id	sid	tid	token	lemma	pos
easat-10856	1	1	edelweiss	edelweiss	PROPN
easat-10856	1	2	applied	apply	VERB
easat-10856	1	3	science	science	NOUN
easat-10856	1	4	and	and	CCONJ
easat-10856	1	5	technology	technology	NOUN
easat-10856	1	6	issn	issn	PROPN
easat-10856	1	7	:	:	PUNCT
easat-10856	1	8	2576	2576	NUM
easat-10856	1	9	-	-	SYM
easat-10856	1	10	8484	8484	NUM
easat-10856	1	11	vol	vol	NOUN
easat-10856	1	12	.	.	PROPN
easat-10856	2	1	9	9	NUM
easat-10856	2	2	,	,	PUNCT
easat-10856	2	3	no	no	INTJ
easat-10856	2	4	.	.	NOUN
easat-10856	2	5	11	11	NUM
easat-10856	2	6	,	,	PUNCT
easat-10856	2	7	274	274	NUM
easat-10856	2	8	-	-	SYM
easat-10856	2	9	288	288	NUM
easat-10856	2	10	2025	2025	NUM
easat-10856	2	11	publisher	publisher	NOUN
easat-10856	2	12	:	:	PUNCT
easat-10856	2	13	learning	learn	VERB
easat-10856	2	14	gate	gate	NOUN
easat-10856	2	15	doi	doi	PROPN
easat-10856	2	16	:	:	PUNCT
easat-10856	2	17	10.55214/2576	10.55214/2576	NUM
easat-10856	2	18	-	-	PUNCT
easat-10856	2	19	8484.v9i11.10856	8484.v9i11.10856	NUM
easat-10856	2	20	©	©	PROPN
easat-10856	2	21	2025	2025	NUM
easat-10856	2	22	by	by	ADP
easat-10856	2	23	the	the	DET
easat-10856	2	24	authors	author	NOUN
easat-10856	2	25	;	;	PUNCT
easat-10856	2	26	licensee	licensee	PROPN
easat-10856	2	27	learning	learning	NOUN
easat-10856	2	28	gate	gate	NOUN
easat-10856	2	29	©	©	PROPN
easat-10856	2	30	2025	2025	NUM
easat-10856	2	31	by	by	ADP
easat-10856	2	32	the	the	DET
easat-10856	2	33	authors	author	NOUN
easat-10856	2	34	;	;	PUNCT
easat-10856	2	35	licensee	licensee	PROPN
easat-10856	2	36	learning	learning	NOUN
easat-10856	2	37	gate	gate	NOUN
easat-10856	2	38	history	history	NOUN
easat-10856	2	39	:	:	PUNCT
easat-10856	2	40	received	receive	VERB
easat-10856	2	41	:	:	PUNCT
easat-10856	2	42	13	13	NUM
easat-10856	2	43	august	august	PROPN
easat-10856	2	44	2025	2025	NUM
easat-10856	2	45	;	;	PUNCT
easat-10856	2	46	revised	revise	VERB
easat-10856	2	47	:	:	PUNCT
easat-10856	2	48	1	1	NUM
easat-10856	2	49	october	october	NOUN
easat-10856	2	50	2025	2025	NUM
easat-10856	2	51	;	;	PUNCT
easat-10856	2	52	accepted	accept	VERB
easat-10856	2	53	:	:	PUNCT
easat-10856	2	54	6	6	NUM
easat-10856	2	55	october	october	NOUN
easat-10856	2	56	2025	2025	NUM
easat-10856	2	57	;	;	PUNCT
easat-10856	2	58	published	publish	VERB
easat-10856	2	59	:	:	PUNCT
easat-10856	3	1	4	4	NUM
easat-10856	3	2	november	november	NOUN
easat-10856	3	3	2025	2025	NUM
easat-10856	3	4	*	*	PUNCT
easat-10856	3	5	correspondence	correspondence	NOUN
easat-10856	3	6	:	:	PUNCT
easat-10856	3	7	omarin@unfv.edu.pe	omarin@unfv.edu.pe	NOUN
easat-10856	3	8	calculation	calculation	NOUN
easat-10856	3	9	and	and	CCONJ
easat-10856	3	10	application	application	NOUN
easat-10856	3	11	of	of	ADP
easat-10856	3	12	the	the	DET
easat-10856	3	13	engineering	engineering	NOUN
easat-10856	3	14	numbers	number	NOUN
easat-10856	3	15	of	of	ADP
easat-10856	3	16	bernoulli	bernoulli	NOUN
easat-10856	3	17	(	(	PUNCT
easat-10856	3	18	b_n	b_n	NUM
easat-10856	3	19	)	)	PUNCT
easat-10856	3	20	and	and	CCONJ
easat-10856	3	21	euler	euler	NOUN
easat-10856	3	22	(	(	PUNCT
easat-10856	3	23	e_n	e_n	NOUN
easat-10856	3	24	)	)	PUNCT
easat-10856	3	25	to	to	ADP
easat-10856	3	26	integral	integral	ADJ
easat-10856	3	27	analysis	analysis	NOUN
easat-10856	3	28	and	and	CCONJ
easat-10856	3	29	other	other	ADJ
easat-10856	3	30	applications	application	NOUN
easat-10856	3	31	marín	marín	NOUN
easat-10856	3	32	-	-	PUNCT
easat-10856	3	33	machuca	machuca	NOUN
easat-10856	3	34	,	,	PUNCT
easat-10856	3	35	olegario1	olegario1	PROPN
easat-10856	3	36	*	*	NOUN
easat-10856	3	37	,	,	PUNCT
easat-10856	3	38	candela	candela	NOUN
easat-10856	3	39	-	-	PUNCT
easat-10856	3	40	díaz	díaz	NOUN
easat-10856	3	41	,	,	PUNCT
easat-10856	3	42	josé	josé	PROPN
easat-10856	3	43	eduardo2	eduardo2	PROPN
easat-10856	3	44	,	,	PUNCT
easat-10856	3	45	rojas	rojas	PROPN
easat-10856	3	46	-	-	PUNCT
easat-10856	3	47	rueda	rueda	PROPN
easat-10856	3	48	,	,	PUNCT
easat-10856	3	49	maría	maría	PROPN
easat-10856	3	50	del	del	PROPN
easat-10856	3	51	pilar3	pilar3	PROPN
easat-10856	3	52	,	,	PUNCT
easat-10856	3	53	chinchay	chinchay	PROPN
easat-10856	3	54	-	-	PUNCT
easat-10856	3	55	barragán	barragán	PROPN
easat-10856	3	56	,	,	PUNCT
easat-10856	3	57	carlos	carlos	PROPN
easat-10856	3	58	enrique4	enrique4	PROPN
easat-10856	3	59	,	,	PUNCT
easat-10856	3	60	pérez	pérez	NOUN
easat-10856	3	61	-	-	PUNCT
easat-10856	3	62	ton	ton	NOUN
easat-10856	3	63	,	,	PUNCT
easat-10856	3	64	luis	luis	PROPN
easat-10856	3	65	adolfo5	adolfo5	PROPN
easat-10856	3	66	,	,	PUNCT
easat-10856	3	67	vargas	vargas	NOUN
easat-10856	3	68	-	-	PUNCT
easat-10856	3	69	ayala	ayala	PROPN
easat-10856	3	70	,	,	PUNCT
easat-10856	3	71	jessica	jessica	PROPN
easat-10856	3	72	blanca6	blanca6	PROPN
easat-10856	4	1	1academic	1academic	NUM
easat-10856	4	2	department	department	PROPN
easat-10856	4	3	of	of	ADP
easat-10856	4	4	food	food	NOUN
easat-10856	4	5	sciences	science	NOUN
easat-10856	4	6	,	,	PUNCT
easat-10856	4	7	faculty	faculty	NOUN
easat-10856	4	8	of	of	ADP
easat-10856	4	9	oceanography	oceanography	NOUN
easat-10856	4	10	,	,	PUNCT
easat-10856	4	11	fisheries	fishery	NOUN
easat-10856	4	12	,	,	PUNCT
easat-10856	4	13	food	food	NOUN
easat-10856	4	14	sciences	science	NOUN
easat-10856	4	15	,	,	PUNCT
easat-10856	4	16	and	and	CCONJ
easat-10856	4	17	aquaculture	aquaculture	NOUN
easat-10856	4	18	.	.	PUNCT
easat-10856	5	1	universidad	universidad	PROPN
easat-10856	5	2	nacional	nacional	PROPN
easat-10856	5	3	federico	federico	PROPN
easat-10856	5	4	villarreal	villarreal	PROPN
easat-10856	5	5	.	.	PUNCT
easat-10856	6	1	lima	lima	PROPN
easat-10856	6	2	1500	1500	NUM
easat-10856	6	3	peru	peru	PROPN
easat-10856	6	4	;	;	PUNCT
easat-10856	6	5	omarín@unfv.edu.pe	omarín@unfv.edu.pe	NOUN
easat-10856	6	6	(	(	PUNCT
easat-10856	6	7	m.m.o	m.m.o	NOUN
easat-10856	6	8	.	.	PUNCT
easat-10856	6	9	)	)	PUNCT
easat-10856	6	10	.	.	PUNCT
easat-10856	7	1	2faculty	2faculty	NUM
easat-10856	7	2	of	of	ADP
easat-10856	7	3	oceanography	oceanography	NOUN
easat-10856	7	4	,	,	PUNCT
easat-10856	7	5	fisheries	fishery	NOUN
easat-10856	7	6	,	,	PUNCT
easat-10856	7	7	food	food	NOUN
easat-10856	7	8	sciences	science	NOUN
easat-10856	7	9	,	,	PUNCT
easat-10856	7	10	and	and	CCONJ
easat-10856	7	11	aquaculture	aquaculture	NOUN
easat-10856	7	12	.	.	PUNCT
easat-10856	8	1	universidad	universidad	PROPN
easat-10856	8	2	nacional	nacional	PROPN
easat-10856	8	3	federico	federico	PROPN
easat-10856	8	4	villarreal	villarreal	PROPN
easat-10856	8	5	.	.	PUNCT
easat-10856	9	1	lima	lima	PROPN
easat-10856	9	2	,	,	PUNCT
easat-10856	9	3	peru	peru	PROPN
easat-10856	9	4	.	.	PUNCT
easat-10856	10	1	jcandela@unfv.edu.pe	jcandela@unfv.edu.pe	NOUN
easat-10856	10	2	(	(	PUNCT
easat-10856	10	3	c.d.j.e	c.d.j.e	PROPN
easat-10856	10	4	.	.	PUNCT
easat-10856	10	5	)	)	PUNCT
easat-10856	10	6	.	.	PUNCT
easat-10856	11	1	3school	3school	NUM
easat-10856	11	2	of	of	ADP
easat-10856	11	3	human	human	ADJ
easat-10856	11	4	medicine	medicine	NOUN
easat-10856	11	5	,	,	PUNCT
easat-10856	11	6	universidad	universidad	PROPN
easat-10856	11	7	norbert	norbert	PROPN
easat-10856	11	8	wiener	wiener	PROPN
easat-10856	11	9	,	,	PUNCT
easat-10856	11	10	lima	lima	PROPN
easat-10856	11	11	,	,	PUNCT
easat-10856	11	12	peru	peru	PROPN
easat-10856	11	13	.	.	PUNCT
easat-10856	12	1	maria.rojasr@uwiener.edu.pe	maria.rojasr@uwiener.edu.pe	NOUN
easat-10856	12	2	(	(	PUNCT
easat-10856	12	3	r.r.m.p	r.r.m.p	NOUN
easat-10856	12	4	.	.	PUNCT
easat-10856	12	5	)	)	PUNCT
easat-10856	12	6	.	.	PUNCT
easat-10856	13	1	4professional	4professional	NUM
easat-10856	13	2	school	school	NOUN
easat-10856	13	3	of	of	ADP
easat-10856	13	4	food	food	NOUN
easat-10856	13	5	engineering	engineering	NOUN
easat-10856	13	6	,	,	PUNCT
easat-10856	13	7	faculty	faculty	NOUN
easat-10856	13	8	of	of	ADP
easat-10856	13	9	fisheries	fishery	NOUN
easat-10856	13	10	and	and	CCONJ
easat-10856	13	11	food	food	NOUN
easat-10856	13	12	engineering	engineering	NOUN
easat-10856	13	13	,	,	PUNCT
easat-10856	13	14	universidad	universidad	PROPN
easat-10856	13	15	nacional	nacional	PROPN
easat-10856	13	16	del	del	PROPN
easat-10856	13	17	callao	callao	PROPN
easat-10856	13	18	.	.	PUNCT
easat-10856	14	1	callao	callao	PROPN
easat-10856	14	2	,	,	PUNCT
easat-10856	14	3	peru	peru	PROPN
easat-10856	14	4	.	.	PUNCT
easat-10856	15	1	cchinchayb@unac.edu.pe	cchinchayb@unac.edu.pe	NOUN
easat-10856	15	2	(	(	PUNCT
easat-10856	15	3	c.b.c.e	c.b.c.e	PROPN
easat-10856	15	4	.	.	PUNCT
easat-10856	15	5	)	)	PUNCT
easat-10856	15	6	.	.	PUNCT
easat-10856	16	1	5professional	5professional	ADJ
easat-10856	16	2	school	school	NOUN
easat-10856	16	3	of	of	ADP
easat-10856	16	4	food	food	NOUN
easat-10856	16	5	engineering	engineering	NOUN
easat-10856	16	6	,	,	PUNCT
easat-10856	16	7	faculty	faculty	NOUN
easat-10856	16	8	of	of	ADP
easat-10856	16	9	fishery	fishery	NOUN
easat-10856	16	10	and	and	CCONJ
easat-10856	16	11	food	food	NOUN
easat-10856	16	12	engineering	engineering	NOUN
easat-10856	16	13	,	,	PUNCT
easat-10856	16	14	universidad	universidad	PROPN
easat-10856	16	15	nacional	nacional	PROPN
easat-10856	16	16	del	del	PROPN
easat-10856	16	17	callao	callao	PROPN
easat-10856	16	18	,	,	PUNCT
easat-10856	16	19	callao	callao	PROPN
easat-10856	16	20	,	,	PUNCT
easat-10856	16	21	peru	peru	PROPN
easat-10856	16	22	.	.	PUNCT
easat-10856	17	1	laperezt@unac.edu.pe	laperezt@unac.edu.pe	PROPN
easat-10856	17	2	(	(	PUNCT
easat-10856	17	3	p.t.l.a	p.t.l.a	PROPN
easat-10856	17	4	.	.	PUNCT
easat-10856	17	5	)	)	PUNCT
easat-10856	17	6	.	.	PUNCT
easat-10856	18	1	6academic	6academic	NUM
easat-10856	18	2	department	department	NOUN
easat-10856	18	3	of	of	ADP
easat-10856	18	4	aquaculture	aquaculture	NOUN
easat-10856	18	5	,	,	PUNCT
easat-10856	18	6	faculty	faculty	NOUN
easat-10856	18	7	of	of	ADP
easat-10856	18	8	oceanography	oceanography	NOUN
easat-10856	18	9	,	,	PUNCT
easat-10856	18	10	fisheries	fishery	NOUN
easat-10856	18	11	,	,	PUNCT
easat-10856	18	12	food	food	NOUN
easat-10856	18	13	sciences	science	NOUN
easat-10856	18	14	and	and	CCONJ
easat-10856	18	15	aquaculture	aquaculture	NOUN
easat-10856	18	16	,	,	PUNCT
easat-10856	18	17	universidad	universidad	PROPN
easat-10856	18	18	nacional	nacional	PROPN
easat-10856	18	19	federico	federico	PROPN
easat-10856	18	20	villarreal	villarreal	PROPN
easat-10856	18	21	,	,	PUNCT
easat-10856	18	22	lima	lima	PROPN
easat-10856	18	23	15074	15074	NUM
easat-10856	18	24	,	,	PUNCT
easat-10856	18	25	peru	peru	PROPN
easat-10856	18	26	.	.	PUNCT
easat-10856	19	1	jvargas@unfv.edu.pe	jvargas@unfv.edu.pe	PROPN
easat-10856	19	2	(	(	PUNCT
easat-10856	19	3	v.a.j.b	v.a.j.b	PROPN
easat-10856	19	4	.	.	PUNCT
easat-10856	19	5	)	)	PUNCT
easat-10856	19	6	.	.	PUNCT
easat-10856	20	1	abstract	abstract	ADV
easat-10856	20	2	:	:	PUNCT
easat-10856	20	3	the	the	DET
easat-10856	20	4	calculation	calculation	NOUN
easat-10856	20	5	of	of	ADP
easat-10856	20	6	bernoulli	bernoulli	PROPN
easat-10856	20	7	and	and	CCONJ
easat-10856	20	8	euler	euler	NOUN
easat-10856	20	9	numbers	number	NOUN
easat-10856	20	10	is	be	AUX
easat-10856	20	11	based	base	VERB
easat-10856	20	12	on	on	ADP
easat-10856	20	13	the	the	DET
easat-10856	20	14	fact	fact	NOUN
easat-10856	20	15	that	that	SCONJ
easat-10856	20	16	these	these	DET
easat-10856	20	17	numbers	number	NOUN
easat-10856	20	18	appear	appear	VERB
easat-10856	20	19	in	in	ADP
easat-10856	20	20	various	various	ADJ
easat-10856	20	21	mathematical	mathematical	ADJ
easat-10856	20	22	expressions	expression	NOUN
easat-10856	20	23	and	and	CCONJ
easat-10856	20	24	engineering	engineering	NOUN
easat-10856	20	25	phenomena	phenomenon	NOUN
easat-10856	20	26	.	.	PUNCT
