARDINAL
ejpam-6146	236	1	second	ORDINAL
ejpam-6146	236	2	y′′ + p	ORG
ejpam-6146	237	1	0	CARDINAL
ejpam-6146	237	2	18	CARDINAL
ejpam-6146	237	3	q(x	PERSON
ejpam-6146	238	1	zeros	CARDINAL
ejpam-6146	238	2	two	CARDINAL
ejpam-6146	238	3	jacques charles françois sturm	PERSON
ejpam-6146	238	4	1803-1855	DATE
ejpam-6146	239	1	2	CARDINAL
ejpam-6146	239	2	sturm	PERSON
ejpam-6146	239	3	two	CARDINAL
ejpam-6146	239	4	y′′	ORG
ejpam-6146	241	1	zeros	CARDINAL
ejpam-6146	241	2	two	CARDINAL
ejpam-6146	241	3	zeros	CARDINAL
ejpam-6146	243	1	two	CARDINAL
ejpam-6146	243	2	zeros	CARDINAL
ejpam-6146	251	1	19	CARDINAL
ejpam-6146	254	1	w	GPE
ejpam-6146	254	2	xj	ORG
ejpam-6146	254	3	0	CARDINAL
ejpam-6146	254	4	1	CARDINAL
ejpam-6146	254	5	2	CARDINAL
ejpam-6146	255	1	20	CARDINAL
ejpam-6146	255	2	zeros	CARDINAL
ejpam-6146	262	1	two	CARDINAL
ejpam-6146	262	2	zeros	CARDINAL
ejpam-6146	262	3	only one zero	CARDINAL
ejpam-6146	265	1	aij = aji	PERSON
ejpam-6146	266	1	aij	ORG
ejpam-6146	266	2	1	CARDINAL
ejpam-6146	266	3	2	DATE
ejpam-6146	266	4	3	DATE
ejpam-6146	268	1	1	CARDINAL
ejpam-6146	268	2	2	DATE
ejpam-6146	268	3	3	DATE
ejpam-6146	270	1	1	CARDINAL
ejpam-6146	270	2	2	DATE
ejpam-6146	270	3	3	DATE
ejpam-6146	275	1	s. a. khan	PERSON
ejpam-6146	275	2	m. m. kankarej	PERSON
ejpam-6146	275	3	m. n. i. khan	PERSON
ejpam-6146	276	1	j. pure	PERSON
ejpam-6146	276	2	18	CARDINAL
ejpam-6146	276	3	4	CARDINAL
ejpam-6146	276	4	2025	CARDINAL
ejpam-6146	276	5	6146 9	DATE
ejpam-6146	276	6	14	CARDINAL
ejpam-6146	277	1	0	CARDINAL
ejpam-6146	277	2	two	CARDINAL
ejpam-6146	277	3	y2 cos	ORG
ejpam-6146	277	4	1	CARDINAL
ejpam-6146	278	1	zeros	CARDINAL
ejpam-6146	279	1	two	CARDINAL
ejpam-6146	280	1	one zero	CARDINAL
ejpam-6146	281	1	0	CARDINAL
ejpam-6146	281	2	two	CARDINAL
ejpam-6146	284	1	one zero	CARDINAL
ejpam-6146	284	2	two	CARDINAL
ejpam-6146	285	1	q(x	PERSON
ejpam-6146	286	1	q(x	PERSON
ejpam-6146	287	1	q(x	PERSON
ejpam-6146	287	2	0	CARDINAL
ejpam-6146	287	3	4	CARDINAL
ejpam-6146	288	1	18	CARDINAL
ejpam-6146	289	1	0 q(x	PERSON
ejpam-6146	290	1	1 4	CARDINAL
ejpam-6146	290	2	1 2	CARDINAL
ejpam-6146	291	1	21	CARDINAL
ejpam-6146	291	2	18	CARDINAL
ejpam-6146	291	3	0	CARDINAL
ejpam-6146	294	1	18	CARDINAL
ejpam-6146	294	2	0	CARDINAL
ejpam-6146	295	1	zero	CARDINAL
ejpam-6146	296	1	0	CARDINAL
ejpam-6146	297	1	1 2	CARDINAL
ejpam-6146	297	2	∫ p dx.	ORG
ejpam-6146	299	1	18	CARDINAL
ejpam-6146	300	1	21	CARDINAL
ejpam-6146	301	1	zeros	CARDINAL
ejpam-6146	302	1	18	CARDINAL
ejpam-6146	304	1	four	CARDINAL
