id	sid	eid	entity	type
ejpam-4507	1	1	european journal	ORG
ejpam-4507	2	1	15	CARDINAL
ejpam-4507	2	2	4	CARDINAL
ejpam-4507	2	3	2022	DATE
ejpam-4507	2	4	new york	GPE
ejpam-4507	2	5	bernoulli	PERSON
ejpam-4507	2	6	euler	PERSON
ejpam-4507	2	7	cristina b. corcino1,2	PERSON
ejpam-4507	2	8	roberto b. corcino1,2,∗ 1	PERSON
ejpam-4507	2	9	6000	CARDINAL
ejpam-4507	2	10	cebu city	GPE
ejpam-4507	2	11	philippines 2 department	ORG
ejpam-4507	2	12	6000	CARDINAL
ejpam-4507	2	13	cebu city	GPE
ejpam-4507	2	14	philippines	GPE
ejpam-4507	3	1	bernoulli	PERSON
ejpam-4507	3	2	euler	PERSON
ejpam-4507	5	1	2020	DATE
ejpam-4507	5	2	11b68	CARDINAL
ejpam-4507	5	3	42a16	DATE
ejpam-4507	5	4	11m35	CARDINAL
ejpam-4507	5	5	bernoulli	PERSON
ejpam-4507	5	6	euler	PERSON
ejpam-4507	5	7	1	CARDINAL
ejpam-4507	6	1	1)-(3	CARDINAL
ejpam-4507	6	2	euler	PERSON
ejpam-4507	7	1	0	CARDINAL
ejpam-4507	8	1	α cxt =	PERSON
ejpam-4507	9	1	∞∑ n=0 b(α	PERSON
ejpam-4507	9	2	2π	CARDINAL
ejpam-4507	9	3	1	CARDINAL
ejpam-4507	9	4	2	CARDINAL
ejpam-4507	9	5	α cxt = ∞∑ n=0	PERSON
ejpam-4507	9	6	2	CARDINAL
ejpam-4507	9	7	2	CARDINAL
ejpam-4507	9	8	α cxt = ∞∑ n=0 g(α	PERSON
ejpam-4507	10	1	3	CARDINAL
ejpam-4507	11	1	r. corcino	PERSON
ejpam-4507	12	1	2022	CARDINAL
ejpam-4507	13	1	c. corcino	PERSON
ejpam-4507	13	2	r. corcino	PERSON
ejpam-4507	14	1	j. pure	PERSON
ejpam-4507	14	2	15	CARDINAL
ejpam-4507	14	3	4	CARDINAL
ejpam-4507	14	4	2022	CARDINAL
ejpam-4507	14	5	1662-1682 1663	DATE
ejpam-4507	14	6	euler	PERSON
ejpam-4507	15	1	9	CARDINAL
ejpam-4507	16	1	6	CARDINAL
ejpam-4507	17	1	8	CARDINAL
ejpam-4507	18	1	10	CARDINAL
ejpam-4507	19	1	bernoulli	PERSON
ejpam-4507	19	2	euler	PERSON
ejpam-4507	19	3	genocchi	PERSON
ejpam-4507	19	4	1–4	CARDINAL
ejpam-4507	23	1	5	CARDINAL
ejpam-4507	24	1	2	CARDINAL
ejpam-4507	24	2	1	CARDINAL
ejpam-4507	24	3	2.1	CARDINAL
ejpam-4507	25	1	n ≥ 2	ORG
ejpam-4507	25	2	about zero	CARDINAL
ejpam-4507	25	3	2nπ−ε)/b	CARDINAL
ejpam-4507	25	4	a−	ORG
ejpam-4507	25	5	2π	CARDINAL
ejpam-4507	27	1	lim	PERSON
ejpam-4507	30	1	cxt	PRODUCT
ejpam-4507	31	1	cxt	PRODUCT
ejpam-4507	32	1	cxt = ext	PERSON
ejpam-4507	34	1	∈	ORG
ejpam-4507	36	1	2nπ	ORDINAL
ejpam-4507	36	2	2nπ	ORDINAL
ejpam-4507	36	3	0 ≤	MONEY
ejpam-4507	36	4	2π	CARDINAL
ejpam-4507	37	1	|cxt|	GPE
ejpam-4507	37	2	2eγb	CARDINAL
ejpam-4507	37	3	+ 1	DATE
ejpam-4507	37	4	1 2	CARDINAL
ejpam-4507	37	5	c. corcino	GPE
ejpam-4507	37	6	r. corcino	PERSON
ejpam-4507	38	1	j. pure	PERSON
ejpam-4507	38	2	15	CARDINAL
ejpam-4507	38	3	4	CARDINAL
ejpam-4507	38	4	2022	CARDINAL
ejpam-4507	38	5	1662-1682 1664	DATE
ejpam-4507	38	6	1	CARDINAL
ejpam-4507	38	7	2eγb	CARDINAL
ejpam-4507	38	8	+ 1] 1 2	DATE
ejpam-4507	39	1	2π	CARDINAL
ejpam-4507	39	2	a−	ORG
ejpam-4507	39	3	2π	CARDINAL
ejpam-4507	39	4	2π	CARDINAL
ejpam-4507	41	1	2π	CARDINAL
ejpam-4507	42	1	2πn	ORDINAL
ejpam-4507	42	2	1	CARDINAL
ejpam-4507	43	1	1	CARDINAL
ejpam-4507	43	2	|cxt|	GPE
ejpam-4507	44	1	2eγb	CARDINAL
ejpam-4507	44	2	+ 1] 1 2	DATE
ejpam-4507	45	1	zero	CARDINAL
ejpam-4507	46	1	0 ≤	MONEY
ejpam-4507	46	2	3	CARDINAL
ejpam-4507	46	3	1	CARDINAL
ejpam-4507	46	4	2eγb	CARDINAL
ejpam-4507	47	1	+ 1 −→ 1	QUANTITY