easat-10856	21	1	although	although	SCONJ
easat-10856	21	2	computers	computer	NOUN
easat-10856	21	3	and	and	CCONJ
easat-10856	21	4	software	software	NOUN
easat-10856	21	5	programs	program	NOUN
easat-10856	21	6	can	can	AUX
easat-10856	21	7	generate	generate	VERB
easat-10856	21	8	large	large	ADJ
easat-10856	21	9	quantities	quantity	NOUN
easat-10856	21	10	of	of	ADP
easat-10856	21	11	these	these	DET
easat-10856	21	12	numbers	number	NOUN
easat-10856	21	13	,	,	PUNCT
easat-10856	21	14	only	only	ADV
easat-10856	21	15	a	a	DET
easat-10856	21	16	limited	limited	ADJ
easat-10856	21	17	number	number	NOUN
easat-10856	21	18	are	be	AUX
easat-10856	21	19	published	publish	VERB
easat-10856	21	20	in	in	ADP
easat-10856	21	21	current	current	ADJ
easat-10856	21	22	references	reference	NOUN
easat-10856	21	23	.	.	PUNCT
easat-10856	22	1	consequently	consequently	ADV
easat-10856	22	2	,	,	PUNCT
easat-10856	22	3	their	their	PRON
easat-10856	22	4	use	use	NOUN
easat-10856	22	5	often	often	ADV
easat-10856	22	6	results	result	VERB
easat-10856	22	7	in	in	ADP
easat-10856	22	8	unsatisfactory	unsatisfactory	ADJ
easat-10856	22	9	approximations	approximation	NOUN
easat-10856	22	10	.	.	PUNCT
easat-10856	23	1	the	the	DET
easat-10856	23	2	objective	objective	NOUN
easat-10856	23	3	was	be	AUX
easat-10856	23	4	to	to	PART
easat-10856	23	5	calculate	calculate	VERB
easat-10856	23	6	and	and	CCONJ
easat-10856	23	7	evaluate	evaluate	VERB
easat-10856	23	8	the	the	DET
easat-10856	23	9	first	first	ADJ
easat-10856	23	10	twenty	twenty	NUM
easat-10856	23	11	(	(	PUNCT
easat-10856	23	12	20	20	NUM
easat-10856	23	13	)	)	PUNCT
easat-10856	23	14	bernoulli	bernoulli	PROPN
easat-10856	23	15	and	and	CCONJ
easat-10856	23	16	euler	euler	NOUN
easat-10856	23	17	numbers	number	NOUN
easat-10856	23	18	,	,	PUNCT
easat-10856	23	19	subsequently	subsequently	ADV
easat-10856	23	20	applying	apply	VERB
easat-10856	23	21	them	they	PRON
easat-10856	23	22	to	to	ADP
easat-10856	23	23	mathematics	mathematic	NOUN
easat-10856	23	24	and	and	CCONJ
easat-10856	23	25	proposing	propose	VERB
easat-10856	23	26	their	their	PRON
easat-10856	23	27	use	use	NOUN
easat-10856	23	28	in	in	ADP
easat-10856	23	29	environmental	environmental	ADJ
easat-10856	23	30	engineering	engineering	NOUN
easat-10856	23	31	.	.	PUNCT
easat-10856	24	1	there	there	PRON
easat-10856	24	2	is	be	VERB
easat-10856	24	3	a	a	DET
easat-10856	24	4	wide	wide	ADJ
easat-10856	24	5	variety	variety	NOUN
easat-10856	24	6	of	of	ADP
easat-10856	24	7	relationships	relationship	NOUN
easat-10856	24	8	involving	involve	VERB
easat-10856	24	9	bernoulli	bernoulli	NOUN
easat-10856	24	10	and	and	CCONJ
easat-10856	24	11	euler	euler	NOUN
easat-10856	24	12	numbers	number	NOUN
easat-10856	24	13	that	that	PRON
easat-10856	24	14	appear	appear	VERB
easat-10856	24	15	in	in	ADP
easat-10856	24	16	several	several	ADJ
easat-10856	24	17	practical	practical	ADJ
easat-10856	24	18	mathematical	mathematical	ADJ
easat-10856	24	19	applications	application	NOUN
easat-10856	24	20	.	.	PUNCT
easat-10856	25	1	in	in	ADP
easat-10856	25	2	both	both	DET
easat-10856	25	3	cases	case	NOUN
easat-10856	25	4	,	,	PUNCT
easat-10856	25	5	the	the	DET
easat-10856	25	6	most	most	ADV
easat-10856	25	7	effective	effective	ADJ
easat-10856	25	8	relationships	relationship	NOUN
easat-10856	25	9	used	use	VERB
easat-10856	25	10	in	in	ADP
easat-10856	25	11	this	this	DET
easat-10856	25	12	study	study	NOUN
easat-10856	25	13	are	be	AUX
easat-10856	25	14	binomial	binomial	ADJ
easat-10856	25	15	expansions	expansion	NOUN
easat-10856	25	16	.	.	PUNCT
easat-10856	26	1	by	by	ADP
easat-10856	26	2	employing	employ	VERB
easat-10856	26	3	the	the	DET
easat-10856	26	4	appropriate	appropriate	ADJ
easat-10856	26	5	and	and	CCONJ
easat-10856	26	6	proposed	propose	VERB
easat-10856	26	7	equations	equation	NOUN
easat-10856	26	8	,	,	PUNCT
easat-10856	26	9	the	the	DET
easat-10856	26	10	bernoulli	bernoulli	PROPN
easat-10856	26	11	and	and	CCONJ
easat-10856	26	12	euler	euler	NOUN
easat-10856	26	13	numbers	number	NOUN
easat-10856	26	14	were	be	AUX
easat-10856	26	15	calculated	calculate	VERB
easat-10856	26	16	both	both	CCONJ
easat-10856	26	17	manually	manually	ADV
easat-10856	26	18	and	and	CCONJ
easat-10856	26	19	mechanically	mechanically	ADV
easat-10856	26	20	,	,	PUNCT
easat-10856	26	21	successfully	successfully	ADV
easat-10856	26	22	determining	determine	VERB
easat-10856	26	23	the	the	DET
easat-10856	26	24	number	number	NOUN
easat-10856	26	25	of	of	ADP
easat-10856	26	26	values	value	NOUN
easat-10856	26	27	set	set	VERB
easat-10856	26	28	as	as	ADP
easat-10856	26	29	the	the	DET
easat-10856	26	30	goal	goal	NOUN
easat-10856	26	31	.	.	PUNCT
easat-10856	27	1	finally	finally	ADV
easat-10856	27	2	,	,	PUNCT
easat-10856	27	3	bernoulli	bernoulli	PROPN
easat-10856	27	4	and	and	CCONJ
easat-10856	27	5	euler	euler	NOUN
easat-10856	27	6	numbers	number	NOUN
easat-10856	27	7	significantly	significantly	ADV
easat-10856	27	8	contribute	contribute	VERB
easat-10856	27	9	to	to	ADP
easat-10856	27	10	the	the	DET
easat-10856	27	11	estimation	estimation	NOUN
easat-10856	27	12	of	of	ADP
easat-10856	27	13	various	various	ADJ
easat-10856	27	14	processes	process	NOUN
easat-10856	27	15	and	and	CCONJ
easat-10856	27	16	mathematical	mathematical	ADJ
easat-10856	27	17	applications	application	NOUN
easat-10856	27	18	,	,	PUNCT
easat-10856	27	19	such	such	ADJ
easat-10856	27	20	as	as	ADP
easat-10856	27	21	calculating	calculate	VERB
easat-10856	27	22	the	the	DET
easat-10856	27	23	integrals	integral	NOUN
easat-10856	27	24	of	of	ADP
easat-10856	27	25	ln⁡(𝑐𝑜𝑠𝑥	ln⁡(𝑐𝑜𝑠𝑥	PROPN
easat-10856	27	26	)	)	PUNCT
easat-10856	27	27	and	and	CCONJ
easat-10856	27	28	sec⁡(𝑎𝑥	sec⁡(𝑎𝑥	NOUN
easat-10856	27	29	)	)	PUNCT
easat-10856	27	30	𝑥⁄	𝑥⁄	PROPN
easat-10856	27	31	;	;	PUNCT
easat-10856	27	32	respectively	respectively	ADV
easat-10856	27	33	.	.	PUNCT
easat-10856	28	1	keywords	keyword	NOUN
easat-10856	28	2	:	:	PUNCT
easat-10856	28	3	applications	application	NOUN
easat-10856	28	4	,	,	PUNCT
easat-10856	28	5	engineering	engineering	NOUN
easat-10856	28	6	,	,	PUNCT
easat-10856	28	7	bernoulli	bernoulli	PROPN
easat-10856	28	8	-	-	PUNCT
easat-10856	28	9	euler	euler	NOUN
easat-10856	28	10	numbers	number	NOUN
easat-10856	28	11	,	,	PUNCT
easat-10856	28	12	integrals	integral	NOUN
easat-10856	28	13	.	.	PUNCT
easat-10856	29	1	1	1	X
easat-10856	29	2	.	.	X
easat-10856	29	3	introduction	introduction	NOUN
easat-10856	29	4	benton	benton	PROPN
easat-10856	29	5	[	[	X
easat-10856	29	6	1	1	NUM
easat-10856	29	7	]	]	PUNCT
easat-10856	29	8	notes	note	VERB
easat-10856	29	9	that	that	SCONJ
easat-10856	29	10	the	the	DET
easat-10856	29	11	bernoulli	bernoulli	PROPN
easat-10856	29	12	numbers	number	NOUN
easat-10856	29	13	originate	originate	VERB
easat-10856	29	14	from	from	ADP
easat-10856	29	15	a	a	DET
easat-10856	29	16	family	family	NOUN
easat-10856	29	17	closely	closely	ADV
easat-10856	29	18	associated	associate	VERB
easat-10856	29	19	with	with	ADP
easat-10856	29	20	mathematics	mathematic	NOUN
easat-10856	29	21	and	and	CCONJ
easat-10856	29	22	engineering	engineering	NOUN
easat-10856	29	23	for	for	ADP
easat-10856	29	24	several	several	ADJ
easat-10856	29	25	decades	decade	NOUN
easat-10856	29	26	,	,	PUNCT
easat-10856	29	27	even	even	ADV
easat-10856	29	28	offering	offer	VERB
easat-10856	29	29	solutions	solution	NOUN
easat-10856	29	30	to	to	ADP
easat-10856	29	31	problems	problem	NOUN
easat-10856	29	32	in	in	ADP
easat-10856	29	33	mathematical	mathematical	ADJ
easat-10856	29	34	analysis	analysis	NOUN
easat-10856	29	35	in	in	ADP
easat-10856	29	36	the	the	DET
easat-10856	29	37	field	field	NOUN
easat-10856	29	38	of	of	ADP
easat-10856	29	39	differential	differential	ADJ
easat-10856	29	40	equations	equation	NOUN
easat-10856	29	41	and	and	CCONJ
easat-10856	29	42	their	their	PRON
easat-10856	29	43	solution	solution	NOUN
easat-10856	29	44	methods	method	NOUN
easat-10856	29	45	.	.	PUNCT
easat-10856	30	1	boyer	boyer	PROPN
easat-10856	31	1	[	[	X
easat-10856	31	2	2	2	NUM
easat-10856	31	3	]	]	PUNCT
easat-10856	31	4	mentions	mention	NOUN
easat-10856	31	5	that	that	PRON
easat-10856	31	6	euler	euler	NOUN
easat-10856	31	7	numbers	number	NOUN
easat-10856	31	8	appear	appear	VERB
easat-10856	31	9	in	in	ADP
easat-10856	31	10	the	the	DET
easat-10856	31	11	brilliant	brilliant	ADJ
easat-10856	31	12	works	work	NOUN
easat-10856	31	13	of	of	ADP
easat-10856	31	14	leonhard	leonhard	PROPN
easat-10856	31	15	euler	euler	PROPN
easat-10856	31	16	on	on	ADP
easat-10856	31	17	introduction	introduction	NOUN
easat-10856	31	18	to	to	ADP
easat-10856	31	19	analysis	analysis	NOUN
easat-10856	31	20	,	,	PUNCT
easat-10856	31	21	institutiones	institutione	VERB
easat-10856	31	22	calculi	calculi	PROPN
easat-10856	31	23	differentialis	differentialis	PROPN
easat-10856	31	24	,	,	PUNCT
easat-10856	31	25	and	and	CCONJ
easat-10856	31	26	algebra	algebra	NOUN
easat-10856	31	27	.	.	PUNCT
easat-10856	32	1	courant	courant	PROPN
easat-10856	32	2	and	and	CCONJ
easat-10856	32	3	john	john	PROPN
easat-10856	33	1	[	[	X
easat-10856	33	2	3	3	X
easat-10856	33	3	]	]	PUNCT
easat-10856	33	4	state	state	NOUN
easat-10856	33	5	that	that	SCONJ
easat-10856	33	6	the	the	DET
easat-10856	33	7	difficulty	difficulty	NOUN
easat-10856	33	8	,	,	PUNCT
easat-10856	33	9	or	or	CCONJ
easat-10856	33	10	indeed	indeed	ADV
easat-10856	33	11	the	the	DET
easat-10856	33	12	problem	problem	NOUN
easat-10856	33	13	,	,	PUNCT
easat-10856	33	14	in	in	ADP
easat-10856	33	15	determining	determine	VERB
easat-10856	33	16	bernoulli	bernoulli	PROPN
easat-10856	33	17	and	and	CCONJ
easat-10856	33	18	euler	euler	NOUN
easat-10856	33	19	numbers	number	NOUN
easat-10856	33	20	lies	lie	VERB
easat-10856	33	21	in	in	ADP
easat-10856	33	22	the	the	DET
easat-10856	33	23	fact	fact	NOUN
easat-10856	33	24	that	that	SCONJ
easat-10856	33	25	there	there	PRON
easat-10856	33	26	are	be	VERB
easat-10856	33	27	scientific	scientific	ADJ
easat-10856	33	28	processes	process	NOUN
easat-10856	33	29	and	and	CCONJ
easat-10856	33	30	phenomena	phenomenon	NOUN
easat-10856	33	31	in	in	ADP
easat-10856	33	32	engineering	engineering	NOUN
easat-10856	33	33	sciences	science	NOUN
easat-10856	33	34	where	where	SCONJ
easat-10856	33	35	functions	function	NOUN
easat-10856	33	36	strongly	strongly	ADV
easat-10856	33	37	correlate	correlate	VERB
easat-10856	33	38	with	with	ADP
easat-10856	33	39	these	these	DET
easat-10856	33	40	numbers	number	NOUN
easat-10856	33	41	and	and	CCONJ
easat-10856	33	42	must	must	AUX
easat-10856	33	43	be	be	AUX
easat-10856	33	44	analyzed	analyze	VERB
easat-10856	33	45	,	,	PUNCT
easat-10856	33	46	evaluated	evaluate	VERB
easat-10856	33	47	,	,	PUNCT
easat-10856	33	48	and	and	CCONJ
easat-10856	33	49	interpreted	interpret	VERB
easat-10856	33	50	carefully	carefully	ADV
easat-10856	33	51	and	and	CCONJ
easat-10856	33	52	meticulously	meticulously	ADV
easat-10856	33	53	.	.	PUNCT
easat-10856	34	1	despite	despite	SCONJ
easat-10856	34	2	frequent	frequent	ADJ
easat-10856	34	3	mentions	mention	NOUN
easat-10856	34	4	of	of	ADP
easat-10856	34	5	the	the	DET
easat-10856	34	6	extensive	extensive	ADJ
easat-10856	34	7	range	range	NOUN
easat-10856	34	8	of	of	ADP
easat-10856	34	9	bernoulli	bernoulli	PROPN
easat-10856	34	10	and	and	CCONJ
easat-10856	34	11	euler	euler	NOUN
easat-10856	34	12	numbers	number	NOUN
easat-10856	34	13	,	,	PUNCT
easat-10856	34	14	only	only	ADV
easat-10856	34	15	a	a	DET
easat-10856	34	16	limited	limited	ADJ
easat-10856	34	17	subset	subset	NOUN
easat-10856	34	18	is	be	AUX
easat-10856	34	19	published	publish	VERB
easat-10856	34	20	,	,	PUNCT
easat-10856	34	21	resulting	result	VERB