ejpam-6146	304	2	second	ORDINAL
ejpam-6146	307	1	3	CARDINAL
ejpam-6146	307	2	q(x	PERSON
ejpam-6146	307	3	u(x	ORG
ejpam-6146	307	4	u(x	ORG
ejpam-6146	307	5	one zero	CARDINAL
ejpam-6146	308	1	3	CARDINAL
ejpam-6146	308	2	6–9	CARDINAL
ejpam-6146	310	1	4	CARDINAL
ejpam-6146	311	1	q(x	PERSON
ejpam-6146	312	1	0	CARDINAL
ejpam-6146	314	1	u(x	ORG
ejpam-6146	314	2	zeros	CARDINAL
ejpam-6146	315	1	s. a. khan	PERSON
ejpam-6146	315	2	m. m. kankarej	PERSON
ejpam-6146	315	3	m. n. i. khan	PERSON
ejpam-6146	316	1	j. pure	PERSON
ejpam-6146	316	2	18	CARDINAL
ejpam-6146	316	3	4	CARDINAL
ejpam-6146	316	4	2025	CARDINAL
ejpam-6146	316	5	6146 10	DATE
ejpam-6146	316	6	14	DATE
ejpam-6146	316	7	4	CARDINAL
ejpam-6146	316	8	6–9	CARDINAL
ejpam-6146	319	1	5	CARDINAL
ejpam-6146	319	2	zeros	CARDINAL
ejpam-6146	319	3	0	CARDINAL
ejpam-6146	320	1	zeros	CARDINAL
ejpam-6146	321	1	5	CARDINAL
ejpam-6146	321	2	6–9	CARDINAL
ejpam-6146	322	1	2	CARDINAL
ejpam-6146	322	2	zeros	CARDINAL
ejpam-6146	322	3	two	CARDINAL
ejpam-6146	323	1	18	CARDINAL
ejpam-6146	324	1	zeros	CARDINAL
ejpam-6146	324	2	two	CARDINAL
ejpam-6146	324	3	more than one	CARDINAL
ejpam-6146	325	1	q(x	PERSON
ejpam-6146	326	1	zeros	CARDINAL
ejpam-6146	326	2	q(x	PERSON
ejpam-6146	328	1	0	CARDINAL
ejpam-6146	328	2	zeros	CARDINAL
ejpam-6146	330	1	6	CARDINAL
ejpam-6146	331	1	sturm	PERSON
ejpam-6146	331	2	z(x	ORG
ejpam-6146	331	3	y′′	ORG
ejpam-6146	331	4	+ q(x)y	PERSON
ejpam-6146	331	5	z′′	PERSON
ejpam-6146	331	6	0	CARDINAL
ejpam-6146	331	7	q(x	PERSON
ejpam-6146	331	8	r(x	PERSON
ejpam-6146	331	9	q(x	PERSON
ejpam-6146	331	10	r(x	PERSON
ejpam-6146	332	1	two	CARDINAL
ejpam-6146	332	2	zeros	CARDINAL
ejpam-6146	332	3	z(x	ORG
ejpam-6146	335	1	21	CARDINAL
ejpam-6146	335	2	q(x	PERSON
ejpam-6146	336	1	4	CARDINAL
ejpam-6146	336	2	0	CARDINAL
ejpam-6146	337	1	22	CARDINAL
ejpam-6146	338	1	only one zero	CARDINAL
ejpam-6146	339	1	e−x	PERSON
ejpam-6146	339	2	e+x	PERSON
ejpam-6146	339	3	zeros	CARDINAL
ejpam-6146	340	1	two	CARDINAL
ejpam-6146	341	1	23	CARDINAL
ejpam-6146	341	2	s. a. khan	PERSON
ejpam-6146	341	3	m. m. kankarej	PERSON
ejpam-6146	341	4	m. n. i. khan	PERSON
ejpam-6146	342	1	j. pure	PERSON
ejpam-6146	342	2	18	CARDINAL
ejpam-6146	342	3	4	CARDINAL
ejpam-6146	342	4	2025	CARDINAL
ejpam-6146	342	5	6146 11	DATE
ejpam-6146	342	6	14 5	DATE
ejpam-6146	342	7	x2y′′ + xy′	GPE
ejpam-6146	346	1	0	CARDINAL
ejpam-6146	347	1	24	CARDINAL
ejpam-6146	348	1	24	CARDINAL
ejpam-6146	349	1	21	CARDINAL
ejpam-6146	349	2	0	CARDINAL