ejpam-4507	47	2	0	CARDINAL
ejpam-4507	47	3	2	CARDINAL
ejpam-4507	48	1	2eγb	CARDINAL
ejpam-4507	48	2	1− 2 cos	LAW
ejpam-4507	49	1	0	CARDINAL
ejpam-4507	49	2	3	CARDINAL
ejpam-4507	49	3	0	CARDINAL
ejpam-4507	50	1	2eγb	CARDINAL
ejpam-4507	50	2	2− 2 cos	DATE
ejpam-4507	51	1	0	CARDINAL
ejpam-4507	52	1	cos[(±2nπ	CARDINAL
ejpam-4507	53	1	1	CARDINAL
ejpam-4507	53	2	2nπ	CARDINAL
ejpam-4507	53	3	2kπ	ORDINAL
ejpam-4507	54	1	2(n	CARDINAL
ejpam-4507	54	2	c. corcino	GPE
ejpam-4507	54	3	r. corcino	PERSON
ejpam-4507	55	1	j. pure	PERSON
ejpam-4507	55	2	15	CARDINAL
ejpam-4507	55	3	4	CARDINAL
ejpam-4507	55	4	2022	CARDINAL
ejpam-4507	55	5	1662-1682 1665	DATE
ejpam-4507	56	1	3	CARDINAL
ejpam-4507	57	1	that∣∣∣∣	ORG
ejpam-4507	58	1	2nπ	CARDINAL
ejpam-4507	58	2	2nπ	ORDINAL
ejpam-4507	58	3	ε)n	ORDINAL
ejpam-4507	59	1	2mπbn−1	CARDINAL
ejpam-4507	59	2	2nπ	CARDINAL
ejpam-4507	60	1	2.2	CARDINAL
ejpam-4507	62	1	bn(x	PERSON
ejpam-4507	62	2	bn(x	PERSON
ejpam-4507	64	1	1	CARDINAL
ejpam-4507	64	2	a−	ORG
ejpam-4507	64	3	2π	CARDINAL
ejpam-4507	66	1	0	CARDINAL
ejpam-4507	67	1	1	CARDINAL
ejpam-4507	67	2	1	CARDINAL
ejpam-4507	67	3	cxt	PRODUCT
ejpam-4507	67	4	n=0 bn(x	PERSON
ejpam-4507	67	5	2π	CARDINAL
ejpam-4507	69	1	1 2πi	CARDINAL
ejpam-4507	69	2	0	DATE
ejpam-4507	69	3	less than 2π	CARDINAL
ejpam-4507	70	1	cxt	PRODUCT
ejpam-4507	71	1	c. corcino	GPE
ejpam-4507	71	2	r. corcino	PERSON
ejpam-4507	72	1	j. pure	PERSON
ejpam-4507	72	2	15	CARDINAL
ejpam-4507	72	3	4	CARDINAL
ejpam-4507	72	4	2022	CARDINAL
ejpam-4507	72	5	1662-1682 1666	DATE
ejpam-4507	72	6	0	CARDINAL
ejpam-4507	73	1	0	CARDINAL
ejpam-4507	77	1	1	CARDINAL
ejpam-4507	77	2	1	CARDINAL
ejpam-4507	79	1	2kπi	CARDINAL
ejpam-4507	79	2	k ∈ z.	PERSON
ejpam-4507	79	3	2.1	CARDINAL
ejpam-4507	80	1	lim	PERSON
ejpam-4507	80	2	1	CARDINAL
ejpam-4507	80	3	2πi	ORDINAL
ejpam-4507	80	4	k ̸=0 res(f(t	ORG
ejpam-4507	81	1	lemma 2.1	ORG
ejpam-4507	81	2	0	CARDINAL
ejpam-4507	81	3	k ̸=0 res(f(t	ORG
ejpam-4507	81	4	0	CARDINAL
ejpam-4507	83	1	k ̸=0 res(f(t	ORG
ejpam-4507	85	1	k ̸=0 res(f(t	ORG
ejpam-4507	87	1	2cxt	CARDINAL
ejpam-4507	88	1	etk	ORG
ejpam-4507	88	2	etk	ORG
ejpam-4507	88	3	r. corcino	PERSON
ejpam-4507	89	1	j. pure	PERSON
ejpam-4507	89	2	15	CARDINAL
ejpam-4507	89	3	4	CARDINAL
ejpam-4507	89	4	2022	CARDINAL
ejpam-4507	89	5	1662-1682 1667	EVENT
ejpam-4507	89	6	etk	ORG
ejpam-4507	89	7	b−ln	GPE
ejpam-4507	89	8	etk	ORG
ejpam-4507	89	9	etk ln a.	ORG
ejpam-4507	89	10	etk	ORG
ejpam-4507	92	1	1	CARDINAL
ejpam-4507	92	2	k ̸=0 etk(x ln c−ln	ORG
ejpam-4507	93	1	2.3	CARDINAL
ejpam-4507	95	1	n ≥ 1	DATE
ejpam-4507	95	2	about zero	CARDINAL
ejpam-4507	96	1	a− b π − ε	ORG
ejpam-4507	97	1	lim	PERSON
ejpam-4507	97	2	cxt bt	PERSON
ejpam-4507	98	1	0	CARDINAL
ejpam-4507	100	1	cxt	PRODUCT
ejpam-4507	101	1	2.3	CARDINAL
ejpam-4507	102	1	2.1	CARDINAL
ejpam-4507	102	2	|cxt|	GPE
ejpam-4507	102	3	+ 1] 1 2	DATE
ejpam-4507	102	4	2n + 1)π	CARDINAL
ejpam-4507	102	5	2n + 1)π	CARDINAL
ejpam-4507	102	6	0 ≤	MONEY
ejpam-4507	104	1	2n + 1)π	CARDINAL
ejpam-4507	105	1	c. corcino	PERSON
ejpam-4507	105	2	r. corcino	PERSON
ejpam-4507	106	1	j. pure	PERSON
ejpam-4507	106	2	15	CARDINAL
ejpam-4507	106	3	4	CARDINAL