easat-10856	34	22	in	in	ADP
easat-10856	34	23	the	the	DET
easat-10856	34	24	use	use	NOUN
easat-10856	34	25	of	of	ADP
easat-10856	34	26	alternative	alternative	ADJ
easat-10856	34	27	solutions	solution	NOUN
easat-10856	34	28	such	such	ADJ
easat-10856	34	29	as	as	ADP
easat-10856	34	30	approximation	approximation	NOUN
easat-10856	34	31	techniques	technique	NOUN
easat-10856	34	32	.	.	PUNCT
easat-10856	35	1	in	in	ADP
easat-10856	35	2	this	this	DET
easat-10856	35	3	sense	sense	NOUN
easat-10856	35	4	,	,	PUNCT
easat-10856	35	5	their	their	PRON
easat-10856	35	6	determination	determination	NOUN
easat-10856	35	7	is	be	AUX
easat-10856	35	8	well	well	ADV
easat-10856	35	9	justified	justified	ADJ
easat-10856	35	10	.	.	PUNCT
easat-10856	36	1	benton	benton	PROPN
easat-10856	37	1	[	[	X
easat-10856	37	2	1	1	X
easat-10856	37	3	]	]	PUNCT
easat-10856	37	4	reports	report	VERB
easat-10856	37	5	that	that	SCONJ
easat-10856	37	6	https://orcid.org/0000-0002-0515-5875	https://orcid.org/0000-0002-0515-5875	PROPN
easat-10856	37	7	https://orcid.org/0000-0002-4198-5745	https://orcid.org/0000-0002-4198-5745	PROPN
easat-10856	37	8	https://orcid.org/0000-0003-3812-7579	https://orcid.org/0000-0003-3812-7579	PROPN
easat-10856	37	9	https://orcid.org/0000-0003-0053-4865	https://orcid.org/0000-0003-0053-4865	PROPN
easat-10856	37	10	https://orcid.org/0000-0001-7040-1502	https://orcid.org/0000-0001-7040-1502	PROPN
easat-10856	37	11	https://orcid.org/0000-0002-8889-0954	https://orcid.org/0000-0002-8889-0954	PROPN
easat-10856	37	12	275	275	NUM
easat-10856	37	13	edelweiss	edelweiss	PROPN
easat-10856	37	14	applied	apply	VERB
easat-10856	37	15	science	science	NOUN
easat-10856	37	16	and	and	CCONJ
easat-10856	37	17	technology	technology	NOUN
easat-10856	37	18	issn	issn	PROPN
easat-10856	37	19	:	:	PUNCT
easat-10856	37	20	2576	2576	NUM
easat-10856	37	21	-	-	SYM
easat-10856	37	22	8484	8484	NUM
easat-10856	37	23	vol	vol	NOUN
easat-10856	37	24	.	.	PROPN
easat-10856	38	1	9	9	NUM
easat-10856	38	2	,	,	PUNCT
easat-10856	38	3	no	no	INTJ
easat-10856	38	4	.	.	NOUN
easat-10856	38	5	11	11	NUM
easat-10856	38	6	:	:	PUNCT
easat-10856	38	7	274	274	NUM
easat-10856	38	8	-	-	SYM
easat-10856	38	9	288	288	NUM
easat-10856	38	10	,	,	PUNCT
easat-10856	38	11	2025	2025	NUM
easat-10856	38	12	doi	doi	NOUN
easat-10856	38	13	:	:	PUNCT
easat-10856	38	14	10.55214/2576	10.55214/2576	NUM
easat-10856	38	15	-	-	PUNCT
easat-10856	38	16	8484.v9i11.10856	8484.v9i11.10856	NUM
easat-10856	38	17	©	©	PROPN
easat-10856	38	18	2025	2025	NUM
easat-10856	38	19	by	by	ADP
easat-10856	38	20	the	the	DET
easat-10856	38	21	authors	author	NOUN
easat-10856	38	22	;	;	PUNCT
easat-10856	38	23	licensee	licensee	PROPN
easat-10856	38	24	learning	learning	PROPN
easat-10856	38	25	gate	gate	PROPN
easat-10856	38	26	jacob	jacob	PROPN
easat-10856	38	27	bernoulli	bernoulli	PROPN
easat-10856	38	28	published	publish	VERB
easat-10856	38	29	his	his	PRON
easat-10856	38	30	book	book	NOUN
easat-10856	38	31	ars	ar	NOUN
easat-10856	38	32	conjectandi	conjectandi	NOUN
easat-10856	38	33	,	,	PUNCT
easat-10856	38	34	where	where	SCONJ
easat-10856	38	35	,	,	PUNCT
easat-10856	38	36	for	for	ADP
easat-10856	38	37	the	the	DET
easat-10856	38	38	first	first	ADJ
easat-10856	38	39	and	and	CCONJ
easat-10856	38	40	only	only	ADJ
easat-10856	38	41	time	time	NOUN
easat-10856	38	42	,	,	PUNCT
easat-10856	38	43	a	a	DET
easat-10856	38	44	large	large	ADJ
easat-10856	38	45	set	set	NOUN
easat-10856	38	46	of	of	ADP
easat-10856	38	47	mathematical	mathematical	ADJ
easat-10856	38	48	expressions	expression	NOUN
easat-10856	38	49	and	and	CCONJ
easat-10856	38	50	relationships	relationship	NOUN
easat-10856	38	51	was	be	AUX
easat-10856	38	52	presented	present	VERB
easat-10856	38	53	,	,	PUNCT
easat-10856	38	54	defined	define	VERB
easat-10856	38	55	as	as	ADP
easat-10856	38	56	important	important	ADJ
easat-10856	38	57	and	and	CCONJ
easat-10856	38	58	suitable	suitable	ADJ
easat-10856	38	59	formulas	formula	NOUN
easat-10856	38	60	for	for	ADP
easat-10856	38	61	calculating	calculate	VERB
easat-10856	38	62	the	the	DET
easat-10856	38	63	sums	sum	NOUN
easat-10856	38	64	of	of	ADP
easat-10856	38	65	positive	positive	ADJ
easat-10856	38	66	integer	integer	NOUN
easat-10856	38	67	powers	power	NOUN
easat-10856	38	68	of	of	ADP
easat-10856	38	69	the	the	DET
easat-10856	38	70	first	first	ADJ
easat-10856	38	71	n	n	CCONJ
easat-10856	38	72	natural	natural	ADJ
easat-10856	38	73	numbers	number	NOUN
easat-10856	38	74	abramowitz	abramowitz	NOUN
easat-10856	38	75	and	and	CCONJ
easat-10856	38	76	stegun	stegun	PRON
easat-10856	39	1	[	[	X
easat-10856	39	2	4	4	NUM
easat-10856	39	3	]	]	X
easat-10856	39	4	further	further	ADJ
easat-10856	39	5	states	state	NOUN
easat-10856	39	6	that	that	SCONJ
easat-10856	39	7	all	all	DET
easat-10856	39	8	bernoulli	bernoulli	NOUN
easat-10856	39	9	numbers	number	NOUN
easat-10856	39	10	are	be	AUX
easat-10856	39	11	positive	positive	ADJ
easat-10856	39	12	and	and	CCONJ
easat-10856	39	13	,	,	PUNCT
easat-10856	39	14	from	from	ADP
easat-10856	39	15	the	the	DET
easat-10856	39	16	fourth	fourth	ADJ
easat-10856	39	17	onward	onward	NOUN
easat-10856	39	18	,	,	PUNCT
easat-10856	39	19	grow	grow	VERB
easat-10856	39	20	without	without	ADP
easat-10856	39	21	bound	bind	VERB
easat-10856	39	22	.	.	PUNCT
easat-10856	40	1	this	this	DET
easat-10856	40	2	growth	growth	NOUN
easat-10856	40	3	can	can	AUX
easat-10856	40	4	be	be	AUX
easat-10856	40	5	expressed	express	VERB
easat-10856	40	6	by	by	ADP
easat-10856	40	7	the	the	DET
easat-10856	40	8	relationship	relationship	NOUN
easat-10856	40	9	𝑙í𝑚	𝑙í𝑚	NOUN
easat-10856	40	10	𝑚	𝑚	NOUN
easat-10856	41	1	=	=	SYM
easat-10856	41	2	∞	∞	PROPN
easat-10856	41	3	(	(	PUNCT
easat-10856	41	4	𝐵𝑚	𝐵𝑚	NOUN
easat-10856	41	5	𝐵𝑚−1	𝐵𝑚−1	PROPN
easat-10856	41	6	)	)	PUNCT
easat-10856	42	1	=	=	SYM
easat-10856	42	2	𝑚2	𝑚2	NOUN
easat-10856	42	3	𝜋2	𝜋2	NOUN
easat-10856	42	4	.	.	PUNCT
easat-10856	43	1	according	accord	VERB
easat-10856	43	2	to	to	ADP
easat-10856	43	3	fernández	fernández	PROPN
easat-10856	43	4	[	[	X
easat-10856	43	5	5	5	NUM
easat-10856	43	6	]	]	PUNCT
easat-10856	43	7	and	and	CCONJ
easat-10856	43	8	vera	vera	NOUN
easat-10856	44	1	[	[	X
easat-10856	44	2	6	6	NUM
easat-10856	44	3	]	]	PUNCT
easat-10856	44	4	,	,	PUNCT
easat-10856	44	5	the	the	DET
easat-10856	44	6	bernoulli	bernoulli	NOUN
easat-10856	44	7	were	be	AUX
easat-10856	44	8	first	first	ADV
easat-10856	44	9	used	use	VERB
easat-10856	44	10	in	in	ADP
easat-10856	44	11	numerous	numerous	ADJ
easat-10856	44	12	practical	practical	ADJ
easat-10856	44	13	cases	case	NOUN
easat-10856	44	14	by	by	ADP
easat-10856	44	15	moivre	moivre	NOUN
easat-10856	44	16	and	and	CCONJ
easat-10856	44	17	euler	euler	PROPN
easat-10856	44	18	.	.	PUNCT
easat-10856	44	19	bronshtein	bronshtein	PROPN
easat-10856	44	20	and	and	CCONJ
easat-10856	44	21	semendiaev	semendiaev	VERB
easat-10856	45	1	[	[	X
easat-10856	45	2	7	7	X
easat-10856	45	3	]	]	PUNCT
easat-10856	45	4	indicate	indicate	VERB
easat-10856	45	5	that	that	SCONJ
easat-10856	45	6	euler	euler	NOUN
easat-10856	45	7	numbers	number	NOUN
easat-10856	45	8	are	be	AUX
easat-10856	45	9	quantitatively	quantitatively	ADV
easat-10856	45	10	considered	consider	VERB
easat-10856	45	11	and	and	CCONJ
easat-10856	45	12	generally	generally	ADV
easat-10856	45	13	related	relate	VERB
easat-10856	45	14	through	through	ADP
easat-10856	45	15	simple	simple	ADJ
easat-10856	45	16	and	and	CCONJ
easat-10856	45	17	complex	complex	ADJ
easat-10856	45	18	relationships	relationship	NOUN
easat-10856	45	19	,	,	PUNCT
easat-10856	45	20	equations	equation	NOUN
easat-10856	45	21	,	,	PUNCT
easat-10856	45	22	and	and	CCONJ
easat-10856	45	23	functions	function	NOUN
easat-10856	45	24	within	within	ADP
easat-10856	45	25	integral	integral	ADJ
easat-10856	45	26	and	and	CCONJ
easat-10856	45	27	differential	differential	ADJ
easat-10856	45	28	calculus	calculus	NOUN
easat-10856	45	29	,	,	PUNCT
easat-10856	45	30	and	and	CCONJ
easat-10856	45	31	in	in	ADP
easat-10856	45	32	phenomena	phenomenon	NOUN
easat-10856	45	33	that	that	PRON
easat-10856	45	34	interconnect	interconnect	VERB
easat-10856	45	35	these	these	DET
easat-10856	45	36	mathematical	mathematical	ADJ
easat-10856	45	37	concepts	concept	NOUN
easat-10856	45	38	.	.	PUNCT
easat-10856	46	1	bronshtein	bronshtein	PROPN
easat-10856	46	2	and	and	CCONJ
easat-10856	46	3	semendiaev	semendiaev	VERB
easat-10856	47	1	[	[	X
easat-10856	47	2	7	7	X
easat-10856	47	3	]	]	PUNCT
easat-10856	47	4	and	and	CCONJ
easat-10856	47	5	marín	marín	PROPN
easat-10856	47	6	[	[	X
easat-10856	47	7	8	8	NUM
easat-10856	47	8	]	]	PUNCT
easat-10856	47	9	mention	mention	VERB
easat-10856	47	10	that	that	SCONJ
easat-10856	47	11	both	both	CCONJ
easat-10856	47	12	bernoulli	bernoulli	PROPN
easat-10856	47	13	and	and	CCONJ
easat-10856	47	14	euler	euler	NOUN
easat-10856	47	15	numbers	number	NOUN
easat-10856	47	16	have	have	VERB
easat-10856	47	17	practical	practical	ADJ
easat-10856	47	18	applications	application	NOUN
easat-10856	47	19	in	in	ADP
easat-10856	47	20	applied	apply	VERB
easat-10856	47	21	and	and	CCONJ
easat-10856	47	22	abstract	abstract	ADJ
easat-10856	47	23	mathematical	mathematical	ADJ
easat-10856	47	24	sciences	science	NOUN
easat-10856	47	25	across	across	ADP
easat-10856	47	26	various	various	ADJ
easat-10856	47	27	fields	field	NOUN
easat-10856	47	28	of	of	ADP
easat-10856	47	29	knowledge	knowledge	NOUN
easat-10856	47	30	and	and	CCONJ
easat-10856	47	31	in	in	ADP
easat-10856	47	32	some	some	DET
easat-10856	47	33	engineering	engineering	NOUN
easat-10856	47	34	science	science	NOUN
easat-10856	47	35	applications	application	NOUN
easat-10856	47	36	.	.	PUNCT
easat-10856	48	1	one	one	NUM
easat-10856	48	2	of	of	ADP
easat-10856	48	3	the	the	DET
easat-10856	48	4	eleven	eleven	NUM
easat-10856	48	5	descendants	descendant	NOUN
easat-10856	48	6	and	and	CCONJ
easat-10856	48	7	disciples	disciple	NOUN
easat-10856	48	8	of	of	ADP
easat-10856	48	9	the	the	DET
easat-10856	48	10	famous	famous	ADJ
easat-10856	48	11	bernoulli	bernoulli	PROPN
easat-10856	48	12	family	family	NOUN
easat-10856	48	13	moved	move	VERB
easat-10856	48	14	to	to	ADP
easat-10856	48	15	basel	basel	PROPN
easat-10856	48	16	,	,	PUNCT
easat-10856	48	17	switzerland	switzerland	PROPN
easat-10856	48	18	,	,	PUNCT
easat-10856	48	19	to	to	PART
easat-10856	48	20	continue	continue	VERB
easat-10856	48	21	mathematical	mathematical	ADJ
easat-10856	48	22	training	training	NOUN
easat-10856	48	23	and	and	CCONJ
easat-10856	48	24	preserve	preserve	VERB
easat-10856	48	25	the	the	DET
easat-10856	48	26	legacy	legacy	NOUN
easat-10856	48	27	of	of	ADP
easat-10856	48	28	the	the	DET
easat-10856	48	29	bernoulli	bernoulli	PROPN
easat-10856	48	30	lineage	lineage	NOUN
easat-10856	48	31	.	.	PUNCT
easat-10856	49	1	child	child	NOUN
easat-10856	50	1	[	[	X
easat-10856	50	2	9	9	NUM
easat-10856	50	3	]	]	PUNCT
easat-10856	50	4	and	and	CCONJ
easat-10856	50	5	fernández	fernández	PROPN
easat-10856	50	6	[	[	X
easat-10856	50	7	5	5	NUM
easat-10856	50	8	]	]	PUNCT
easat-10856	50	9	mention	mention	VERB
easat-10856	50	10	that	that	SCONJ
easat-10856	50	11	,	,	PUNCT
easat-10856	50	12	due	due	ADP
easat-10856	50	13	to	to	ADP
easat-10856	50	14	the	the	DET
easat-10856	50	15	great	great	ADJ
easat-10856	50	16	importance	importance	NOUN
easat-10856	50	17	and	and	CCONJ
easat-10856	50	18	versatility	versatility	NOUN
easat-10856	50	19	of	of	ADP
easat-10856	50	20	bernoulli	bernoulli	NOUN
easat-10856	50	21	numbers	number	NOUN
easat-10856	50	22	,	,	PUNCT
easat-10856	50	23	they	they	PRON
easat-10856	50	24	were	be	AUX
easat-10856	50	25	published	publish	VERB