ejpam-6146	350	1	25	CARDINAL
ejpam-6146	350	2	section 2	LAW
ejpam-6146	351	1	7	CARDINAL
ejpam-6146	353	1	0 ≤	MONEY
ejpam-6146	354	1	1/2	CARDINAL
ejpam-6146	354	2	at least one zero	CARDINAL
ejpam-6146	354	3	1/2	CARDINAL
ejpam-6146	354	4	zeros	CARDINAL
ejpam-6146	354	5	1/2	CARDINAL
ejpam-6146	356	1	25	CARDINAL
ejpam-6146	356	2	7	CARDINAL
ejpam-6146	358	1	24	CARDINAL
ejpam-6146	359	1	24	CARDINAL
ejpam-6146	359	2	second	ORDINAL
ejpam-6146	359	3	two	CARDINAL
ejpam-6146	360	1	one	CARDINAL
ejpam-6146	360	2	two	CARDINAL
ejpam-6146	360	3	first	ORDINAL
ejpam-6146	361	1	1 m!γ(m+	QUANTITY
ejpam-6146	361	2	2	CARDINAL
ejpam-6146	361	3	2m+p	CARDINAL
ejpam-6146	361	4	26	CARDINAL
ejpam-6146	361	5	γ(n	ORG
ejpam-6146	362	1	γ(n	ORG
ejpam-6146	366	1	1	CARDINAL
ejpam-6146	366	2	m!(m+	ORG
ejpam-6146	367	1	2	CARDINAL
ejpam-6146	367	2	2m+n	CARDINAL
ejpam-6146	368	1	27	CARDINAL
ejpam-6146	368	2	7	CARDINAL
ejpam-6146	370	1	7	CARDINAL
ejpam-6146	370	2	1/2	CARDINAL
ejpam-6146	371	1	j 1 2	FAC
ejpam-6146	371	2	1 2	CARDINAL
ejpam-6146	371	3	cosx	ORG
ejpam-6146	372	1	s. a. khan	PERSON
ejpam-6146	372	2	m. m. kankarej	PERSON
ejpam-6146	372	3	m. n. i. khan	PERSON
ejpam-6146	373	1	j. pure	PERSON
ejpam-6146	373	2	18	CARDINAL
ejpam-6146	373	3	4	CARDINAL
ejpam-6146	373	4	2025	CARDINAL
ejpam-6146	373	5	6146 12	DATE
ejpam-6146	373	6	14 6	DATE
ejpam-6146	374	1	if∫	NORP
ejpam-6146	375	1	∀n ≥ 0	DATE
ejpam-6146	376	1	28	CARDINAL
ejpam-6146	376	2	jacobi polynomials	ORG
ejpam-6146	377	1	∀n ≥ 0	DATE
ejpam-6146	378	1	29	CARDINAL
ejpam-6146	378	2	jacobi polynomials	ORG
ejpam-6146	378	3	legendre	PERSON
ejpam-6146	378	4	zernike	GPE
ejpam-6146	380	1	second	ORDINAL
ejpam-6146	380	2	sturm-liouville	ORG
ejpam-6146	381	1	0	CARDINAL
ejpam-6146	381	2	30	CARDINAL
ejpam-6146	381	3	q(x	PERSON
ejpam-6146	381	4	l(x	PERSON
ejpam-6146	382	1	q(x	PERSON
ejpam-6146	382	2	l(x	PERSON
ejpam-6146	382	3	y′′	ORG
ejpam-6146	382	4	2xy′	CARDINAL
ejpam-6146	382	5	0	CARDINAL
ejpam-6146	383	1	0	CARDINAL
ejpam-6146	383	2	1	DATE
ejpam-6146	383	3	2	DATE
ejpam-6146	383	4	3	DATE
ejpam-6146	386	1	1− x)y′	TIME
ejpam-6146	387	1	0	CARDINAL
ejpam-6146	390	1	zeros	CARDINAL
ejpam-6146	391	1	xn	ORG
ejpam-6146	391	2	k}nk=1	PERSON
ejpam-6146	391	3	zeros	CARDINAL
ejpam-6146	391	4	1	CARDINAL
ejpam-6146	391	5	1	CARDINAL
ejpam-6146	391	6	2	CARDINAL
ejpam-6146	391	7	2	CARDINAL
ejpam-6146	393	1	31	CARDINAL
ejpam-6146	394	1	the s. a. khan	ORG
ejpam-6146	394	2	m. m. kankarej	PERSON
ejpam-6146	394	3	m. n. i. khan	PERSON
ejpam-6146	395	1	j. pure	PERSON