ejpam-4507	106	4	2022	CARDINAL
ejpam-4507	106	5	1662-1682 1668	DATE
ejpam-4507	106	6	1 eγ(ln	CARDINAL
ejpam-4507	106	7	|cxt|	GPE
ejpam-4507	107	1	+ 1] 1 2	DATE
ejpam-4507	108	1	zero	CARDINAL
ejpam-4507	109	1	cos θ	PERSON
ejpam-4507	109	2	0	CARDINAL
ejpam-4507	109	3	2.1	CARDINAL
ejpam-4507	110	1	0	CARDINAL
ejpam-4507	111	1	0	CARDINAL
ejpam-4507	112	1	+ 1	DATE
ejpam-4507	112	2	2 + 2 cos	DATE
ejpam-4507	113	1	cos	PRODUCT
ejpam-4507	113	2	0	CARDINAL
ejpam-4507	113	3	±1	PERSON
ejpam-4507	113	4	2n + 1)π	CARDINAL
ejpam-4507	114	1	−1	DATE
ejpam-4507	114	2	2n + 1)π	CARDINAL
ejpam-4507	114	3	2k + 1)π	DATE
ejpam-4507	114	4	2n + 1)π	CARDINAL
ejpam-4507	114	5	2k + 1)π	DATE
ejpam-4507	114	6	2(n	CARDINAL
ejpam-4507	114	7	cxt	PRODUCT
ejpam-4507	115	1	|cxt|	GPE
ejpam-4507	116	1	cxt bt +	PERSON
ejpam-4507	116	2	∣∣∣∣ cxt bt	PERSON
ejpam-4507	117	1	|dt|	ORG
ejpam-4507	117	2	2n +	CARDINAL
ejpam-4507	118	1	2π	CARDINAL
ejpam-4507	118	2	2m∗πbn	CARDINAL
ejpam-4507	118	3	zero	CARDINAL
ejpam-4507	118	4	n → +∞.	ORG
ejpam-4507	118	5	c. corcino	PERSON
ejpam-4507	118	6	r. corcino	PERSON
ejpam-4507	119	1	j. pure	PERSON
ejpam-4507	119	2	15	CARDINAL
ejpam-4507	119	3	4	CARDINAL
ejpam-4507	119	4	2022	CARDINAL
ejpam-4507	119	5	1669	CARDINAL
ejpam-4507	119	6	2.4	DATE
ejpam-4507	121	1	euler	PERSON
ejpam-4507	122	1	2	CARDINAL
ejpam-4507	122	2	a− b π − ε	ORG
ejpam-4507	124	1	2k + 1)πi	QUANTITY
ejpam-4507	124	2	0	CARDINAL
ejpam-4507	125	1	1	CARDINAL
ejpam-4507	125	2	2	CARDINAL
ejpam-4507	125	3	2	CARDINAL
ejpam-4507	125	4	cxt = ∞∑ n=0	PERSON
ejpam-4507	127	1	1 2πi	CARDINAL
ejpam-4507	128	1	2cxt	CARDINAL
ejpam-4507	128	2	about zero	CARDINAL
ejpam-4507	129	1	g(t	NORP
ejpam-4507	130	1	2cxt	CARDINAL
ejpam-4507	131	1	g(t	NORP
ejpam-4507	131	2	0	CARDINAL
ejpam-4507	132	1	0	CARDINAL
ejpam-4507	133	1	2k +	QUANTITY
ejpam-4507	134	1	k ∈ z	PERSON
ejpam-4507	134	2	2.2	CARDINAL
ejpam-4507	135	1	2.3	CARDINAL
ejpam-4507	136	1	lim	ORG
ejpam-4507	136	2	1	CARDINAL
ejpam-4507	136	3	2πi	ORDINAL
ejpam-4507	138	1	2.3	CARDINAL
ejpam-4507	141	1	g(t	NORP
ejpam-4507	144	1	2extk	PRODUCT
ejpam-4507	144	2	c. corcino	GPE
ejpam-4507	144	3	r. corcino	PERSON
ejpam-4507	145	1	j. pure	PERSON
ejpam-4507	145	2	15	CARDINAL
ejpam-4507	145	3	4	CARDINAL
ejpam-4507	145	4	2022	CARDINAL
ejpam-4507	145	5	1662-1682 1670	DATE
ejpam-4507	147	1	etk ln a.	ORG
ejpam-4507	148	1	ct−n−1 k −b	PERSON
ejpam-4507	148	2	etk	ORG
ejpam-4507	148	3	tn+1 k	PERSON
ejpam-4507	151	1	2	CARDINAL
ejpam-4507	151	2	tn+1 k	PERSON
ejpam-4507	152	1	2.5	CARDINAL
ejpam-4507	155	1	2	CARDINAL
ejpam-4507	155	2	a− b π − ε	ORG
ejpam-4507	157	1	2k + 1)πi	QUANTITY
ejpam-4507	157	2	0	CARDINAL
ejpam-4507	158	1	2.4	CARDINAL
ejpam-4507	159	1	3	CARDINAL
ejpam-4507	160	1	2	CARDINAL
ejpam-4507	160	2	3.1	CARDINAL
ejpam-4507	162	1	2	CARDINAL
ejpam-4507	162	2	z+	ORG
ejpam-4507	162	3	about zero	CARDINAL
ejpam-4507	162	4	0	CARDINAL
ejpam-4507	163	1	2π	CARDINAL
ejpam-4507	164	1	lim	PERSON
ejpam-4507	164	2	cxt	PRODUCT
ejpam-4507	165	1	c. corcino	PERSON
ejpam-4507	165	2	r. corcino	PERSON
ejpam-4507	166	1	j. pure	PERSON
ejpam-4507	166	2	15	CARDINAL
ejpam-4507	166	3	4	CARDINAL