easat-10856	50	26	for	for	ADP
easat-10856	50	27	the	the	DET
easat-10856	50	28	first	first	ADJ
easat-10856	50	29	time	time	NOUN
easat-10856	50	30	in	in	ADP
easat-10856	50	31	1713	1713	NUM
easat-10856	50	32	,	,	PUNCT
easat-10856	50	33	in	in	ADP
easat-10856	50	34	the	the	DET
easat-10856	50	35	splendid	splendid	ADJ
easat-10856	50	36	,	,	PUNCT
easat-10856	50	37	magnificent	magnificent	ADJ
easat-10856	50	38	,	,	PUNCT
easat-10856	50	39	and	and	CCONJ
easat-10856	50	40	excellent	excellent	ADJ
easat-10856	50	41	work	work	NOUN
easat-10856	50	42	titled	title	VERB
easat-10856	50	43	ars	ar	NOUN
easat-10856	50	44	conjectandi	conjectandi	NOUN
easat-10856	50	45	,	,	PUNCT
easat-10856	50	46	after	after	SCONJ
easat-10856	50	47	a	a	DET
easat-10856	50	48	period	period	NOUN
easat-10856	50	49	of	of	ADP
easat-10856	50	50	eight	eight	NUM
easat-10856	50	51	years	year	NOUN
easat-10856	50	52	had	have	AUX
easat-10856	50	53	passed	pass	VERB
easat-10856	50	54	since	since	SCONJ
easat-10856	50	55	the	the	DET
easat-10856	50	56	death	death	NOUN
easat-10856	50	57	of	of	ADP
easat-10856	50	58	its	its	PRON
easat-10856	50	59	great	great	ADJ
easat-10856	50	60	author	author	NOUN
easat-10856	50	61	,	,	PUNCT
easat-10856	50	62	jacob	jacob	PROPN
easat-10856	50	63	bernoulli	bernoulli	PROPN
easat-10856	50	64	.	.	PUNCT
easat-10856	51	1	ruíz	ruíz	VERB
easat-10856	52	1	[	[	X
easat-10856	52	2	10	10	NUM
easat-10856	52	3	]	]	PUNCT
easat-10856	52	4	and	and	CCONJ
easat-10856	52	5	martínez	martínez	PROPN
easat-10856	52	6	et	et	PROPN
easat-10856	52	7	al	al	PROPN
easat-10856	52	8	.	.	PUNCT
easat-10856	53	1	[	[	X
easat-10856	53	2	11	11	NUM
easat-10856	53	3	]	]	PUNCT
easat-10856	53	4	indicate	indicate	VERB
easat-10856	53	5	,	,	PUNCT
easat-10856	53	6	after	after	ADP
easat-10856	53	7	a	a	DET
easat-10856	53	8	rigorous	rigorous	ADJ
easat-10856	53	9	mathematical	mathematical	ADJ
easat-10856	53	10	analysis	analysis	NOUN
easat-10856	53	11	,	,	PUNCT
easat-10856	53	12	that	that	SCONJ
easat-10856	53	13	with	with	ADP
easat-10856	53	14	respect	respect	NOUN
easat-10856	53	15	to	to	ADP
easat-10856	53	16	bernoulli	bernoulli	NOUN
easat-10856	53	17	numbers	number	NOUN
easat-10856	53	18	,	,	PUNCT
easat-10856	53	19	the	the	DET
easat-10856	53	20	frequent	frequent	ADJ
easat-10856	53	21	and	and	CCONJ
easat-10856	53	22	accurate	accurate	ADJ
easat-10856	53	23	relationships	relationship	NOUN
easat-10856	53	24	,	,	PUNCT
easat-10856	53	25	in	in	ADP
easat-10856	53	26	the	the	DET
easat-10856	53	27	form	form	NOUN
easat-10856	53	28	of	of	ADP
easat-10856	53	29	series	series	NOUN
easat-10856	53	30	,	,	PUNCT
easat-10856	53	31	are	be	AUX
easat-10856	53	32	those	those	PRON
easat-10856	53	33	that	that	PRON
easat-10856	53	34	contain	contain	VERB
easat-10856	53	35	these	these	DET
easat-10856	53	36	everyday	everyday	ADJ
easat-10856	53	37	,	,	PUNCT
easat-10856	53	38	immeasurable	immeasurable	ADJ
easat-10856	53	39	,	,	PUNCT
easat-10856	53	40	and	and	CCONJ
easat-10856	53	41	greatly	greatly	ADV
easat-10856	53	42	important	important	ADJ
easat-10856	53	43	numbers	number	NOUN
easat-10856	53	44	.	.	PUNCT
easat-10856	54	1	with	with	ADP
easat-10856	54	2	respect	respect	NOUN
easat-10856	54	3	to	to	ADP
easat-10856	54	4	bernoulli	bernoulli	NOUN
easat-10856	54	5	numbers	number	NOUN
easat-10856	54	6	,	,	PUNCT
easat-10856	54	7	the	the	DET
easat-10856	54	8	series	series	NOUN
easat-10856	54	9	-	-	PUNCT
easat-10856	54	10	form	form	NOUN
easat-10856	54	11	relationships	relationship	NOUN
easat-10856	54	12	are	be	AUX
easat-10856	54	13	those	those	PRON
easat-10856	54	14	that	that	PRON
easat-10856	54	15	contain	contain	VERB
easat-10856	54	16	these	these	DET
easat-10856	54	17	numbers	number	NOUN
easat-10856	54	18	,	,	PUNCT
easat-10856	54	19	martínez	martínez	PROPN
easat-10856	54	20	et	et	PROPN
easat-10856	54	21	al	al	PROPN
easat-10856	54	22	.	.	PUNCT
easat-10856	55	1	[	[	X
easat-10856	55	2	11	11	NUM
easat-10856	55	3	]	]	PUNCT
easat-10856	55	4	and	and	CCONJ
easat-10856	55	5	ruíz	ruíz	VERB
easat-10856	56	1	[	[	X
easat-10856	56	2	10	10	NUM
easat-10856	56	3	]	]	PUNCT
easat-10856	56	4	.	.	PUNCT
easat-10856	57	1	vega	vega	PROPN
easat-10856	57	2	-	-	PUNCT
easat-10856	57	3	calderón	calderón	PROPN
easat-10856	57	4	et	et	PROPN
easat-10856	57	5	al	al	PROPN
easat-10856	57	6	.	.	PUNCT
easat-10856	58	1	[	[	X
easat-10856	58	2	12	12	NUM
easat-10856	58	3	]	]	PUNCT
easat-10856	58	4	indicate	indicate	VERB
easat-10856	58	5	that	that	SCONJ
easat-10856	58	6	bernoulli	bernoulli	PROPN
easat-10856	58	7	numbers	number	NOUN
easat-10856	58	8	have	have	VERB
easat-10856	58	9	no	no	DET
easat-10856	58	10	direct	direct	ADJ
easat-10856	58	11	relationship	relationship	NOUN
easat-10856	58	12	with	with	ADP
easat-10856	58	13	bernoulli	bernoulli	PROPN
easat-10856	58	14	's	's	PART
easat-10856	58	15	equation	equation	NOUN
easat-10856	58	16	,	,	PUNCT
easat-10856	58	17	and	and	CCONJ
easat-10856	58	18	that	that	SCONJ
easat-10856	58	19	this	this	DET
easat-10856	58	20	equation	equation	NOUN
easat-10856	58	21	,	,	PUNCT
easat-10856	58	22	regarding	regard	VERB
easat-10856	58	23	fluid	fluid	ADJ
easat-10856	58	24	flow	flow	NOUN
easat-10856	58	25	,	,	PUNCT
easat-10856	58	26	presents	present	VERB
easat-10856	58	27	certain	certain	ADJ
easat-10856	58	28	difficulties	difficulty	NOUN
easat-10856	58	29	for	for	ADP
easat-10856	58	30	students	student	NOUN
easat-10856	58	31	of	of	ADP
easat-10856	58	32	subjects	subject	NOUN
easat-10856	58	33	that	that	PRON
easat-10856	58	34	describe	describe	VERB
easat-10856	58	35	fluid	fluid	ADJ
easat-10856	58	36	flow	flow	NOUN
easat-10856	58	37	phenomena	phenomenon	NOUN
easat-10856	58	38	or	or	CCONJ
easat-10856	58	39	behaviors	behavior	NOUN
easat-10856	58	40	of	of	ADP
easat-10856	58	41	water	water	NOUN
easat-10856	58	42	properties	property	NOUN
easat-10856	58	43	.	.	PUNCT
easat-10856	59	1	it	it	PRON
easat-10856	59	2	is	be	AUX
easat-10856	59	3	also	also	ADV
easat-10856	59	4	mentioned	mention	VERB
easat-10856	59	5	that	that	SCONJ
easat-10856	59	6	bernoulli	bernoulli	PROPN
easat-10856	59	7	numbers	number	NOUN
easat-10856	59	8	were	be	AUX
easat-10856	59	9	published	publish	VERB
easat-10856	59	10	and	and	CCONJ
easat-10856	59	11	initially	initially	ADV
easat-10856	59	12	corroborated	corroborate	VERB
easat-10856	59	13	as	as	ADP
easat-10856	59	14	validation	validation	NOUN
easat-10856	59	15	and	and	CCONJ
easat-10856	59	16	proof	proof	NOUN
easat-10856	59	17	in	in	ADP
easat-10856	59	18	the	the	DET
easat-10856	59	19	year	year	NOUN
easat-10856	59	20	1713	1713	NUM
easat-10856	59	21	,	,	PUNCT
easat-10856	59	22	in	in	ADP
easat-10856	59	23	the	the	DET
easat-10856	59	24	work	work	NOUN
easat-10856	59	25	titled	title	VERB
easat-10856	59	26	ars	ar	NOUN
easat-10856	59	27	conjectandi	conjectandi	NOUN
easat-10856	59	28	,	,	PUNCT
easat-10856	59	29	ten	ten	NUM
easat-10856	59	30	years	year	NOUN
easat-10856	59	31	after	after	ADP
easat-10856	59	32	the	the	DET
easat-10856	59	33	death	death	NOUN
easat-10856	59	34	of	of	ADP
easat-10856	59	35	its	its	PRON
easat-10856	59	36	progenitor	progenitor	NOUN
easat-10856	59	37	and	and	CCONJ
easat-10856	59	38	author	author	NOUN
easat-10856	59	39	,	,	PUNCT
easat-10856	59	40	fernández	fernández	PROPN
easat-10856	60	1	[	[	X
easat-10856	60	2	5	5	NUM
easat-10856	60	3	]	]	PUNCT
easat-10856	60	4	and	and	CCONJ
easat-10856	60	5	child	child	NOUN
easat-10856	61	1	[	[	X
easat-10856	61	2	9	9	NUM
easat-10856	61	3	]	]	PUNCT
easat-10856	61	4	.	.	PUNCT
easat-10856	62	1	vega	vega	PROPN
easat-10856	62	2	-	-	PUNCT
easat-10856	62	3	calderón	calderón	PROPN
easat-10856	62	4	et	et	PROPN
easat-10856	62	5	al	al	PROPN
easat-10856	62	6	.	.	PUNCT
easat-10856	63	1	[	[	X
easat-10856	63	2	12	12	NUM
easat-10856	63	3	]	]	PUNCT
easat-10856	63	4	mention	mention	NOUN
easat-10856	63	5	,	,	PUNCT
easat-10856	63	6	after	after	ADP
easat-10856	63	7	extensive	extensive	ADJ
easat-10856	63	8	and	and	CCONJ
easat-10856	63	9	rigorous	rigorous	ADJ
easat-10856	63	10	discussion	discussion	NOUN
easat-10856	63	11	and	and	CCONJ
easat-10856	63	12	analysis	analysis	NOUN
easat-10856	63	13	,	,	PUNCT
easat-10856	63	14	that	that	SCONJ
easat-10856	63	15	bernoulli	bernoulli	NOUN
easat-10856	63	16	numbers	number	NOUN
easat-10856	63	17	have	have	VERB
easat-10856	63	18	no	no	DET
easat-10856	63	19	direct	direct	ADJ
easat-10856	63	20	or	or	CCONJ
easat-10856	63	21	indirect	indirect	ADJ
easat-10856	63	22	relationship	relationship	NOUN
easat-10856	63	23	with	with	ADP
easat-10856	63	24	bernoulli	bernoulli	PROPN
easat-10856	63	25	's	's	PART
easat-10856	63	26	equation	equation	NOUN
easat-10856	63	27	,	,	PUNCT
easat-10856	63	28	widely	widely	ADV
easat-10856	63	29	applied	apply	VERB
easat-10856	63	30	and	and	CCONJ
easat-10856	63	31	used	use	VERB
easat-10856	63	32	in	in	ADP
easat-10856	63	33	the	the	DET
easat-10856	63	34	treatment	treatment	NOUN
easat-10856	63	35	of	of	ADP
easat-10856	63	36	phenomena	phenomenon	NOUN
easat-10856	63	37	and	and	CCONJ
easat-10856	63	38	processes	process	NOUN
easat-10856	63	39	involving	involve	VERB
easat-10856	63	40	the	the	DET
easat-10856	63	41	flow	flow	NOUN
easat-10856	63	42	of	of	ADP
easat-10856	63	43	substances	substance	NOUN
easat-10856	63	44	with	with	ADP
easat-10856	63	45	thermophysical	thermophysical	ADJ
easat-10856	63	46	properties	property	NOUN
easat-10856	63	47	analogous	analogous	ADJ
easat-10856	63	48	to	to	ADP
easat-10856	63	49	water	water	NOUN
easat-10856	63	50	,	,	PUNCT
easat-10856	63	51	and	and	CCONJ
easat-10856	63	52	the	the	DET
easat-10856	63	53	different	different	ADJ
easat-10856	63	54	relationships	relationship	NOUN
easat-10856	63	55	with	with	ADP
easat-10856	63	56	said	say	VERB
easat-10856	63	57	equation	equation	NOUN
easat-10856	63	58	,	,	PUNCT
easat-10856	63	59	regarding	regard	VERB
easat-10856	63	60	fluid	fluid	ADJ
easat-10856	63	61	flow	flow	NOUN
easat-10856	63	62	,	,	PUNCT
easat-10856	63	63	present	present	ADJ
easat-10856	63	64	certain	certain	ADJ
easat-10856	63	65	difficulties	difficulty	NOUN
easat-10856	63	66	to	to	PART
easat-10856	63	67	be	be	AUX
easat-10856	63	68	understood	understand	VERB
easat-10856	63	69	and	and	CCONJ
easat-10856	63	70	applied	apply	VERB
easat-10856	63	71	by	by	ADP
easat-10856	63	72	students	student	NOUN
easat-10856	63	73	of	of	ADP
easat-10856	63	74	subjects	subject	NOUN
easat-10856	63	75	dealing	deal	VERB
easat-10856	63	76	with	with	ADP
easat-10856	63	77	runoff	runoff	NOUN
easat-10856	63	78	processes	process	NOUN
easat-10856	63	79	and	and	CCONJ
easat-10856	63	80	describing	describe	VERB
easat-10856	63	81	fluid	fluid	NOUN
easat-10856	63	82	flow	flow	NOUN
easat-10856	63	83	phenomena	phenomenon	NOUN
easat-10856	63	84	,	,	PUNCT
easat-10856	63	85	whatever	whatever	PRON
easat-10856	63	86	these	these	PRON
easat-10856	63	87	may	may	AUX
easat-10856	63	88	be	be	AUX
easat-10856	63	89	.	.	PUNCT
easat-10856	64	1	sierra	sierra	PROPN
easat-10856	64	2	cotes	cotes	PROPN
easat-10856	64	3	and	and	CCONJ
easat-10856	64	4	gómez	gómez	NOUN
easat-10856	64	5	yance	yance	NOUN
easat-10856	65	1	[	[	X
easat-10856	65	2	13	13	NUM
easat-10856	65	3	]	]	PUNCT
easat-10856	65	4	indicate	indicate	VERB
easat-10856	65	5	that	that	SCONJ
easat-10856	65	6	,	,	PUNCT
easat-10856	65	7	when	when	SCONJ
easat-10856	65	8	studying	study	VERB
easat-10856	65	9	the	the	DET
easat-10856	65	10	behavior	behavior	NOUN
easat-10856	65	11	of	of	ADP
easat-10856	65	12	diameter	diameter	NOUN
easat-10856	65	13	,	,	PUNCT
easat-10856	65	14	jet	jet	NOUN
easat-10856	65	15	velocity	velocity	NOUN
easat-10856	65	16	,	,	PUNCT
easat-10856	65	17	and	and	CCONJ
easat-10856	65	18	flow	flow	VERB
easat-10856	65	19	with	with	ADP