ejpam-6146	395	2	18	CARDINAL
ejpam-6146	395	3	4	CARDINAL
ejpam-6146	395	4	2025	CARDINAL
ejpam-6146	395	5	6146 13	DATE
ejpam-6146	395	6	14	CARDINAL
ejpam-6146	395	7	one	CARDINAL
ejpam-6146	396	1	chebyshev polynomials	ORG
ejpam-6146	396	2	first	ORDINAL
ejpam-6146	396	3	cos(nθ	DATE
ejpam-6146	397	1	second	ORDINAL
ejpam-6146	397	2	sin(nθ	DATE
ejpam-6146	398	1	−1	CARDINAL
ejpam-6146	398	2	1	CARDINAL
ejpam-6146	401	1	1	CARDINAL
ejpam-6146	402	1	32	CARDINAL
ejpam-6146	402	2	k n+ 1 π	ORG
ejpam-6146	403	1	1	CARDINAL
ejpam-6146	406	1	33	CARDINAL
ejpam-6146	408	1	one	CARDINAL
ejpam-6146	409	1	7	CARDINAL
ejpam-6146	409	2	cosx	ORG
ejpam-6146	411	1	sinx	ORG
ejpam-6146	411	2	cosx	ORG
ejpam-6146	412	1	two	CARDINAL
ejpam-6146	415	1	second	ORDINAL
ejpam-6146	416	1	zeros	CARDINAL
ejpam-6146	416	2	two	CARDINAL
ejpam-6146	421	1	1	CARDINAL
ejpam-6146	421	2	v. katter	PERSON
ejpam-6146	422	1	historische	ORG
ejpam-6146	422	2	logische und individuelle genese der trigonometrie aus	PERSON
ejpam-6146	423	1	2023	CARDINAL
ejpam-6146	424	1	2	CARDINAL
ejpam-6146	424	2	l. rico e. mart́ın-fernández	PERSON
ejpam-6146	424	3	j. f. ruiz-hidalgo	PERSON
ejpam-6146	426	1	eurasia journal of mathematics	ORG
ejpam-6146	426	2	15(12):em1782	CARDINAL
ejpam-6146	426	3	2019	DATE
ejpam-6146	427	1	s. a. khan	PERSON
ejpam-6146	427	2	m. m. kankarej	PERSON
ejpam-6146	427	3	m. n. i. khan	PERSON
ejpam-6146	428	1	j. pure	PERSON
ejpam-6146	428	2	18	CARDINAL
ejpam-6146	428	3	4	CARDINAL
ejpam-6146	428	4	2025	CARDINAL
ejpam-6146	428	5	6146 14	DATE
ejpam-6146	428	6	3	CARDINAL
ejpam-6146	428	7	s. l. loney	PERSON
ejpam-6146	429	1	aitbs publishers	ORG
ejpam-6146	429	2	india	GPE
ejpam-6146	429	3	2019	DATE
ejpam-6146	430	1	4	CARDINAL
ejpam-6146	430	2	s. l. loney	PERSON
ejpam-6146	432	1	aitbs	PERSON
ejpam-6146	432	2	india	GPE
ejpam-6146	432	3	2019	DATE
ejpam-6146	433	1	5	CARDINAL
ejpam-6146	434	1	delights	TIME
ejpam-6146	435	1	princeton university press	ORG
ejpam-6146	435	2	2013	DATE
ejpam-6146	436	1	6	CARDINAL
ejpam-6146	436	2	g. f. simmons	PERSON
ejpam-6146	438	1	taylor & francis	ORG
ejpam-6146	438	2	2016	DATE
ejpam-6146	439	1	7	CARDINAL
ejpam-6146	439	2	e. rainville	PERSON
ejpam-6146	439	3	r. bedient	PERSON
ejpam-6146	441	1	pearson, 2014	ORG
ejpam-6146	442	1	8	CARDINAL
ejpam-6146	442	2	m. d. weir	PERSON
ejpam-6146	442	3	j. r. hass	PERSON
ejpam-6146	442	4	c. e. heil	PERSON
ejpam-6146	443	1	thomas	PERSON
ejpam-6146	443	2	15th	ORDINAL
ejpam-6146	444	1	pearson	ORG
ejpam-6146	444	2	2022	CARDINAL