ejpam-4507	166	4	2022	CARDINAL
ejpam-4507	166	5	1662-1682 1671	DATE
ejpam-4507	167	1	cxt	PRODUCT
ejpam-4507	168	1	2.1	CARDINAL
ejpam-4507	168	2	2eγb	CARDINAL
ejpam-4507	169	1	+ 1] 1 2	DATE
ejpam-4507	169	2	∈	ORG
ejpam-4507	170	1	2nπ	ORDINAL
ejpam-4507	170	2	2nπ	ORDINAL
ejpam-4507	170	3	0 ≤	MONEY
ejpam-4507	170	4	2π	CARDINAL
ejpam-4507	172	1	eαγ	PERSON
ejpam-4507	172	2	2eγb	CARDINAL
ejpam-4507	172	3	+ 1	DATE
ejpam-4507	172	4	2	CARDINAL
ejpam-4507	172	5	cxt	PRODUCT
ejpam-4507	173	1	2	CARDINAL
ejpam-4507	174	1	2nπ	CARDINAL
ejpam-4507	174	2	∀n ≥ 1	DATE
ejpam-4507	175	1	2π	CARDINAL
ejpam-4507	176	1	2π	CARDINAL
ejpam-4507	176	2	1	CARDINAL
ejpam-4507	176	3	e. consequently	PERSON
ejpam-4507	176	4	cxt	PRODUCT
ejpam-4507	177	1	2eγb	CARDINAL
ejpam-4507	177	2	+ 1	DATE
ejpam-4507	177	3	2	CARDINAL
ejpam-4507	178	1	2.1	CARDINAL
ejpam-4507	178	2	cxt	PRODUCT
ejpam-4507	179	1	2π	CARDINAL
ejpam-4507	179	2	cxt	PRODUCT
ejpam-4507	179	3	2nπ	CARDINAL
ejpam-4507	179	4	2π	CARDINAL
ejpam-4507	179	5	2nπ	ORDINAL
ejpam-4507	179	6	c. corcino	PERSON
ejpam-4507	179	7	r. corcino	PERSON
ejpam-4507	180	1	j. pure	PERSON
ejpam-4507	180	2	15	CARDINAL
ejpam-4507	180	3	4	CARDINAL
ejpam-4507	180	4	2022	CARDINAL
ejpam-4507	180	5	1662-1682 1672	ORG
ejpam-4507	180	6	2πmbα−n	CARDINAL
ejpam-4507	180	7	2nπ	CARDINAL
ejpam-4507	182	1	n → +∞.	ORG
ejpam-4507	182	2	3.2	CARDINAL
ejpam-4507	183	1	∈	ORG
ejpam-4507	183	2	∈	ORG
ejpam-4507	183	3	ν	NORP
ejpam-4507	184	1	0	CARDINAL
ejpam-4507	186	1	α cxt	PERSON
ejpam-4507	186	2	∞∑ n=0 b(α	PERSON
ejpam-4507	187	1	∞∑ n=0	PERSON
ejpam-4507	192	1	∞∑ n=0 b(α	PERSON
ejpam-4507	193	1	c)(y	PERSON
ejpam-4507	194	1	c)(y	PERSON
ejpam-4507	197	1	0	CARDINAL
ejpam-4507	197	2	c)(z	PERSON
ejpam-4507	199	1	0	CARDINAL
ejpam-4507	200	1	3.3	CARDINAL
ejpam-4507	201	1	2	CARDINAL
ejpam-4507	201	2	about zero	CARDINAL
ejpam-4507	201	3	2nπ	ORDINAL
ejpam-4507	202	1	0	CARDINAL
ejpam-4507	203	1	c. corcino	GPE
ejpam-4507	203	2	r. corcino	PERSON
ejpam-4507	204	1	j. pure	PERSON
ejpam-4507	204	2	15	CARDINAL
ejpam-4507	204	3	4	CARDINAL
ejpam-4507	204	4	2022	CARDINAL
ejpam-4507	204	5	1662-1682 1673	ORG
ejpam-4507	205	1	k ̸=0	ORG
ejpam-4507	205	2	ν=0	PERSON
ejpam-4507	208	1	2kπi)n	CARDINAL
ejpam-4507	208	2	2π	CARDINAL
ejpam-4507	209	1	0	CARDINAL
ejpam-4507	209	2	3.2	CARDINAL
ejpam-4507	211	1	1	CARDINAL
ejpam-4507	212	1	1 2πi	CARDINAL
ejpam-4507	212	2	cxt	PRODUCT
ejpam-4507	212	3	less than 2π	CARDINAL
ejpam-4507	213	1	cxt	PRODUCT
ejpam-4507	214	1	n − α + 1	ORG
ejpam-4507	214	2	zeros	CARDINAL
ejpam-4507	214	3	2kπi	CARDINAL
ejpam-4507	214	4	k ∈ z.	PERSON
ejpam-4507	214	5	1	CARDINAL
ejpam-4507	214	6	3.1	CARDINAL
ejpam-4507	215	1	lim	ORG
ejpam-4507	215	2	1	CARDINAL
ejpam-4507	215	3	2πi	ORDINAL
ejpam-4507	215	4	cxt	PRODUCT
ejpam-4507	216	1	k ̸=0 res(fα(t	ORG
ejpam-4507	217	1	3.1	CARDINAL
ejpam-4507	217	2	0	CARDINAL
ejpam-4507	217	3	k ̸=0 res(fα(t	ORG
ejpam-4507	219	1	k ̸=0 res(fα(t	ORG
ejpam-4507	221	1	k ̸=0 res(fα(t	ORG
ejpam-4507	222	1	4	CARDINAL
ejpam-4507	222	2	1	CARDINAL
ejpam-4507	222	3	1	CARDINAL
ejpam-4507	223	1	lim t→tk dα−1 dtα−1	PERSON
ejpam-4507	223	2	1	CARDINAL
ejpam-4507	223	3	1	CARDINAL