easat-10856	65	20	different	different	ADJ
easat-10856	65	21	vertical	vertical	ADJ
easat-10856	65	22	discharge	discharge	NOUN
easat-10856	65	23	heights	height	NOUN
easat-10856	65	24	,	,	PUNCT
easat-10856	65	25	the	the	DET
easat-10856	65	26	process	process	NOUN
easat-10856	65	27	followed	follow	VERB
easat-10856	65	28	the	the	DET
easat-10856	65	29	trends	trend	NOUN
easat-10856	65	30	of	of	ADP
easat-10856	65	31	bernoulli	bernoulli	PROPN
easat-10856	65	32	number	number	NOUN
easat-10856	65	33	functions	function	NOUN
easat-10856	65	34	,	,	PUNCT
easat-10856	65	35	which	which	PRON
easat-10856	65	36	consisted	consist	VERB
easat-10856	65	37	of	of	ADP
easat-10856	65	38	the	the	DET
easat-10856	65	39	study	study	NOUN
easat-10856	65	40	of	of	ADP
easat-10856	65	41	flow	flow	NOUN
easat-10856	65	42	through	through	ADP
easat-10856	65	43	an	an	DET
easat-10856	65	44	orifice	orifice	NOUN
easat-10856	65	45	,	,	PUNCT
easat-10856	65	46	where	where	SCONJ
easat-10856	65	47	the	the	DET
easat-10856	65	48	velocity	velocity	NOUN
easat-10856	65	49	of	of	ADP
easat-10856	65	50	the	the	DET
easat-10856	65	51	fluid	fluid	NOUN
easat-10856	65	52	is	be	AUX
easat-10856	65	53	studied	study	VERB
easat-10856	65	54	analogous	analogous	ADJ
easat-10856	65	55	to	to	ADP
easat-10856	65	56	what	what	PRON
easat-10856	65	57	the	the	DET
easat-10856	65	58	bernoulli	bernoulli	PROPN
easat-10856	65	59	numbers	number	NOUN
easat-10856	65	60	and	and	CCONJ
easat-10856	65	61	equation	equation	NOUN
easat-10856	65	62	describe	describe	VERB
easat-10856	65	63	for	for	ADP
easat-10856	65	64	the	the	DET
easat-10856	65	65	outflow	outflow	NOUN
easat-10856	65	66	of	of	ADP
easat-10856	65	67	regulatory	regulatory	ADJ
easat-10856	65	68	boxes	box	NOUN
easat-10856	65	69	.	.	PUNCT
easat-10856	66	1	huancapaza	huancapaza	PROPN
easat-10856	67	1	[	[	X
easat-10856	67	2	14	14	NUM
easat-10856	67	3	]	]	PUNCT
easat-10856	67	4	indicates	indicate	VERB
easat-10856	67	5	that	that	SCONJ
easat-10856	67	6	his	his	PRON
easat-10856	67	7	objective	objective	NOUN
easat-10856	67	8	was	be	AUX
easat-10856	67	9	to	to	PART
easat-10856	67	10	determine	determine	VERB
easat-10856	67	11	which	which	DET
easat-10856	67	12	numerical	numerical	ADJ
easat-10856	67	13	method	method	NOUN
easat-10856	67	14	is	be	AUX
easat-10856	67	15	most	most	ADV
easat-10856	67	16	effective	effective	ADJ
easat-10856	67	17	for	for	ADP
easat-10856	67	18	obtaining	obtain	VERB
easat-10856	67	19	the	the	DET
easat-10856	67	20	dynamic	dynamic	ADJ
easat-10856	67	21	response	response	NOUN
easat-10856	67	22	of	of	ADP
easat-10856	67	23	multi	multi	ADJ
easat-10856	67	24	-	-	NOUN
easat-10856	67	25	degree	degree	NOUN
easat-10856	67	26	-	-	PUNCT
easat-10856	67	27	of	of	ADP
easat-10856	67	28	-	-	PUNCT
easat-10856	67	29	freedom	freedom	NOUN
easat-10856	67	30	structures	structure	NOUN
easat-10856	67	31	,	,	PUNCT
easat-10856	67	32	resulting	result	VERB
easat-10856	67	33	in	in	ADP
easat-10856	67	34	euler	euler	NOUN
easat-10856	67	35	numbers	number	NOUN
easat-10856	67	36	describing	describe	VERB
easat-10856	67	37	a	a	DET
easat-10856	67	38	gaussian	gaussian	ADJ
easat-10856	67	39	behavior	behavior	NOUN
easat-10856	67	40	with	with	ADP
easat-10856	67	41	increasing	increase	VERB
easat-10856	67	42	time	time	NOUN
easat-10856	67	43	.	.	PUNCT
easat-10856	68	1	torres	torre	VERB
easat-10856	68	2	[	[	X
easat-10856	68	3	15	15	NUM
easat-10856	68	4	]	]	X
easat-10856	68	5	states	state	NOUN
easat-10856	68	6	in	in	ADP
easat-10856	68	7	his	his	PRON
easat-10856	68	8	research	research	NOUN
easat-10856	68	9	,	,	PUNCT
easat-10856	68	10	"	"	PUNCT
easat-10856	68	11	generation	generation	NOUN
easat-10856	68	12	of	of	ADP
easat-10856	68	13	a	a	DET
easat-10856	68	14	mathematical	mathematical	ADJ
easat-10856	68	15	model	model	NOUN
easat-10856	68	16	for	for	ADP
easat-10856	68	17	the	the	DET
easat-10856	68	18	study	study	NOUN
easat-10856	68	19	of	of	ADP
easat-10856	68	20	reservoir	reservoir	PROPN
easat-10856	68	21	operation	operation	NOUN
easat-10856	68	22	with	with	ADP
easat-10856	68	23	a	a	DET
easat-10856	68	24	multipurpose	multipurpose	NOUN
easat-10856	68	25	approach	approach	NOUN
easat-10856	68	26	,	,	PUNCT
easat-10856	68	27	"	"	PUNCT
easat-10856	68	28	where	where	SCONJ
easat-10856	68	29	the	the	DET
easat-10856	68	30	objective	objective	NOUN
easat-10856	68	31	was	be	AUX
easat-10856	68	32	the	the	DET
easat-10856	68	33	development	development	NOUN
easat-10856	68	34	of	of	ADP
easat-10856	68	35	a	a	DET
easat-10856	68	36	mathematical	mathematical	ADJ
easat-10856	68	37	model	model	NOUN
easat-10856	68	38	using	use	VERB
easat-10856	68	39	the	the	DET
easat-10856	68	40	principles	principle	NOUN
easat-10856	68	41	of	of	ADP
easat-10856	68	42	normal	normal	ADJ
easat-10856	68	43	distribution	distribution	NOUN
easat-10856	68	44	mechanics	mechanic	NOUN
easat-10856	68	45	to	to	PART
easat-10856	68	46	simulate	simulate	VERB
easat-10856	68	47	reservoir	reservoir	NOUN
easat-10856	68	48	operations	operation	NOUN
easat-10856	68	49	,	,	PUNCT
easat-10856	68	50	resulting	result	VERB
easat-10856	68	51	in	in	ADP
easat-10856	68	52	euler	euler	NOUN
easat-10856	68	53	numbers	number	NOUN
easat-10856	68	54	and	and	CCONJ
easat-10856	68	55	their	their	PRON
easat-10856	68	56	method	method	NOUN
easat-10856	68	57	being	be	AUX
easat-10856	68	58	the	the	DET
easat-10856	68	59	simplest	simple	ADJ
easat-10856	68	60	numerical	numerical	ADJ
easat-10856	68	61	scheme	scheme	NOUN
easat-10856	68	62	.	.	PUNCT
easat-10856	69	1	zamora	zamora	PROPN
easat-10856	69	2	et	et	PROPN
easat-10856	69	3	al	al	PROPN
easat-10856	69	4	.	.	PUNCT
easat-10856	70	1	[	[	X
easat-10856	70	2	16	16	NUM
easat-10856	70	3	]	]	PUNCT
easat-10856	70	4	argue	argue	VERB
easat-10856	70	5	that	that	SCONJ
easat-10856	70	6	bernoulli	bernoulli	NOUN
easat-10856	70	7	numbers	number	NOUN
easat-10856	70	8	represent	represent	VERB
easat-10856	70	9	asymptotic	asymptotic	ADJ
easat-10856	70	10	decay	decay	NOUN
easat-10856	70	11	processes	process	NOUN
easat-10856	70	12	regarding	regard	VERB
easat-10856	70	13	the	the	DET
easat-10856	70	14	conservation	conservation	NOUN
easat-10856	70	15	of	of	ADP
easat-10856	70	16	mechanical	mechanical	ADJ
easat-10856	70	17	energy	energy	NOUN
easat-10856	70	18	,	,	PUNCT
easat-10856	70	19	allowing	allow	VERB
easat-10856	70	20	analytical	analytical	ADJ
easat-10856	70	21	and	and	CCONJ
easat-10856	70	22	experimental	experimental	ADJ
easat-10856	70	23	methods	method	NOUN
easat-10856	70	24	to	to	PART
easat-10856	70	25	determine	determine	VERB
easat-10856	70	26	different	different	ADJ
easat-10856	70	27	parameters	parameter	NOUN
easat-10856	70	28	such	such	ADJ
easat-10856	70	29	as	as	ADP
easat-10856	70	30	tank	tank	NOUN
easat-10856	70	31	emptying	emptying	NOUN
easat-10856	70	32	time	time	NOUN
easat-10856	70	33	,	,	PUNCT
easat-10856	70	34	pipe	pipe	NOUN
easat-10856	70	35	area	area	NOUN
easat-10856	70	36	,	,	PUNCT
easat-10856	70	37	flow	flow	NOUN
easat-10856	70	38	velocity	velocity	NOUN
easat-10856	70	39	,	,	PUNCT
easat-10856	70	40	and	and	CCONJ
easat-10856	70	41	velocity	velocity	NOUN
easat-10856	70	42	head	head	NOUN
easat-10856	70	43	.	.	PUNCT
easat-10856	71	1	estela	estela	PROPN
easat-10856	71	2	urbina	urbina	PROPN
easat-10856	71	3	et	et	PROPN
easat-10856	71	4	al	al	PROPN
easat-10856	71	5	.	.	PUNCT
easat-10856	72	1	[	[	X
easat-10856	72	2	17	17	NUM
easat-10856	72	3	]	]	PUNCT
easat-10856	72	4	indicate	indicate	VERB
easat-10856	72	5	that	that	SCONJ
easat-10856	72	6	bernoulli	bernoulli	PROPN
easat-10856	72	7	numbers	number	NOUN
easat-10856	72	8	are	be	AUX
easat-10856	72	9	very	very	ADV
easat-10856	72	10	important	important	ADJ
easat-10856	72	11	in	in	ADP
easat-10856	72	12	asymptotic	asymptotic	ADJ
easat-10856	72	13	decay	decay	NOUN
easat-10856	72	14	processes	process	NOUN
easat-10856	72	15	,	,	PUNCT
easat-10856	72	16	276	276	NUM
easat-10856	72	17	edelweiss	edelweiss	PROPN
easat-10856	72	18	applied	apply	VERB
easat-10856	72	19	science	science	NOUN
easat-10856	72	20	and	and	CCONJ
easat-10856	72	21	technology	technology	NOUN
easat-10856	72	22	issn	issn	PROPN
easat-10856	72	23	:	:	PUNCT
easat-10856	72	24	2576	2576	NUM
easat-10856	72	25	-	-	SYM
easat-10856	72	26	8484	8484	NUM
easat-10856	72	27	vol	vol	NOUN
easat-10856	72	28	.	.	PROPN
easat-10856	73	1	9	9	NUM
easat-10856	73	2	,	,	PUNCT
easat-10856	73	3	no	no	INTJ
easat-10856	73	4	.	.	NOUN
easat-10856	73	5	11	11	NUM
easat-10856	73	6	:	:	PUNCT
easat-10856	73	7	274	274	NUM
easat-10856	73	8	-	-	SYM
easat-10856	73	9	288	288	NUM
easat-10856	73	10	,	,	PUNCT
easat-10856	73	11	2025	2025	NUM
easat-10856	73	12	doi	doi	NOUN
easat-10856	73	13	:	:	PUNCT
easat-10856	73	14	10.55214/2576	10.55214/2576	NUM
easat-10856	73	15	-	-	PUNCT
easat-10856	73	16	8484.v9i11.10856	8484.v9i11.10856	NUM
easat-10856	73	17	©	©	PROPN
easat-10856	73	18	2025	2025	NUM
easat-10856	73	19	by	by	ADP
easat-10856	73	20	the	the	DET
easat-10856	73	21	authors	author	NOUN
easat-10856	73	22	;	;	PUNCT
easat-10856	73	23	licensee	licensee	PROPN
easat-10856	73	24	learning	learning	NOUN
easat-10856	73	25	gate	gate	NOUN
easat-10856	73	26	being	be	AUX
easat-10856	73	27	an	an	DET
easat-10856	73	28	adequate	adequate	ADJ
easat-10856	73	29	strategy	strategy	NOUN
easat-10856	73	30	to	to	PART
easat-10856	73	31	solve	solve	VERB
easat-10856	73	32	problematic	problematic	ADJ
easat-10856	73	33	situations	situation	NOUN
easat-10856	73	34	of	of	ADP
easat-10856	73	35	complex	complex	ADJ
easat-10856	73	36	short	short	ADJ
easat-10856	73	37	transitions	transition	NOUN
easat-10856	73	38	,	,	PUNCT
easat-10856	73	39	considering	consider	VERB
easat-10856	73	40	that	that	SCONJ
easat-10856	73	41	friction	friction	NOUN
easat-10856	73	42	or	or	CCONJ
easat-10856	73	43	drag	drag	NOUN
easat-10856	73	44	losses	loss	NOUN
easat-10856	73	45	are	be	AUX
easat-10856	73	46	negligible	negligible	ADJ
easat-10856	73	47	.	.	PUNCT
easat-10856	74	1	estela	estela	PROPN
easat-10856	74	2	urbina	urbina	PROPN
easat-10856	74	3	et	et	PROPN
easat-10856	74	4	al	al	PROPN
easat-10856	74	5	.	.	PUNCT
easat-10856	75	1	[	[	X
easat-10856	75	2	17	17	NUM
easat-10856	75	3	]	]	PUNCT
easat-10856	75	4	affirm	affirm	NOUN
easat-10856	75	5	that	that	SCONJ
easat-10856	75	6	bernoulli	bernoulli	PROPN
easat-10856	75	7	numbers	number	NOUN
easat-10856	75	8	are	be	AUX
easat-10856	75	9	very	very	ADV
easat-10856	75	10	important	important	ADJ
easat-10856	75	11	in	in	ADP
easat-10856	75	12	asymptotic	asymptotic	ADJ
easat-10856	75	13	decay	decay	NOUN
easat-10856	75	14	processes	process	NOUN
easat-10856	75	15	,	,	PUNCT
easat-10856	75	16	being	be	AUX
easat-10856	75	17	an	an	DET
easat-10856	75	18	adequate	adequate	ADJ
easat-10856	75	19	strategy	strategy	NOUN
easat-10856	75	20	to	to	PART
easat-10856	75	21	solve	solve	VERB
easat-10856	75	22	problematic	problematic	ADJ
easat-10856	75	23	situations	situation	NOUN
easat-10856	75	24	of	of	ADP
easat-10856	75	25	complex	complex	ADJ
easat-10856	75	26	short	short	ADJ
easat-10856	75	27	transitions	transition	NOUN
easat-10856	75	28	,	,	PUNCT
easat-10856	75	29	considering	consider	VERB
easat-10856	75	30	that	that	SCONJ
easat-10856	75	31	friction	friction	NOUN
easat-10856	75	32	or	or	CCONJ
easat-10856	75	33	drag	drag	NOUN
easat-10856	75	34	losses	loss	NOUN
easat-10856	75	35	are	be	AUX
easat-10856	75	36	negligible	negligible	ADJ
easat-10856	75	37	.	.	PUNCT
easat-10856	76	1	marín	marín	NOUN
easat-10856	76	2	-	-	PUNCT
easat-10856	76	3	machuca	machuca	NOUN
easat-10856	76	4	et	et	PROPN
easat-10856	76	5	al	al	PROPN
easat-10856	76	6	.	.	PUNCT
easat-10856	77	1	[	[	X
easat-10856	77	2	18	18	NUM
easat-10856	77	3	]	]	PUNCT
easat-10856	77	4	mention	mention	NOUN