ejpam-6146	445	1	9	CARDINAL
ejpam-6146	445	2	h. j. weber g. b. arfken	PERSON
ejpam-6146	445	3	f. e. harris	PERSON
ejpam-6146	447	1	london	GPE
ejpam-6146	447	2	uk	GPE
ejpam-6146	447	3	2012	DATE
ejpam-6146	448	1	10	CARDINAL
ejpam-6146	449	1	kragujevac journal of mathematics	ORG
ejpam-6146	449	2	45(2):203–214	DATE
ejpam-6146	449	3	2021	DATE
ejpam-6146	450	1	11	CARDINAL
ejpam-6146	452	1	72(4):461–474	CARDINAL
ejpam-6146	452	2	2024	DATE
ejpam-6146	453	1	12	CARDINAL
ejpam-6146	453	2	h. k. sevindir s. çetinkaya	PERSON
ejpam-6146	453	3	a. demir	PERSON
ejpam-6146	455	1	35(1):243–252	CARDINAL
ejpam-6146	455	2	2020	DATE
ejpam-6146	456	1	13	CARDINAL
ejpam-6146	457	1	bernoulli trigonometric polynomial differential	ORG
ejpam-6146	458	1	2022	CARDINAL
ejpam-6146	459	1	14	CARDINAL
ejpam-6146	459	2	o. o. enoch	PERSON
ejpam-6146	460	1	fifth	ORDINAL
ejpam-6146	460	2	second	ORDINAL
ejpam-6146	461	1	african	NORP
ejpam-6146	461	2	3(2):156	CARDINAL
ejpam-6146	461	3	2024	DATE
ejpam-6146	462	1	15	CARDINAL
ejpam-6146	462	2	b. v. rao	PERSON
ejpam-6146	464	1	18(6):543–557, 2013	DATE
ejpam-6146	465	1	16	CARDINAL
ejpam-6146	465	2	s. a. khan	PERSON
ejpam-6146	467	1	10(9):8685–8702	CARDINAL
ejpam-6146	467	2	2020	DATE
ejpam-6146	468	1	17	CARDINAL
ejpam-6146	468	2	s. a. khan	PERSON
ejpam-6146	470	1	9(6):899–907	CARDINAL
ejpam-6146	470	2	2021	DATE
ejpam-6146	471	1	18	CARDINAL
ejpam-6146	471	2	s. a. khan	PERSON
ejpam-6146	473	1	26(6):813–827	CARDINAL
ejpam-6146	473	2	2021	DATE
ejpam-6146	474	1	19	CARDINAL
ejpam-6146	474	2	j. barrow-green	PERSON
ejpam-6146	475	1	oscar ii’s	PERSON
ejpam-6146	475	2	three	CARDINAL
ejpam-6146	476	1	48:107–131, 1994	DATE
ejpam-6146	477	1	20	CARDINAL
ejpam-6146	477	2	r. chakrabarti	PERSON
ejpam-6146	477	3	r. jagannathan	PERSON
ejpam-6146	478	1	two	CARDINAL
ejpam-6146	479	1	j. phys	PERSON
ejpam-6146	481	1	gen.	PERSON
ejpam-6146	481	2	24	CARDINAL
ejpam-6146	481	3	l718, 1991	ORG
ejpam-6146	482	1	21	CARDINAL
ejpam-6146	482	2	r. jaganathan	PERSON
ejpam-6146	482	3	s. sinha	PERSON
ejpam-6146	485	1	lett.	PERSON
ejpam-6146	486	1	338:277	CARDINAL
ejpam-6146	486	2	287, 2005	DATE
ejpam-6146	487	1	22	CARDINAL
ejpam-6146	487	2	r. jagannathan	PERSON
ejpam-6146	487	3	s. a. khan	PERSON
ejpam-6146	489	1	59(8):2647–2669	CARDINAL
ejpam-6146	489	2	2020	DATE
ejpam-6146	490	1	23	CARDINAL
ejpam-6146	490	2	s. a. khan	PERSON
ejpam-6146	490	3	r. jagannathan	PERSON
ejpam-6146	492	1	bulletin	PERSON
ejpam-6146	492	2	malaysian	NORP
ejpam-6146	492	3	2022	CARDINAL