ejpam-4507	223	4	1	CARDINAL
ejpam-4507	224	1	lim t→tk dα−1 dtα−1	PERSON
ejpam-4507	225	1	5	CARDINAL
ejpam-4507	225	2	c. corcino	GPE
ejpam-4507	225	3	r. corcino	PERSON
ejpam-4507	226	1	j. pure	PERSON
ejpam-4507	226	2	15	CARDINAL
ejpam-4507	226	3	4	CARDINAL
ejpam-4507	226	4	2022	CARDINAL
ejpam-4507	226	5	1662-1682 1674	DATE
ejpam-4507	226	6	0	CARDINAL
ejpam-4507	226	7	1	CARDINAL
ejpam-4507	227	1	∞∑ n=0 b(α	PERSON
ejpam-4507	227	2	0	CARDINAL
ejpam-4507	230	1	∞∑ n=0 b(α	PERSON
ejpam-4507	230	2	0	CARDINAL
ejpam-4507	231	1	6	CARDINAL
ejpam-4507	231	2	6	CARDINAL
ejpam-4507	231	3	αeαtk	PERSON
ejpam-4507	233	1	0	CARDINAL
ejpam-4507	234	1	7	CARDINAL
ejpam-4507	234	2	2kπi)/b	ORDINAL
ejpam-4507	235	1	1	CARDINAL
ejpam-4507	235	2	7	CARDINAL
ejpam-4507	235	3	αeαtk	PERSON
ejpam-4507	235	4	∞∑ n=0 b(α	PERSON
ejpam-4507	235	5	0	CARDINAL
ejpam-4507	237	1	∞∑ n=0 b(α	PERSON
ejpam-4507	237	2	0	CARDINAL
ejpam-4507	238	1	8)	CARDINAL
ejpam-4507	238	2	8)	CARDINAL
ejpam-4507	238	3	5	CARDINAL
ejpam-4507	238	4	res(fα(t	ORG
ejpam-4507	239	1	1	CARDINAL
ejpam-4507	240	1	lim t→tk dα−1 dtα−1 (	PERSON
ejpam-4507	240	2	∞∑ n=0	PERSON
ejpam-4507	243	1	dn dtn	PERSON
ejpam-4507	244	1	n∑ k=0	PERSON
ejpam-4507	244	2	dtk g	ORG
ejpam-4507	246	1	0	CARDINAL
ejpam-4507	247	1	ν=0	PERSON
ejpam-4507	247	2	1 ν	MONEY
ejpam-4507	247	3	c. corcino	GPE
ejpam-4507	247	4	r. corcino	PERSON
ejpam-4507	248	1	j. pure	PERSON
ejpam-4507	248	2	15	CARDINAL
ejpam-4507	248	3	4	CARDINAL
ejpam-4507	248	4	2022	CARDINAL
ejpam-4507	248	5	ν=0	PERSON
ejpam-4507	248	6	1 ν	MONEY
ejpam-4507	248	7	1)α−1−νt α−n−1−(α−1−ν	DATE
ejpam-4507	248	8	ν=0	PERSON
ejpam-4507	248	9	1 ν	MONEY
ejpam-4507	248	10	1)α−1−νt	CARDINAL
ejpam-4507	248	11	9	CARDINAL
ejpam-4507	248	12	2)	DATE
ejpam-4507	250	1	1)α−1−ν	CARDINAL
ejpam-4507	250	2	2)(n− α+ 3	DATE
ejpam-4507	250	3	1⟩α−ν−1	CARDINAL
ejpam-4507	251	1	∞∑ n=0 b(α	PERSON
ejpam-4507	251	2	0	CARDINAL
ejpam-4507	254	1	dtl	PERSON
ejpam-4507	254	2	0	CARDINAL
ejpam-4507	256	1	c)ν−lext	ORG
ejpam-4507	256	2	∑ n≥l b(α	FAC
ejpam-4507	256	3	0	CARDINAL
ejpam-4507	257	1	lim	PERSON
ejpam-4507	260	1	0	CARDINAL
ejpam-4507	261	1	9	CARDINAL
ejpam-4507	261	2	lim t→k dα−1 dtα−1 (fg	ORG
ejpam-4507	261	3	ν=0	PERSON
ejpam-4507	261	4	1 ν	MONEY
ejpam-4507	261	5	1)α−1−ν	CARDINAL
ejpam-4507	263	1	0	CARDINAL
ejpam-4507	264	1	ν=0	PERSON
ejpam-4507	264	2	1 ν	MONEY
ejpam-4507	264	3	1)α−1−ν	CARDINAL
ejpam-4507	264	4	k etk	PERSON
ejpam-4507	264	5	0	CARDINAL
ejpam-4507	265	1	10	CARDINAL
ejpam-4507	265	2	c. corcino	GPE
ejpam-4507	265	3	r. corcino	PERSON
ejpam-4507	266	1	j. pure	PERSON
ejpam-4507	266	2	15	CARDINAL
ejpam-4507	266	3	4	CARDINAL
ejpam-4507	266	4	2022	CARDINAL
ejpam-4507	266	5	1662-1682 1676	ORG
ejpam-4507	266	6	3.2	CARDINAL
ejpam-4507	266	7	10	CARDINAL
ejpam-4507	266	8	lim t→k dα−1 dtα−1 (	PERSON
ejpam-4507	266	9	ν=0	PERSON
ejpam-4507	266	10	1 ν	MONEY
ejpam-4507	266	11	1)α−1−νt	DATE
ejpam-4507	266	12	k etk	PERSON
ejpam-4507	267	1	res(fα(t	ORG
ejpam-4507	267	2	ν=0	PERSON
ejpam-4507	269	1	11	CARDINAL
ejpam-4507	269	2	11	CARDINAL
ejpam-4507	269	3	4	CARDINAL
ejpam-4507	270	1	1	CARDINAL
ejpam-4507	270	2	3.3	CARDINAL