easat-10856	77	5	in	in	ADP
easat-10856	77	6	their	their	PRON
easat-10856	77	7	research	research	NOUN
easat-10856	77	8	"	"	PUNCT
easat-10856	77	9	quantification	quantification	NOUN
easat-10856	77	10	of	of	ADP
easat-10856	77	11	the	the	DET
easat-10856	77	12	alkalinity	alkalinity	NOUN
easat-10856	77	13	of	of	ADP
easat-10856	77	14	natural	natural	ADJ
easat-10856	77	15	water	water	NOUN
easat-10856	77	16	applying	apply	VERB
easat-10856	77	17	bernoulli	bernoulli	NOUN
easat-10856	77	18	numbers	number	NOUN
easat-10856	77	19	and	and	CCONJ
easat-10856	77	20	simpson	simpson	PROPN
easat-10856	77	21	's	's	PART
easat-10856	77	22	approximate	approximate	ADJ
easat-10856	77	23	integral	integral	ADJ
easat-10856	77	24	"	"	PUNCT
easat-10856	77	25	that	that	SCONJ
easat-10856	77	26	the	the	DET
easat-10856	77	27	purpose	purpose	NOUN
easat-10856	77	28	was	be	AUX
easat-10856	77	29	to	to	PART
easat-10856	77	30	calculate	calculate	VERB
easat-10856	77	31	the	the	DET
easat-10856	77	32	first	first	ADJ
easat-10856	77	33	twenty	twenty	NUM
easat-10856	77	34	bernoulli	bernoulli	NOUN
easat-10856	77	35	numbers	number	NOUN
easat-10856	77	36	and	and	CCONJ
easat-10856	77	37	apply	apply	VERB
easat-10856	77	38	them	they	PRON
easat-10856	77	39	to	to	ADP
easat-10856	77	40	mathematics	mathematics	PROPN
easat-10856	77	41	(	(	PUNCT
easat-10856	77	42	∫	∫	PROPN
easat-10856	77	43	ln(𝑐𝑜𝑠𝑥	ln(𝑐𝑜𝑠𝑥	PROPN
easat-10856	77	44	)	)	PUNCT
easat-10856	77	45	𝑑𝑥	𝑑𝑥	NOUN
easat-10856	77	46	)	)	PUNCT
easat-10856	77	47	and	and	CCONJ
easat-10856	77	48	to	to	ADP
easat-10856	77	49	environmental	environmental	ADJ
easat-10856	77	50	engineering	engineering	NOUN
easat-10856	77	51	,	,	PUNCT
easat-10856	77	52	quantifying	quantify	VERB
easat-10856	77	53	the	the	DET
easat-10856	77	54	alkalinity	alkalinity	NOUN
easat-10856	77	55	of	of	ADP
easat-10856	77	56	natural	natural	ADJ
easat-10856	77	57	water	water	NOUN
easat-10856	77	58	in	in	ADP
easat-10856	77	59	the	the	DET
easat-10856	77	60	form	form	NOUN
easat-10856	77	61	of	of	ADP
easat-10856	77	62	calcium	calcium	NOUN
easat-10856	77	63	carbonate	carbonate	NOUN
easat-10856	77	64	(	(	PUNCT
easat-10856	77	65	𝐶𝑎𝐶𝑂3)(𝑚𝑔/𝑙	𝐶𝑎𝐶𝑂3)(𝑚𝑔/𝑙	PROPN
easat-10856	77	66	)	)	PUNCT
easat-10856	77	67	,	,	PUNCT
easat-10856	77	68	measuring	measure	VERB
easat-10856	77	69	the	the	DET
easat-10856	77	70	carbon	carbon	NOUN
easat-10856	77	71	dioxide	dioxide	NOUN
easat-10856	77	72	(	(	PUNCT
easat-10856	77	73	𝐶𝑂2	𝐶𝑂2	PROPN
easat-10856	77	74	)	)	PUNCT
easat-10856	77	75	;	;	PUNCT
easat-10856	77	76	that	that	SCONJ
easat-10856	77	77	there	there	PRON
easat-10856	77	78	exists	exist	VERB
easat-10856	77	79	,	,	PUNCT
easat-10856	77	80	with	with	ADP
easat-10856	77	81	certainty	certainty	NOUN
easat-10856	77	82	and	and	CCONJ
easat-10856	77	83	specifically	specifically	ADV
easat-10856	77	84	,	,	PUNCT
easat-10856	77	85	a	a	DET
easat-10856	77	86	great	great	ADJ
easat-10856	77	87	variety	variety	NOUN
easat-10856	77	88	of	of	ADP
easat-10856	77	89	mathematical	mathematical	ADJ
easat-10856	77	90	relationships	relationship	NOUN
easat-10856	77	91	and	and	CCONJ
easat-10856	77	92	expressions	expression	NOUN
easat-10856	77	93	that	that	PRON
easat-10856	77	94	include	include	VERB
easat-10856	77	95	bernoulli	bernoulli	NOUN
easat-10856	77	96	numbers	number	NOUN
easat-10856	77	97	,	,	PUNCT
easat-10856	77	98	appearing	appear	VERB
easat-10856	77	99	in	in	ADP
easat-10856	77	100	various	various	ADJ
easat-10856	77	101	practical	practical	ADJ
easat-10856	77	102	applications	application	NOUN
easat-10856	77	103	of	of	ADP
easat-10856	77	104	mathematics	mathematic	NOUN
easat-10856	77	105	;	;	PUNCT
easat-10856	77	106	that	that	SCONJ
easat-10856	77	107	the	the	DET
easat-10856	77	108	best	good	ADJ
easat-10856	77	109	relationships	relationship	NOUN
easat-10856	77	110	used	use	VERB
easat-10856	77	111	on	on	ADP
easat-10856	77	112	this	this	DET
easat-10856	77	113	occasion	occasion	NOUN
easat-10856	77	114	are	be	AUX
easat-10856	77	115	binomial	binomial	ADJ
easat-10856	77	116	expansions	expansion	NOUN
easat-10856	77	117	;	;	PUNCT
easat-10856	77	118	that	that	SCONJ
easat-10856	77	119	by	by	ADP
easat-10856	77	120	applying	apply	VERB
easat-10856	77	121	the	the	DET
easat-10856	77	122	proposed	propose	VERB
easat-10856	77	123	and	and	CCONJ
easat-10856	77	124	suitable	suitable	ADJ
easat-10856	77	125	equations	equation	NOUN
easat-10856	77	126	,	,	PUNCT
easat-10856	77	127	bernoulli	bernoulli	NOUN
easat-10856	77	128	numbers	number	NOUN
easat-10856	77	129	were	be	AUX
easat-10856	77	130	satisfactorily	satisfactorily	ADV
easat-10856	77	131	calculated	calculate	VERB
easat-10856	77	132	,	,	PUNCT
easat-10856	77	133	reaching	reach	VERB
easat-10856	77	134	the	the	DET
easat-10856	77	135	number	number	NOUN
easat-10856	77	136	of	of	ADP
easat-10856	77	137	values	value	NOUN
easat-10856	77	138	set	set	VERB
easat-10856	77	139	as	as	ADP
easat-10856	77	140	the	the	DET
easat-10856	77	141	objective	objective	NOUN
easat-10856	77	142	,	,	PUNCT
easat-10856	77	143	and	and	CCONJ
easat-10856	77	144	finally	finally	ADV
easat-10856	77	145	,	,	PUNCT
easat-10856	77	146	bernoulli	bernoulli	NOUN
easat-10856	77	147	numbers	number	NOUN
easat-10856	77	148	decisively	decisively	ADV
easat-10856	77	149	and	and	CCONJ
easat-10856	77	150	significantly	significantly	ADV
easat-10856	77	151	contribute	contribute	VERB
easat-10856	77	152	to	to	ADP
easat-10856	77	153	mathematical	mathematical	ADJ
easat-10856	77	154	processes	process	NOUN
easat-10856	77	155	such	such	ADJ
easat-10856	77	156	as	as	ADP
easat-10856	77	157	calculating	calculate	VERB
easat-10856	77	158	integrals	integral	NOUN
easat-10856	77	159	of	of	ADP
easat-10856	77	160	the	the	DET
easat-10856	77	161	type	type	NOUN
easat-10856	77	162	ln⁡(𝑐𝑜𝑠𝑥	ln⁡(𝑐𝑜𝑠𝑥	PROPN
easat-10856	77	163	)	)	PUNCT
easat-10856	77	164	,	,	PUNCT
easat-10856	77	165	as	as	ADV
easat-10856	77	166	well	well	ADV
easat-10856	77	167	as	as	ADP
easat-10856	77	168	applications	application	NOUN
easat-10856	77	169	in	in	ADP
easat-10856	77	170	environmental	environmental	ADJ
easat-10856	77	171	engineering	engineering	NOUN
easat-10856	77	172	,	,	PUNCT
easat-10856	77	173	evaluating	evaluate	VERB
easat-10856	77	174	water	water	NOUN
easat-10856	77	175	alkalinity	alkalinity	NOUN
easat-10856	77	176	as	as	ADP
easat-10856	77	177	calcium	calcium	NOUN
easat-10856	77	178	carbonate	carbonate	NOUN
easat-10856	77	179	(	(	PUNCT
easat-10856	77	180	𝐶𝑎𝐶𝑂3	𝐶𝑎𝐶𝑂3	PROPN
easat-10856	77	181	)	)	PUNCT
easat-10856	77	182	.	.	PUNCT
easat-10856	78	1	child	child	NOUN
easat-10856	79	1	[	[	X
easat-10856	79	2	9	9	NUM
easat-10856	79	3	]	]	PUNCT
easat-10856	79	4	mention	mention	VERB
easat-10856	79	5	that	that	SCONJ
easat-10856	79	6	the	the	DET
easat-10856	79	7	anecdote	anecdote	NOUN
easat-10856	79	8	told	tell	VERB
easat-10856	79	9	by	by	ADP
easat-10856	79	10	gauss	gauss	PROPN
easat-10856	79	11	(	(	PUNCT
easat-10856	79	12	1777–1855	1777–1855	NUM
easat-10856	79	13	)	)	PUNCT
easat-10856	79	14	about	about	ADP
easat-10856	79	15	his	his	PRON
easat-10856	79	16	early	early	ADJ
easat-10856	79	17	years	year	NOUN
easat-10856	79	18	in	in	ADP
easat-10856	79	19	primary	primary	ADJ
easat-10856	79	20	school	school	NOUN
easat-10856	79	21	is	be	AUX
easat-10856	79	22	well	well	ADV
easat-10856	79	23	known	know	VERB
easat-10856	79	24	,	,	PUNCT
easat-10856	79	25	when	when	SCONJ
easat-10856	79	26	he	he	PRON
easat-10856	79	27	impressed	impress	VERB
easat-10856	79	28	his	his	PRON
easat-10856	79	29	bad	bad	ADV
easat-10856	79	30	-	-	PUNCT
easat-10856	79	31	tempered	temper	VERB
easat-10856	79	32	mathematics	mathematics	NOUN
easat-10856	79	33	teacher	teacher	NOUN
easat-10856	79	34	with	with	ADP
easat-10856	79	35	a	a	DET
easat-10856	79	36	very	very	ADV
easat-10856	79	37	simple	simple	ADJ
easat-10856	79	38	but	but	CCONJ
easat-10856	79	39	ingenious	ingenious	ADJ
easat-10856	79	40	procedure	procedure	NOUN
easat-10856	79	41	for	for	ADP
easat-10856	79	42	summing	sum	VERB
easat-10856	79	43	the	the	DET
easat-10856	79	44	first	first	ADJ
easat-10856	79	45	100	100	NUM
easat-10856	79	46	terms	term	NOUN
easat-10856	79	47	of	of	ADP
easat-10856	79	48	an	an	DET
easat-10856	79	49	arithmetic	arithmetic	ADJ
easat-10856	79	50	progression	progression	NOUN
easat-10856	79	51	;	;	PUNCT
easat-10856	79	52	however	however	ADV
easat-10856	79	53	,	,	PUNCT
easat-10856	79	54	it	it	PRON
easat-10856	79	55	is	be	AUX
easat-10856	79	56	not	not	PART
easat-10856	79	57	as	as	ADV
easat-10856	79	58	well	well	ADV
easat-10856	79	59	known	know	VERB
easat-10856	79	60	that	that	SCONJ
easat-10856	79	61	a	a	DET
easat-10856	79	62	hundred	hundred	NUM
easat-10856	79	63	years	year	NOUN
easat-10856	79	64	earlier	early	ADV
easat-10856	79	65	,	,	PUNCT
easat-10856	79	66	one	one	NUM
easat-10856	79	67	of	of	ADP
easat-10856	79	68	the	the	DET
easat-10856	79	69	most	most	ADV
easat-10856	79	70	outstanding	outstanding	ADJ
easat-10856	79	71	mathematicians	mathematician	NOUN
easat-10856	79	72	of	of	ADP
easat-10856	79	73	the	the	DET
easat-10856	79	74	bernoulli	bernoulli	PROPN
easat-10856	79	75	family	family	NOUN
easat-10856	79	76	,	,	PUNCT
easat-10856	79	77	bernoulli	bernoulli	PROPN
easat-10856	80	1	[	[	X
easat-10856	80	2	19	19	NUM
easat-10856	80	3	]	]	PUNCT
easat-10856	80	4	left	leave	VERB
easat-10856	80	5	for	for	ADP
easat-10856	80	6	posterity	posterity	NOUN
easat-10856	80	7	an	an	DET
easat-10856	80	8	excellent	excellent	ADJ
easat-10856	80	9	,	,	PUNCT
easat-10856	80	10	outstanding	outstanding	ADJ
easat-10856	80	11	,	,	PUNCT
easat-10856	80	12	and	and	CCONJ
easat-10856	80	13	brilliant	brilliant	ADJ
easat-10856	80	14	work	work	NOUN
easat-10856	80	15	,	,	PUNCT
easat-10856	80	16	which	which	PRON
easat-10856	80	17	could	could	AUX
easat-10856	80	18	well	well	ADV
easat-10856	80	19	be	be	AUX
easat-10856	80	20	considered	consider	VERB
easat-10856	80	21	the	the	DET
easat-10856	80	22	first	first	ADJ
easat-10856	80	23	great	great	ADJ
easat-10856	80	24	treatise	treatise	NOUN
easat-10856	80	25	on	on	ADP
easat-10856	80	26	combinatorics	combinatoric	NOUN
easat-10856	80	27	and	and	CCONJ
easat-10856	80	28	probability	probability	NOUN
easat-10856	80	29	:	:	PUNCT
easat-10856	80	30	bernoulli	bernoulli	PROPN
easat-10856	81	1	[	[	X
easat-10856	81	2	19	19	NUM
easat-10856	81	3	]	]	PUNCT
easat-10856	81	4	where	where	SCONJ
easat-10856	81	5	in	in	ADP
easat-10856	81	6	this	this	DET
easat-10856	81	7	brilliant	brilliant	ADJ
easat-10856	81	8	work	work	NOUN
easat-10856	81	9	,	,	PUNCT
easat-10856	81	10	highly	highly	ADV
easat-10856	81	11	recommended	recommended	ADJ
easat-10856	81	12	reading	reading	NOUN
easat-10856	81	13	,	,	PUNCT
easat-10856	81	14	there	there	PRON
easat-10856	81	15	appears	appear	VERB
easat-10856	81	16	a	a	DET
easat-10856	81	17	result	result	NOUN
easat-10856	81	18	far	far	ADV
easat-10856	81	19	superior	superior	ADJ
easat-10856	81	20	to	to	ADP
easat-10856	81	21	gauss	gauss	NOUN
easat-10856	81	22	's	's	PART
easat-10856	81	23	sum	sum	NOUN
easat-10856	81	24	,	,	PUNCT
easat-10856	81	25	asking	ask	VERB
easat-10856	81	26	:	:	PUNCT
easat-10856	81	27	what	what	PRON
easat-10856	81	28	do	do	AUX
easat-10856	81	29	you	you	PRON
easat-10856	81	30	think	think	VERB
easat-10856	81	31	if	if	SCONJ
easat-10856	81	32	we	we	PRON
easat-10856	81	33	calculate	calculate	VERB
easat-10856	81	34	the	the	DET
easat-10856	81	35	sum	sum	NOUN
easat-10856	81	36	of	of	ADP
easat-10856	81	37	the	the	DET
easat-10856	81	38	first	first	ADJ
easat-10856	81	39	1000	1000	NUM
easat-10856	81	40	powers	power	NOUN
easat-10856	81	41	of	of	ADP
easat-10856	81	42	10	10	NUM
easat-10856	81	43	of	of	ADP
easat-10856	81	44	the	the	DET