ejpam-4507	270	3	2.2	CARDINAL
ejpam-4507	271	1	2	CARDINAL
ejpam-4507	271	2	3.3	CARDINAL
ejpam-4507	271	3	2	CARDINAL
ejpam-4507	272	1	2	CARDINAL
ejpam-4507	273	1	k ̸=0 (	ORG
ejpam-4507	275	1	2kπi)n	CARDINAL
ejpam-4507	275	2	3.3	CARDINAL
ejpam-4507	276	1	3.4	CARDINAL
ejpam-4507	277	1	about zero	CARDINAL
ejpam-4507	278	1	0	CARDINAL
ejpam-4507	278	2	a− b π − ε	ORG
ejpam-4507	278	3	12	CARDINAL
ejpam-4507	278	4	lim	PERSON
ejpam-4507	278	5	cxt	PRODUCT
ejpam-4507	280	1	3.2	CARDINAL
ejpam-4507	280	2	eαγ	DATE
ejpam-4507	280	3	+ 1	DATE
ejpam-4507	280	4	2	CARDINAL
ejpam-4507	280	5	∈	ORG
ejpam-4507	280	6	2n + 1)π	CARDINAL
ejpam-4507	280	7	cos θ +	ORG
ejpam-4507	280	8	0 ≤	MONEY
ejpam-4507	281	1	2n + 1)π	CARDINAL
ejpam-4507	281	2	2n + 1)π	CARDINAL
ejpam-4507	281	3	c. corcino	PERSON
ejpam-4507	281	4	r. corcino	PERSON
ejpam-4507	282	1	j. pure	PERSON
ejpam-4507	282	2	15	CARDINAL
ejpam-4507	282	3	4	CARDINAL
ejpam-4507	282	4	2022	CARDINAL
ejpam-4507	282	5	1662-1682 1677	DATE
ejpam-4507	282	6	12	CARDINAL
ejpam-4507	284	1	2n + 1)π	CARDINAL
ejpam-4507	284	2	∀n ≥ 1	DATE
ejpam-4507	285	1	1	CARDINAL
ejpam-4507	285	2	1 e	CARDINAL
ejpam-4507	285	3	2n+1)−ε	CARDINAL
ejpam-4507	285	4	e. consequently,∣∣∣∣ cxt	PERSON
ejpam-4507	285	5	1	CARDINAL
ejpam-4507	285	6	+ 1	DATE
ejpam-4507	285	7	2	CARDINAL
ejpam-4507	285	8	+ 1	DATE
ejpam-4507	285	9	2	CARDINAL
ejpam-4507	287	1	2.3	CARDINAL
ejpam-4507	288	1	∃	ORG
ejpam-4507	288	2	s.t.	PERSON
ejpam-4507	288	3	∣∣∣∣ cxt	PERSON
ejpam-4507	289	1	cxt	PRODUCT
ejpam-4507	289	2	2n + 1)π	CARDINAL
ejpam-4507	289	3	2π	CARDINAL
ejpam-4507	289	4	2πmbn	CARDINAL
ejpam-4507	289	5	1	CARDINAL
ejpam-4507	291	1	n → +∞.	ORG
ejpam-4507	291	2	3.5	CARDINAL
ejpam-4507	292	1	∈	ORG
ejpam-4507	292	2	∈	ORG
ejpam-4507	292	3	ν	NORP
ejpam-4507	292	4	2	CARDINAL
ejpam-4507	294	1	0	CARDINAL
ejpam-4507	296	1	3.2	CARDINAL
ejpam-4507	297	1	3.6	CARDINAL
ejpam-4507	298	1	2	CARDINAL
ejpam-4507	298	2	about zero	CARDINAL
ejpam-4507	298	3	1	CARDINAL
ejpam-4507	298	4	r. corcino	PERSON
ejpam-4507	299	1	j. pure	PERSON
ejpam-4507	299	2	15	CARDINAL
ejpam-4507	299	3	4	CARDINAL
ejpam-4507	299	4	2022	CARDINAL
ejpam-4507	299	5	1662-1682 1678	DATE
ejpam-4507	300	1	euler	PERSON
ejpam-4507	302	1	1	CARDINAL
ejpam-4507	303	1	∑ k∈z	PERSON
ejpam-4507	304	1	ν=0	PERSON
ejpam-4507	304	2	1 ν	MONEY
ejpam-4507	304	3	a− b π − ε	ORG
ejpam-4507	304	4	0	CARDINAL
ejpam-4507	305	1	2	CARDINAL
ejpam-4507	306	1	1 2πi	CARDINAL
ejpam-4507	307	1	2αcxt	CARDINAL
ejpam-4507	307	2	about zero	CARDINAL
ejpam-4507	308	1	cxt	PRODUCT
ejpam-4507	309	1	2α(n	CARDINAL
ejpam-4507	310	1	1 2πi	CARDINAL
ejpam-4507	311	1	n + 1	PRODUCT
ejpam-4507	311	2	zeros	CARDINAL
ejpam-4507	311	3	2k + 1)πi)/b	DATE
ejpam-4507	311	4	k ∈ z.	PERSON
ejpam-4507	311	5	1 2πi	CARDINAL
ejpam-4507	313	1	3.4	CARDINAL
ejpam-4507	313	2	2α(n	CARDINAL
ejpam-4507	316	1	1	CARDINAL
ejpam-4507	316	2	1	CARDINAL
ejpam-4507	317	1	lim t→tk dα−1 dtα−1	PERSON
ejpam-4507	317	2	α cxt	PERSON
ejpam-4507	317	3	1 tn+1	QUANTITY
ejpam-4507	318	1	13	CARDINAL
ejpam-4507	318	2	7	CARDINAL
ejpam-4507	319	1	2k + 1)πi	QUANTITY
ejpam-4507	319	2	−1	DATE
ejpam-4507	320	1	7	CARDINAL
ejpam-4507	320	2	αeαtk	PERSON
ejpam-4507	321	1	∞∑ n=0 b(α	PERSON
ejpam-4507	321	2	0	CARDINAL
ejpam-4507	322	1	c. corcino	PERSON
ejpam-4507	322	2	r. corcino	PERSON
ejpam-4507	323	1	j. pure	PERSON
ejpam-4507	323	2	15	CARDINAL
ejpam-4507	323	3	4	CARDINAL
ejpam-4507	323	4	2022	CARDINAL
ejpam-4507	323	5	1662-1682 1679	EVENT
ejpam-4507	324	1	∞∑ n=0 b(α	PERSON
ejpam-4507	324	2	0	CARDINAL
ejpam-4507	325	1	14	CARDINAL
ejpam-4507	325	2	14	CARDINAL
ejpam-4507	325	3	13	CARDINAL
ejpam-4507	325	4	1	CARDINAL
ejpam-4507	326	1	lim t→tk dα−1 dtα−1 (	PERSON
ejpam-4507	326	2	0	CARDINAL
ejpam-4507	327	1	1	CARDINAL
ejpam-4507	328	1	ν=0	PERSON
ejpam-4507	328	2	1 ν	MONEY
ejpam-4507	328	3	k b(α	PERSON
ejpam-4507	329	1	2α	CARDINAL
ejpam-4507	329	2	1	CARDINAL
ejpam-4507	331	1	ν=0	PERSON
ejpam-4507	331	2	1 ν	MONEY
ejpam-4507	331	3	k b(α	PERSON
ejpam-4507	332	1	2α	CARDINAL
ejpam-4507	332	2	1	CARDINAL
ejpam-4507	333	1	∑ k∈z	PERSON
ejpam-4507	334	1	ν=0	PERSON
ejpam-4507	334	2	1 ν	MONEY
ejpam-4507	334	3	−n− 1)α−1−ν b(α	PRODUCT
ejpam-4507	335	1	1	CARDINAL
ejpam-4507	335	2	3.6	CARDINAL
ejpam-4507	335	3	2.4	CARDINAL
ejpam-4507	336	1	2	CARDINAL
ejpam-4507	336	2	2	CARDINAL
ejpam-4507	336	3	22(n	CARDINAL
ejpam-4507	338	1	−n−	LANGUAGE
ejpam-4507	338	2	2	CARDINAL
ejpam-4507	340	1	2	CARDINAL
ejpam-4507	340	2	tn+1 k	PERSON
ejpam-4507	340	3	2	CARDINAL
ejpam-4507	341	1	1	CARDINAL
ejpam-4507	341	2	15	CARDINAL
ejpam-4507	341	3	2	CARDINAL
ejpam-4507	342	1	a−	ORG
ejpam-4507	343	1	16	CARDINAL
ejpam-4507	343	2	3.7	CARDINAL
ejpam-4507	344	1	z+	ORG
ejpam-4507	344	2	about zero	CARDINAL
ejpam-4507	344	3	2n + 1)π	CARDINAL
ejpam-4507	344	4	a− b π − ε	ORG
ejpam-4507	346	1	lim	PERSON
ejpam-4507	346	2	cxt	PRODUCT
ejpam-4507	347	1	c. corcino	PERSON
ejpam-4507	347	2	r. corcino	PERSON
ejpam-4507	348	1	j. pure	PERSON
ejpam-4507	348	2	15	CARDINAL
ejpam-4507	348	3	4	CARDINAL
ejpam-4507	348	4	2022	CARDINAL
ejpam-4507	349	1	3.4	CARDINAL
ejpam-4507	350	1	3.8	CARDINAL
ejpam-4507	351	1	∈	ORG
ejpam-4507	351	2	∈	ORG
ejpam-4507	351	3	ν	NORP
ejpam-4507	352	1	0	CARDINAL
ejpam-4507	354	1	3.2	CARDINAL
ejpam-4507	355	1	3.9	CARDINAL
ejpam-4507	356	1	2	CARDINAL
ejpam-4507	356	2	about zero	CARDINAL
ejpam-4507	359	1	2α	CARDINAL
ejpam-4507	359	2	1	CARDINAL
ejpam-4507	360	1	∑ k∈z	PERSON
ejpam-4507	361	1	ν=0	PERSON
ejpam-4507	361	2	1 ν	MONEY
ejpam-4507	363	1	3	CARDINAL
ejpam-4507	365	1	2α	CARDINAL
ejpam-4507	365	2	2πi	ORDINAL
ejpam-4507	365	3	cxt	PRODUCT
ejpam-4507	365	4	about zero	CARDINAL
ejpam-4507	365	5	cxt	PRODUCT
ejpam-4507	366	1	n − α + 1	ORG
ejpam-4507	366	2	zeros	CARDINAL
ejpam-4507	367	1	2k +	QUANTITY
ejpam-4507	368	1	k ∈ z.	PERSON
ejpam-4507	368	2	1 2πi	CARDINAL
ejpam-4507	370	1	3.7	CARDINAL
ejpam-4507	371	1	2α	CARDINAL
ejpam-4507	372	1	17	CARDINAL
ejpam-4507	372	2	1	CARDINAL
ejpam-4507	372	3	1	CARDINAL
ejpam-4507	373	1	lim t→tk dα−1 dtα−1	PERSON
ejpam-4507	373	2	α cxt	PERSON
ejpam-4507	373	3	1	CARDINAL
ejpam-4507	374	1	14	CARDINAL
ejpam-4507	374	2	1	CARDINAL
ejpam-4507	375	1	lim t→tk dα−1 dtα−1 (	PERSON
ejpam-4507	375	2	∞∑ n=0 b(α	PERSON
ejpam-4507	375	3	0	CARDINAL
ejpam-4507	376	1	1681	CARDINAL
ejpam-4507	376	2	euler	PERSON
ejpam-4507	376	3	1	CARDINAL