easat-10856	81	45	natural	natural	ADJ
easat-10856	81	46	numbers	number	NOUN
easat-10856	81	47	?	?	PUNCT
easat-10856	82	1	but	but	CCONJ
easat-10856	82	2	of	of	ADP
easat-10856	82	3	course	course	NOUN
easat-10856	82	4	,	,	PUNCT
easat-10856	82	5	with	with	SCONJ
easat-10856	82	6	pencil	pencil	NOUN
easat-10856	82	7	and	and	CCONJ
easat-10856	82	8	paper	paper	NOUN
easat-10856	82	9	,	,	PUNCT
easat-10856	82	10	or	or	CCONJ
easat-10856	82	11	quill	quill	NOUN
easat-10856	82	12	,	,	PUNCT
easat-10856	82	13	which	which	PRON
easat-10856	82	14	were	be	AUX
easat-10856	82	15	the	the	DET
easat-10856	82	16	tools	tool	NOUN
easat-10856	82	17	our	our	PRON
easat-10856	82	18	dear	dear	ADJ
easat-10856	82	19	friend	friend	NOUN
easat-10856	82	20	,	,	PUNCT
easat-10856	82	21	mathematician	mathematician	NOUN
easat-10856	82	22	,	,	PUNCT
easat-10856	82	23	and	and	CCONJ
easat-10856	82	24	teacher	teacher	NOUN
easat-10856	82	25	bernoulli	bernoulli	PROPN
easat-10856	82	26	had	have	VERB
easat-10856	82	27	at	at	ADP
easat-10856	82	28	that	that	DET
easat-10856	82	29	time	time	NOUN
easat-10856	82	30	,	,	PUNCT
easat-10856	82	31	kindly	kindly	ADV
easat-10856	82	32	presenting	present	VERB
easat-10856	82	33	in	in	ADP
easat-10856	82	34	this	this	DET
easat-10856	82	35	article	article	NOUN
easat-10856	82	36	some	some	PRON
easat-10856	82	37	of	of	ADP
easat-10856	82	38	the	the	DET
easat-10856	82	39	essential	essential	ADJ
easat-10856	82	40	and	and	CCONJ
easat-10856	82	41	fundamental	fundamental	ADJ
easat-10856	82	42	ideas	idea	NOUN
easat-10856	82	43	that	that	PRON
easat-10856	82	44	led	lead	VERB
easat-10856	82	45	him	he	PRON
easat-10856	82	46	to	to	PART
easat-10856	82	47	carry	carry	VERB
easat-10856	82	48	out	out	ADP
easat-10856	82	49	such	such	ADJ
easat-10856	82	50	purpose	purpose	NOUN
easat-10856	82	51	and	and	CCONJ
easat-10856	82	52	which	which	PRON
easat-10856	82	53	were	be	AUX
easat-10856	82	54	also	also	ADV
easat-10856	82	55	the	the	DET
easat-10856	82	56	origin	origin	NOUN
easat-10856	82	57	,	,	PUNCT
easat-10856	82	58	beginning	beginning	NOUN
easat-10856	82	59	,	,	PUNCT
easat-10856	82	60	and	and	CCONJ
easat-10856	82	61	foundation	foundation	NOUN
easat-10856	82	62	of	of	ADP
easat-10856	82	63	some	some	DET
easat-10856	82	64	numbers	number	NOUN
easat-10856	82	65	that	that	PRON
easat-10856	82	66	today	today	NOUN
easat-10856	82	67	bear	bear	VERB
easat-10856	82	68	his	his	PRON
easat-10856	82	69	name	name	NOUN
easat-10856	82	70	:	:	PUNCT
easat-10856	82	71	"	"	PUNCT
easat-10856	82	72	the	the	DET
easat-10856	82	73	bernoulli	bernoulli	PROPN
easat-10856	82	74	numbers	number	NOUN
easat-10856	82	75	.	.	PUNCT
easat-10856	82	76	"	"	PUNCT
easat-10856	83	1	martínez	martínez	PROPN
easat-10856	83	2	et	et	PROPN
easat-10856	83	3	al	al	PROPN
easat-10856	83	4	.	.	PUNCT
easat-10856	84	1	[	[	X
easat-10856	84	2	11	11	NUM
easat-10856	84	3	]	]	PUNCT
easat-10856	84	4	have	have	AUX
easat-10856	84	5	developed	develop	VERB
easat-10856	84	6	the	the	DET
easat-10856	84	7	main	main	ADJ
easat-10856	84	8	and	and	CCONJ
easat-10856	84	9	relevant	relevant	ADJ
easat-10856	84	10	aspects	aspect	NOUN
easat-10856	84	11	regarding	regard	VERB
easat-10856	84	12	bernoulli	bernoulli	NOUN
easat-10856	84	13	polynomials	polynomial	NOUN
easat-10856	84	14	and	and	CCONJ
easat-10856	84	15	numbers	number	NOUN
easat-10856	84	16	,	,	PUNCT
easat-10856	84	17	which	which	PRON
easat-10856	84	18	serve	serve	VERB
easat-10856	84	19	,	,	PUNCT
easat-10856	84	20	due	due	ADP
easat-10856	84	21	to	to	ADP
easat-10856	84	22	their	their	PRON
easat-10856	84	23	importance	importance	NOUN
easat-10856	84	24	and	and	CCONJ
easat-10856	84	25	foundation	foundation	NOUN
easat-10856	84	26	,	,	PUNCT
easat-10856	84	27	for	for	ADP
easat-10856	84	28	the	the	DET
easat-10856	84	29	presentation	presentation	NOUN
easat-10856	84	30	of	of	ADP
easat-10856	84	31	the	the	DET
easat-10856	84	32	results	result	NOUN
easat-10856	84	33	found	find	VERB
easat-10856	84	34	to	to	PART
easat-10856	84	35	test	test	VERB
easat-10856	84	36	,	,	PUNCT
easat-10856	84	37	conjecture	conjecture	VERB
easat-10856	84	38	,	,	PUNCT
easat-10856	84	39	and	and	CCONJ
easat-10856	84	40	prove	prove	VERB
easat-10856	84	41	the	the	DET
easat-10856	84	42	faulhaber	faulhaber	NOUN
easat-10856	84	43	formula	formula	NOUN
easat-10856	84	44	theorem	theorem	VERB
easat-10856	84	45	,	,	PUNCT
easat-10856	84	46	in	in	ADP
easat-10856	84	47	which	which	PRON
easat-10856	84	48	the	the	DET
easat-10856	84	49	cotangent	cotangent	NOUN
easat-10856	84	50	function	function	NOUN
easat-10856	84	51	is	be	AUX
easat-10856	84	52	developed	develop	VERB
easat-10856	84	53	in	in	ADP
easat-10856	84	54	a	a	DET
easat-10856	84	55	series	series	NOUN
easat-10856	84	56	,	,	PUNCT
easat-10856	84	57	and	and	CCONJ
easat-10856	84	58	to	to	PART
easat-10856	84	59	infinity	infinity	NOUN
easat-10856	84	60	,	,	PUNCT
easat-10856	84	61	in	in	ADP
easat-10856	84	62	relation	relation	NOUN
easat-10856	84	63	to	to	ADP
easat-10856	84	64	bernoulli	bernoulli	NOUN
easat-10856	84	65	numbers	number	NOUN
easat-10856	84	66	and	and	CCONJ
easat-10856	84	67	in	in	ADP
easat-10856	84	68	this	this	DET
easat-10856	84	69	way	way	NOUN
easat-10856	84	70	the	the	DET
easat-10856	84	71	values	value	NOUN
easat-10856	84	72	of	of	ADP
easat-10856	84	73	the	the	DET
easat-10856	84	74	riemann	riemann	PROPN
easat-10856	84	75	zeta	zeta	PROPN
easat-10856	84	76	function	function	PROPN
easat-10856	84	77	are	be	AUX
easat-10856	84	78	evaluated	evaluate	VERB
easat-10856	84	79	at	at	ADP
easat-10856	84	80	integer	integer	NOUN
easat-10856	84	81	arguments	argument	NOUN
easat-10856	84	82	through	through	ADP
easat-10856	84	83	bernoulli	bernoulli	NOUN
easat-10856	84	84	numbers	number	NOUN
easat-10856	84	85	,	,	PUNCT
easat-10856	84	86	and	and	CCONJ
easat-10856	84	87	finally	finally	ADV
easat-10856	84	88	the	the	DET
easat-10856	84	89	explicit	explicit	ADJ
easat-10856	84	90	formulas	formula	NOUN
easat-10856	84	91	for	for	ADP
easat-10856	84	92	evaluating	evaluate	VERB
easat-10856	84	93	and	and	CCONJ
easat-10856	84	94	calculating	calculate	VERB
easat-10856	84	95	bernoulli	bernoulli	NOUN
easat-10856	84	96	numbers	number	NOUN
easat-10856	84	97	in	in	ADP
easat-10856	84	98	terms	term	NOUN
easat-10856	84	99	of	of	ADP
easat-10856	84	100	stirling	stirling	NOUN
easat-10856	84	101	numbers	number	NOUN
easat-10856	84	102	of	of	ADP
easat-10856	84	103	the	the	DET
easat-10856	84	104	first	first	ADJ
easat-10856	84	105	and	and	CCONJ
easat-10856	84	106	second	second	ADJ
easat-10856	84	107	kind	kind	NOUN
easat-10856	84	108	are	be	AUX
easat-10856	84	109	verified	verify	VERB
easat-10856	84	110	.	.	PUNCT
easat-10856	85	1	the	the	DET
easat-10856	85	2	purpose	purpose	NOUN
easat-10856	85	3	has	have	AUX
easat-10856	85	4	been	be	AUX
easat-10856	85	5	to	to	PART
easat-10856	85	6	determine	determine	VERB
easat-10856	85	7	and	and	CCONJ
easat-10856	85	8	evaluate	evaluate	VERB
easat-10856	85	9	the	the	DET
easat-10856	85	10	first	first	ADJ
easat-10856	85	11	twenty	twenty	NUM
easat-10856	85	12	bernoulli	bernoulli	NOUN
easat-10856	85	13	and	and	CCONJ
easat-10856	85	14	euler	euler	NOUN
easat-10856	85	15	numbers	number	NOUN
easat-10856	85	16	,	,	PUNCT
easat-10856	85	17	to	to	PART
easat-10856	85	18	present	present	VERB
easat-10856	85	19	each	each	PRON
easat-10856	85	20	of	of	ADP
easat-10856	85	21	them	they	PRON
easat-10856	85	22	in	in	ADP
easat-10856	85	23	table	table	NOUN
easat-10856	85	24	form	form	NOUN
easat-10856	85	25	,	,	PUNCT
easat-10856	85	26	and	and	CCONJ
easat-10856	85	27	to	to	PART
easat-10856	85	28	apply	apply	VERB
easat-10856	85	29	them	they	PRON
easat-10856	85	30	,	,	PUNCT
easat-10856	85	31	in	in	ADP
easat-10856	85	32	some	some	DET
easat-10856	85	33	way	way	NOUN
easat-10856	85	34	,	,	PUNCT
easat-10856	85	35	in	in	ADP
easat-10856	85	36	the	the	DET
easat-10856	85	37	calculation	calculation	NOUN
easat-10856	85	38	of	of	ADP
easat-10856	85	39	integrals	integral	NOUN
easat-10856	85	40	with	with	ADP
easat-10856	85	41	expressions	expression	NOUN
easat-10856	85	42	containing	contain	VERB
easat-10856	85	43	said	say	VERB
easat-10856	85	44	numbers	number	NOUN
easat-10856	85	45	.	.	PUNCT
easat-10856	86	1	𝑥	𝑥	DET
easat-10856	86	2	2	2	NUM
easat-10856	86	3	𝑐𝑜𝑡	𝑐𝑜𝑡	NOUN
easat-10856	86	4	𝑥	𝑥	NOUN
easat-10856	86	5	2	2	NUM
easat-10856	86	6	=	=	SYM
easat-10856	86	7	1	1	NUM
easat-10856	86	8	−	−	NOUN
easat-10856	86	9	𝐵1	𝐵1	NOUN
easat-10856	86	10	𝑥2	𝑥2	NOUN
easat-10856	86	11	2	2	NUM
easat-10856	86	12	!	!	PUNCT
easat-10856	87	1	−	−	NOUN
easat-10856	87	2	𝐵2	𝐵2	NOUN
easat-10856	87	3	𝑥4	𝑥4	NOUN
easat-10856	87	4	4	4	NUM
easat-10856	87	5	!	!	PUNCT
easat-10856	88	1	−	−	NOUN
easat-10856	88	2	𝐵3	𝐵3	PROPN
easat-10856	88	3	𝑥6	𝑥6	PROPN
easat-10856	88	4	6	6	NUM
easat-10856	88	5	!	!	PUNCT
easat-10856	89	1	−.	−.	NOUN
easat-10856	89	2	..	..	PUNCT
easat-10856	90	1	𝑥	𝑥	PRON
easat-10856	90	2	2	2	NUM
easat-10856	90	3	𝑒𝑥+1	𝑒𝑥+1	NUM
easat-10856	90	4	𝑒𝑥−1	𝑒𝑥−1	NOUN
easat-10856	90	5	=	=	NOUN
easat-10856	90	6	1	1	NUM
easat-10856	90	7	+	+	NUM
easat-10856	90	8	𝐵1	𝐵1	NOUN
easat-10856	90	9	𝑥2	𝑥2	NOUN
easat-10856	90	10	2	2	NUM
easat-10856	90	11	!	!	PUNCT
easat-10856	91	1	−	−	NOUN
easat-10856	91	2	𝐵2	𝐵2	NOUN
easat-10856	91	3	𝑥4	𝑥4	NOUN
easat-10856	91	4	4	4	NUM
easat-10856	91	5	!	!	PUNCT
easat-10856	92	1	+	+	CCONJ
easat-10856	92	2	𝐵3	𝐵3	PROPN
easat-10856	92	3	𝑥6	𝑥6	PROPN
easat-10856	92	4	6	6	NUM
easat-10856	92	5	!	!	PUNCT
easat-10856	93	1	−.	−.	NOUN
easat-10856	93	2	..	..	PUNCT
easat-10856	94	1	𝐵𝑚	𝐵𝑚	NOUN
easat-10856	94	2	=	=	PUNCT
easat-10856	94	3	(	(	PUNCT
easat-10856	94	4	2𝑚	2𝑚	NOUN
easat-10856	94	5	)	)	PUNCT
easat-10856	94	6	!	!	PUNCT
easat-10856	95	1	22𝑚−1𝜋2𝑚	22𝑚−1𝜋2𝑚	NUM
easat-10856	96	1	[	[	SYM
easat-10856	96	2	1	1	NUM
easat-10856	96	3	+	+	SYM
easat-10856	96	4	1	1	NUM
easat-10856	96	5	22𝑚	22𝑚	NOUN
easat-10856	96	6	+	+	CCONJ
easat-10856	96	7	1	1	NUM
easat-10856	96	8	32𝑚	32𝑚	NOUN
easat-10856	96	9	+	+	CCONJ
easat-10856	96	10	1	1	NUM
easat-10856	96	11	42𝑚	42𝑚	NOUN
easat-10856	96	12	+	+	PROPN
easat-10856	96	13	.	.	PUNCT
easat-10856	96	14	.	.	PUNCT
easat-10856	96	15	.	.	PUNCT
easat-10856	97	1	]	]	PUNCT
easat-10856	98	1	𝐵𝑚	𝐵𝑚	NOUN
easat-10856	98	2	=	=	SYM
easat-10856	98	3	4𝑚∫	4𝑚∫	NUM
easat-10856	98	4	𝑡2𝑚−1.𝑑𝑡	𝑡2𝑚−1.𝑑𝑡	X
easat-10856	98	5	𝑒2𝜋𝑡−1	𝑒2𝜋𝑡−1	VERB
easat-10856	98	6	𝑡𝑔.	𝑡𝑔.	NOUN
easat-10856	98	7	𝑥	𝑥	NOUN
easat-10856	99	1	=	=	SYM
easat-10856	99	2	22(22	22(22	NUM
easat-10856	99	3	−	−	PROPN
easat-10856	99	4	1)𝐵1	1)𝐵1	NUM
easat-10856	99	5	𝑥	𝑥	NOUN
easat-10856	99	6	2	2	NUM
easat-10856	99	7	!	!	PUNCT
easat-10856	100	1	+	+	CCONJ
easat-10856	100	2	24(24	24(24	NUM
easat-10856	100	3	−	−	PROPN
easat-10856	100	4	1)𝐵2	1)𝐵2	NUM
easat-10856	100	5	𝑥3	𝑥3	NOUN
easat-10856	100	6	4	4	NUM
easat-10856	100	7	!	!	PUNCT
easat-10856	101	1	+	+	X
easat-10856	101	2	.	.	PUNCT
easat-10856	101	3	..	..	PUNCT
easat-10856	101	4	𝑙𝑜𝑔	𝑙𝑜𝑔	PROPN
easat-10856	102	1	𝑠𝑒𝑛.𝑥	𝑠𝑒𝑛.𝑥	NUM
easat-10856	102	2	𝑥	𝑥	NOUN
easat-10856	102	3	=	=	SYM
easat-10856	102	4	−	−	PROPN
easat-10856	102	5	2	2	NUM
easat-10856	102	6	1	1	NUM
easat-10856	102	7	𝐵1	𝐵1	NOUN
easat-10856	102	8	𝑥2	𝑥2	NOUN
easat-10856	102	9	2	2	NUM
easat-10856	102	10	!	!	PUNCT
easat-10856	103	1	−	−	NOUN
easat-10856	103	2	23	23	NUM
easat-10856	103	3	2	2	NUM
easat-10856	103	4	𝐵2	𝐵2	NOUN
easat-10856	103	5	𝑥4	𝑥4	NOUN
easat-10856	103	6	4	4	NUM
easat-10856	103	7	!	!	PUNCT
easat-10856	104	1	−	−	NOUN
easat-10856	104	2	25	25	NUM
easat-10856	104	3	3	3	NUM
easat-10856	104	4	𝐵3	𝐵3	PROPN
easat-10856	104	5	𝑥6	𝑥6	PROPN
easat-10856	104	6	6	6	NUM
easat-10856	104	7	!	!	PUNCT
easat-10856	105	1	−.	−.	ADV
easat-10856	105	2	.	.	PUNCT
easat-10856	105	3	.	.	PUNCT
easat-10856	106	1	..	..	PUNCT