ejpam-4507	378	1	ν=0	PERSON
ejpam-4507	378	2	1 ν	MONEY
ejpam-4507	378	3	1)α−1−ν	CARDINAL
ejpam-4507	378	4	k b(α	PERSON
ejpam-4507	379	1	18	CARDINAL
ejpam-4507	379	2	18	CARDINAL
ejpam-4507	379	3	17	CARDINAL
ejpam-4507	380	1	1	CARDINAL
ejpam-4507	380	2	3.9	CARDINAL
ejpam-4507	380	3	2.5	CARDINAL
ejpam-4507	381	1	2	CARDINAL
ejpam-4507	381	2	2	CARDINAL
ejpam-4507	381	3	22(4	CARDINAL
ejpam-4507	383	1	2	CARDINAL
ejpam-4507	386	1	2k + 1)πi)4	DATE
ejpam-4507	386	2	2	CARDINAL
ejpam-4507	387	1	2k + 1)πi)3	DATE
ejpam-4507	387	2	2	CARDINAL
ejpam-4507	389	1	2	CARDINAL
ejpam-4507	389	2	15	CARDINAL
ejpam-4507	389	3	16	CARDINAL
ejpam-4507	390	1	4	CARDINAL
ejpam-4507	394	1	1	CARDINAL
ejpam-4507	394	2	d.	NORP
ejpam-4507	394	3	ortega	PERSON
ejpam-4507	394	4	m.	PERSON
ejpam-4507	394	5	ramirez	PERSON
ejpam-4507	394	6	w.	PERSON
ejpam-4507	394	7	a.	PERSON
ejpam-4507	396	1	2020	DATE
ejpam-4507	396	2	article 534	LAW
ejpam-4507	397	1	2	CARDINAL
ejpam-4507	397	2	d.	NORP
ejpam-4507	397	3	ortega	PERSON
ejpam-4507	397	4	m.	PERSON
ejpam-4507	397	5	ramirez	PERSON
ejpam-4507	397	6	w.	PERSON
ejpam-4507	399	1	55	CARDINAL
ejpam-4507	399	2	2021	CARDINAL
ejpam-4507	399	3	10-23	CARDINAL
ejpam-4507	400	1	3	CARDINAL
ejpam-4507	400	2	w.	PERSON
ejpam-4507	400	3	khan	GPE
ejpam-4507	400	4	s.	PERSON
ejpam-4507	402	1	15	CARDINAL
ejpam-4507	402	2	2022	CARDINAL
ejpam-4507	402	3	1-10	CARDINAL
ejpam-4507	403	1	4	CARDINAL
ejpam-4507	403	2	w.	PERSON
ejpam-4507	403	3	generalized apostolbernoulli	PERSON
ejpam-4507	403	4	apostol-euler	PERSON
ejpam-4507	403	5	carpathian	NORP
ejpam-4507	405	1	2022	CARDINAL
ejpam-4507	406	1	1682	DATE
ejpam-4507	406	2	5	CARDINAL
ejpam-4507	406	3	r. v.	PERSON
ejpam-4507	406	4	j. w.	PERSON
ejpam-4507	406	5	8th	ORDINAL
ejpam-4507	406	6	mcgrawhill book:	ORG
ejpam-4507	406	7	new york	GPE
ejpam-4507	406	8	ny, usa, 2008	ORG
ejpam-4507	407	1	6	CARDINAL
ejpam-4507	407	2	corcino	NORP
ejpam-4507	407	3	w.	PERSON
ejpam-4507	407	4	corcino	GPE
ejpam-4507	407	5	r.	NORP
ejpam-4507	407	6	132(1	CARDINAL
ejpam-4507	407	7	2022	CARDINAL
ejpam-4507	407	8	133	CARDINAL
ejpam-4507	408	1	7	CARDINAL
ejpam-4507	408	2	corcino	NORP
ejpam-4507	408	3	c.	GPE
ejpam-4507	408	4	corcino	NORP
ejpam-4507	408	5	r.	NORP
ejpam-4507	408	6	tangent-bernoulli	ORG
ejpam-4507	408	7	11(3	CARDINAL
ejpam-4507	408	8	2022	CARDINAL
ejpam-4507	408	9	article 86	LAW
ejpam-4507	409	1	8	CARDINAL
ejpam-4507	409	2	corcino	NORP
ejpam-4507	409	3	c.	GPE
ejpam-4507	409	4	corcino	NORP
ejpam-4507	409	5	r.	NORP
ejpam-4507	409	6	j.	PERSON
ejpam-4507	409	7	european journal	ORG
ejpam-4507	409	8	2021	CARDINAL
ejpam-4507	409	9	1457-1466	CARDINAL
ejpam-4507	410	1	9	CARDINAL
ejpam-4507	410	2	khan	GPE
ejpam-4507	410	3	w.	PERSON
ejpam-4507	410	4	srivastava	PERSON
ejpam-4507	410	5	d.	NORP
ejpam-4507	410	6	33(7	CARDINAL
ejpam-4507	410	7	2019	CARDINAL
ejpam-4507	410	8	1967-1977	DATE
ejpam-4507	411	1	10	CARDINAL
ejpam-4507	411	2	corcino	NORP
ejpam-4507	411	3	r.	NORP
ejpam-4507	411	4	corcino	GPE
ejpam-4507	411	5	c. j. inequal	PERSON
ejpam-4507	413	1	funct	PERSON
ejpam-4507	414	1	12 (	CARDINAL
ejpam-4507	414	2	2021	CARDINAL
ejpam-4507	414	3	54-72	DATE