easat-10856	107	1	277	277	NUM
easat-10856	107	2	edelweiss	edelweiss	PROPN
easat-10856	107	3	applied	apply	VERB
easat-10856	107	4	science	science	NOUN
easat-10856	107	5	and	and	CCONJ
easat-10856	107	6	technology	technology	NOUN
easat-10856	107	7	issn	issn	PROPN
easat-10856	107	8	:	:	PUNCT
easat-10856	107	9	2576	2576	NUM
easat-10856	107	10	-	-	SYM
easat-10856	107	11	8484	8484	NUM
easat-10856	107	12	vol	vol	NOUN
easat-10856	107	13	.	.	PROPN
easat-10856	108	1	9	9	NUM
easat-10856	108	2	,	,	PUNCT
easat-10856	108	3	no	no	INTJ
easat-10856	108	4	.	.	NOUN
easat-10856	108	5	11	11	NUM
easat-10856	108	6	:	:	PUNCT
easat-10856	108	7	274	274	NUM
easat-10856	108	8	-	-	SYM
easat-10856	108	9	288	288	NUM
easat-10856	108	10	,	,	PUNCT
easat-10856	108	11	2025	2025	NUM
easat-10856	108	12	doi	doi	NOUN
easat-10856	108	13	:	:	PUNCT
easat-10856	108	14	10.55214/2576	10.55214/2576	NUM
easat-10856	108	15	-	-	PUNCT
easat-10856	108	16	8484.v9i11.10856	8484.v9i11.10856	NUM
easat-10856	108	17	©	©	PROPN
easat-10856	108	18	2025	2025	NUM
easat-10856	108	19	by	by	ADP
easat-10856	108	20	the	the	DET
easat-10856	108	21	authors	author	NOUN
easat-10856	108	22	;	;	PUNCT
easat-10856	108	23	licensee	licensee	PROPN
easat-10856	108	24	learning	learning	NOUN
easat-10856	108	25	gate	gate	VERB
easat-10856	108	26	𝑥	𝑥	DET
easat-10856	108	27	𝑒𝑥−1	𝑒𝑥−1	NOUN
easat-10856	108	28	=	=	PUNCT
easat-10856	108	29	∑	∑	PUNCT
easat-10856	108	30	𝐵𝑛.𝑥	𝐵𝑛.𝑥	PROPN
easat-10856	108	31	𝑛	𝑛	ADP
easat-10856	108	32	𝑛	𝑛	PROPN
easat-10856	108	33	!	!	PUNCT
easat-10856	109	1	∞	∞	NUM
easat-10856	109	2	𝑛=0	𝑛=0	X
easat-10856	109	3	=	=	PUNCT
easat-10856	110	1	𝐵0	𝐵0	PROPN
easat-10856	110	2	+	+	CCONJ
easat-10856	110	3	𝐵1𝑥	𝐵1𝑥	PROPN
easat-10856	110	4	+	+	CCONJ
easat-10856	110	5	𝐵2	𝐵2	NOUN
easat-10856	110	6	2	2	NUM
easat-10856	110	7	!	!	PUNCT
easat-10856	110	8	𝑥2	𝑥2	NOUN
easat-10856	110	9	+	+	CCONJ
easat-10856	110	10	𝐵3	𝐵3	PROPN
easat-10856	110	11	3	3	X
easat-10856	110	12	!	!	X
easat-10856	110	13	𝑥3	𝑥3	NOUN
easat-10856	110	14	+	+	PROPN
easat-10856	110	15	.	.	PUNCT
easat-10856	110	16	..	..	PUNCT
easat-10856	111	1	𝑥	𝑥	DET
easat-10856	111	2	𝑒𝑥−1	𝑒𝑥−1	NOUN
easat-10856	111	3	=	=	NOUN
easat-10856	111	4	1	1	NUM
easat-10856	111	5	−	−	NOUN
easat-10856	111	6	𝑥	𝑥	NOUN
easat-10856	111	7	2	2	NUM
easat-10856	111	8	+	+	CCONJ
easat-10856	111	9	𝐵1𝑥	𝐵1𝑥	ADJ
easat-10856	111	10	2	2	NUM
easat-10856	111	11	2	2	NUM
easat-10856	111	12	!	!	PUNCT
easat-10856	112	1	−	−	PROPN
easat-10856	113	1	𝐵2𝑥	𝐵2𝑥	PROPN
easat-10856	113	2	4	4	NUM
easat-10856	113	3	4	4	NUM
easat-10856	113	4	!	!	PUNCT
easat-10856	114	1	+	+	CCONJ
easat-10856	114	2	𝐵3𝑥	𝐵3𝑥	PROPN
easat-10856	114	3	6	6	NUM
easat-10856	114	4	6	6	NUM
easat-10856	114	5	!	!	PUNCT
easat-10856	115	1	−.	−.	NOUN
easat-10856	115	2	..	..	PUNCT
easat-10856	116	1	𝑥.	𝑥.	X
easat-10856	116	2	𝑐𝑜𝑡.	𝑐𝑜𝑡.	VERB
easat-10856	117	1	𝑥	𝑥	X
easat-10856	117	2	=	=	SYM
easat-10856	117	3	∑	∑	PROPN
easat-10856	117	4	(	(	PUNCT
easat-10856	117	5	−1)𝑛𝐵2𝑛(2𝑥	−1)𝑛𝐵2𝑛(2𝑥	PROPN
easat-10856	117	6	)	)	PUNCT
easat-10856	117	7	2𝑛	2𝑛	PROPN
easat-10856	117	8	(	(	PUNCT
easat-10856	117	9	2𝑛	2𝑛	NUM
easat-10856	117	10	)	)	PUNCT
easat-10856	117	11	!	!	PUNCT
easat-10856	118	1	∞	∞	NUM
easat-10856	118	2	𝑛=0	𝑛=0	NOUN
easat-10856	118	3	1	1	NUM
easat-10856	118	4	−	−	NOUN
easat-10856	119	1	𝑥	𝑥	SYM
easat-10856	119	2	2	2	NUM
easat-10856	119	3	𝑐𝑜𝑡	𝑐𝑜𝑡	NOUN
easat-10856	119	4	𝑥	𝑥	NOUN
easat-10856	119	5	2	2	NUM
easat-10856	119	6	=	=	SYM
easat-10856	119	7	𝐵1𝑥	𝐵1𝑥	ADJ
easat-10856	119	8	2	2	NUM
easat-10856	119	9	2	2	NUM
easat-10856	119	10	!	!	PUNCT
easat-10856	120	1	+	+	CCONJ
easat-10856	120	2	𝐵2𝑥	𝐵2𝑥	PROPN
easat-10856	120	3	4	4	NUM
easat-10856	120	4	4	4	NUM
easat-10856	120	5	!	!	PUNCT
easat-10856	121	1	+	+	CCONJ
easat-10856	121	2	𝐵3𝑥	𝐵3𝑥	PROPN
easat-10856	121	3	6	6	NUM
easat-10856	121	4	6	6	NUM
easat-10856	121	5	!	!	PUNCT
easat-10856	122	1	+	+	ADJ
easat-10856	122	2	.	.	PUNCT
easat-10856	122	3	..	..	PUNCT
easat-10856	123	1	𝐵2𝑛	𝐵2𝑛	PROPN
easat-10856	123	2	=	=	SYM
easat-10856	123	3	2(−1)𝑛−1(2𝑛	2(−1)𝑛−1(2𝑛	NUM
easat-10856	123	4	)	)	PUNCT
easat-10856	123	5	!	!	PUNCT
easat-10856	124	1	(	(	PUNCT
easat-10856	124	2	2𝜋)2𝑛	2𝜋)2𝑛	NUM
easat-10856	124	3	(	(	PUNCT
easat-10856	124	4	1	1	NUM
easat-10856	124	5	+	+	NUM
easat-10856	124	6	1	1	NUM
easat-10856	124	7	22𝑛	22𝑛	NOUN
easat-10856	124	8	+	+	CCONJ
easat-10856	124	9	1	1	NUM
easat-10856	124	10	32𝑛	32𝑛	NOUN
easat-10856	124	11	+	+	CCONJ
easat-10856	124	12	1	1	NUM
easat-10856	124	13	42𝑛	42𝑛	NOUN
easat-10856	124	14	+	+	ADJ
easat-10856	124	15	.	.	PUNCT
easat-10856	124	16	.	.	PUNCT
easat-10856	124	17	.	.	PUNCT
easat-10856	124	18	)	)	PUNCT
easat-10856	125	1	(	(	PUNCT
easat-10856	125	2	2𝑛	2𝑛	NOUN
easat-10856	125	3	+	+	CCONJ
easat-10856	125	4	1	1	NUM
easat-10856	125	5	2	2	NUM
easat-10856	125	6	)	)	PUNCT
easat-10856	125	7	22𝐵1	22𝐵1	NUM
easat-10856	125	8	−	−	PROPN
easat-10856	126	1	(	(	PUNCT
easat-10856	126	2	2𝑛	2𝑛	NOUN
easat-10856	126	3	+	+	CCONJ
easat-10856	126	4	1	1	NUM
easat-10856	126	5	4	4	NUM
easat-10856	126	6	)	)	PUNCT
easat-10856	126	7	24𝐵2	24𝐵2	NUM
easat-10856	127	1	+	+	CCONJ
easat-10856	127	2	(	(	PUNCT
easat-10856	127	3	2𝑛	2𝑛	NUM
easat-10856	127	4	+	+	CCONJ
easat-10856	127	5	1	1	NUM
easat-10856	127	6	6	6	NUM
easat-10856	127	7	)	)	PUNCT
easat-10856	127	8	26𝐵3−.	26𝐵3−.	NUM
easat-10856	127	9	.	.	PUNCT
easat-10856	127	10	.	.	PUNCT
easat-10856	128	1	(	(	PUNCT
easat-10856	128	2	−1	−1	NOUN
easat-10856	128	3	)	)	PUNCT
easat-10856	128	4	𝑛−1(2𝑛	𝑛−1(2𝑛	NOUN
easat-10856	129	1	+	+	CCONJ
easat-10856	129	2	1)22𝑛𝐵𝑛	1)22𝑛𝐵𝑛	NUM
easat-10856	129	3	=	=	SYM
easat-10856	129	4	2𝑛	2𝑛	PROPN
easat-10856	129	5	bronshtein	bronshtein	PROPN
easat-10856	129	6	and	and	CCONJ
easat-10856	129	7	semendiaev	semendiaev	VERB
easat-10856	130	1	[	[	X
easat-10856	130	2	7	7	X
easat-10856	130	3	]	]	PUNCT
easat-10856	130	4	mention	mention	VERB
easat-10856	130	5	the	the	DET
easat-10856	130	6	other	other	ADJ
easat-10856	130	7	series	series	NOUN
easat-10856	130	8	that	that	PRON
easat-10856	130	9	relate	relate	VERB
easat-10856	130	10	to	to	ADP
easat-10856	130	11	the	the	DET
easat-10856	130	12	bernoulli	bernoulli	NOUN
easat-10856	130	13	numbers	number	NOUN
easat-10856	130	14	:	:	PUNCT
easat-10856	130	15	𝐵𝑛	𝐵𝑛	PROPN
easat-10856	130	16	=	=	SYM
easat-10856	130	17	2(2𝑛	2(2𝑛	NUM
easat-10856	130	18	)	)	PUNCT
easat-10856	130	19	!	!	PUNCT
easat-10856	131	1	(	(	PUNCT
easat-10856	131	2	22𝑛−1)𝜋2𝑛	22𝑛−1)𝜋2𝑛	NUM
easat-10856	131	3	(	(	PUNCT
easat-10856	131	4	1	1	NUM
easat-10856	131	5	+	+	SYM
easat-10856	131	6	1	1	NUM
easat-10856	131	7	32𝑛	32𝑛	NOUN
easat-10856	131	8	+	+	CCONJ
easat-10856	131	9	1	1	NUM
easat-10856	131	10	52𝑛	52𝑛	NUM
easat-10856	131	11	+	+	SYM
easat-10856	131	12	1	1	NUM
easat-10856	131	13	72𝑛	72𝑛	NOUN
easat-10856	131	14	+	+	PROPN
easat-10856	131	15	.	.	PUNCT
easat-10856	131	16	.	.	PUNCT
easat-10856	131	17	.	.	PUNCT
easat-10856	131	18	)	)	PUNCT
easat-10856	132	1	𝐵𝑛	𝐵𝑛	PROPN
easat-10856	132	2	=	=	SYM
easat-10856	132	3	(	(	PUNCT
easat-10856	132	4	2𝑛	2𝑛	NUM
easat-10856	132	5	)	)	PUNCT
easat-10856	132	6	!	!	PUNCT
easat-10856	133	1	(	(	PUNCT
easat-10856	133	2	22𝑛−1−1)𝜋2𝑛	22𝑛−1−1)𝜋2𝑛	NUM
easat-10856	133	3	(	(	PUNCT
easat-10856	133	4	1	1	NUM
easat-10856	133	5	−	−	NUM
easat-10856	133	6	1	1	NUM
easat-10856	133	7	22𝑛	22𝑛	NOUN
easat-10856	133	8	+	+	CCONJ
easat-10856	133	9	1	1	NUM
easat-10856	133	10	32𝑛	32𝑛	NOUN
easat-10856	133	11	−	−	PROPN
easat-10856	133	12	1	1	NUM
easat-10856	133	13	42𝑛	42𝑛	NOUN
easat-10856	133	14	+	+	PROPN
easat-10856	133	15	.	.	PUNCT
easat-10856	133	16	.	.	PUNCT
easat-10856	133	17	.	.	PUNCT
easat-10856	133	18	)	)	PUNCT
easat-10856	134	1	𝐵𝑛	𝐵𝑛	PROPN
easat-10856	134	2	=	=	SYM
easat-10856	134	3	(	(	PUNCT
easat-10856	134	4	2𝑛	2𝑛	NUM
easat-10856	134	5	)	)	PUNCT
easat-10856	134	6	!	!	PUNCT
easat-10856	135	1	22𝑛−1𝜋2𝑛	22𝑛−1𝜋2𝑛	NUM
easat-10856	135	2	(	(	PUNCT
easat-10856	135	3	1	1	NUM
easat-10856	135	4	+	+	NUM
easat-10856	135	5	1	1	NUM
easat-10856	135	6	22𝑛	22𝑛	NOUN
easat-10856	135	7	+	+	CCONJ
easat-10856	135	8	1	1	NUM
easat-10856	135	9	32𝑛	32𝑛	NOUN
easat-10856	135	10	+	+	CCONJ
easat-10856	135	11	1	1	NUM
easat-10856	135	12	42𝑛	42𝑛	NOUN
easat-10856	135	13	+	+	CCONJ
easat-10856	135	14	1	1	NUM
easat-10856	135	15	52𝑛	52𝑛	NOUN
easat-10856	135	16	+	+	PROPN
easat-10856	135	17	.	.	PUNCT
easat-10856	135	18	.	.	PUNCT
easat-10856	135	19	.	.	PUNCT
easat-10856	135	20	)	)	PUNCT
easat-10856	136	1	𝐵𝑛	𝐵𝑛	PROPN
easat-10856	136	2	=	=	SYM
easat-10856	136	3	𝑛	𝑛	PROPN
easat-10856	136	4	!	!	NOUN
easat-10856	136	5	×	×	NOUN
easat-10856	137	1	|	|	ADV
easat-10856	137	2	|	|	ADV
easat-10856	137	3	1	1	NUM
easat-10856	137	4	2	2	NUM
easat-10856	137	5	!	!	NOUN
easat-10856	137	6	1	1	NUM
easat-10856	137	7	0	0	NUM
easat-10856	137	8	.	.	PUNCT
easat-10856	137	9	.	.	PUNCT
easat-10856	138	1	.	.	PUNCT
easat-10856	139	1	0	0	NUM
easat-10856	139	2	1	1	NUM
easat-10856	139	3	3	3	NUM
easat-10856	139	4	!	!	NOUN
easat-10856	139	5	1	1	NUM
easat-10856	139	6	2	2	NUM
easat-10856	139	7	!	!	NOUN
easat-10856	139	8	1	1	NUM
easat-10856	139	9	.	.	PUNCT
easat-10856	139	10	.	.	PUNCT
easat-10856	140	1	.	.	PUNCT
easat-10856	140	2	0	0	PUNCT
easat-10856	140	3	.	.	PUNCT
easat-10856	140	4	.	.	PUNCT
easat-10856	141	1	.	.	PUNCT
easat-10856	141	2	.	.	PUNCT
easat-10856	142	1	.	.	PUNCT
easat-10856	142	2	.	.	PUNCT
easat-10856	143	1	.	.	PUNCT
easat-10856	144	1	1	1	NUM
easat-10856	144	2	(	(	PUNCT
easat-10856	144	3	𝑛+1	𝑛+1	NOUN
easat-10856	144	4	)	)	PUNCT
easat-10856	144	5	!	!	PUNCT
easat-10856	145	1	1	1	NUM
easat-10856	145	2	𝑛	𝑛	X
easat-10856	145	3	!	!	NOUN
easat-10856	145	4	1	1	NUM
easat-10856	145	5	(	(	PUNCT
easat-10856	145	6	𝑛−1	𝑛−1	NOUN
easat-10856	145	7	)	)	PUNCT
easat-10856	145	8	!	!	PUNCT
easat-10856	145	9	.	.	PUNCT
easat-10856	145	10	.	.	PUNCT
easat-10856	145	11	.	.	PUNCT
easat-10856	146	1	1	1	NUM
easat-10856	146	2	2	2	NUM
easat-10856	146	3	!	!	PUNCT
easat-10856	147	1	|	|	ADV
easat-10856	147	2	|	|	ADV
easat-10856	147	3	fernández	fernández	VERB
easat-10856	148	1	[	[	X
easat-10856	148	2	5	5	NUM
easat-10856	148	3	]	]	PUNCT
easat-10856	148	4	,	,	PUNCT
easat-10856	148	5	varadarajan	varadarajan	ADJ
easat-10856	148	6	[	[	X
easat-10856	148	7	20	20	NUM
easat-10856	148	8	]	]	PUNCT
easat-10856	148	9	and	and	CCONJ
easat-10856	148	10	bronshtein	bronshtein	PROPN
easat-10856	148	11	and	and	CCONJ
easat-10856	148	12	semendiaev	semendiaev	VERB
easat-10856	149	1	[	[	X
easat-10856	149	2	7	7	X
easat-10856	149	3	]	]	PUNCT
easat-10856	149	4	indicate	indicate	VERB
easat-10856	149	5	that	that	SCONJ
easat-10856	149	6	the	the	DET
easat-10856	149	7	expressions	expression	NOUN
easat-10856	149	8	relating	relate	VERB
easat-10856	149	9	to	to	PART
easat-10856	149	10	euler	euler	VERB
easat-10856	149	11	numbers	number	NOUN
easat-10856	149	12	are	be	AUX
easat-10856	149	13	:	:	PUNCT
easat-10856	149	14	1	1	NUM
easat-10856	149	15	−	−	PROPN
easat-10856	149	16	1	1	NUM
easat-10856	149	17	32𝑛+1	32𝑛+1	NUM
easat-10856	149	18	+	+	CCONJ
easat-10856	149	19	1	1	NUM
easat-10856	149	20	52𝑛+1	52𝑛+1	NUM
easat-10856	149	21	−	−	NOUN
easat-10856	149	22	1	1	NUM
easat-10856	149	23	72𝑛+1	72𝑛+1	NUM
easat-10856	149	24	+	+	PROPN
easat-10856	149	25	.	.	PUNCT
easat-10856	149	26	.	.	PUNCT
easat-10856	149	27	.	.	PUNCT
easat-10856	150	1	±	±	NOUN
easat-10856	150	2	1	1	NUM
easat-10856	150	3	(	(	PUNCT
easat-10856	150	4	2𝑛−1)2𝑛+1	2𝑛−1)2𝑛+1	NUM
easat-10856	150	5	∓.	∓.	PROPN
easat-10856	150	6	.	.	PUNCT
easat-10856	150	7	.	.	PUNCT
easat-10856	151	1	=	=	PRON
easat-10856	151	2	𝜋2𝑛+1	𝜋2𝑛+1	NUM
easat-10856	151	3	22𝑛+2×(2𝑛	22𝑛+2×(2𝑛	NUM
easat-10856	151	4	)	)	PUNCT
easat-10856	151	5	!	!	PUNCT
easat-10856	152	1	×	×	NOUN
easat-10856	153	1	𝐸𝑛	𝐸𝑛	ADP
easat-10856	153	2	𝑠𝑒𝑐.	𝑠𝑒𝑐.	NOUN
easat-10856	153	3	𝑥	𝑥	NOUN
easat-10856	153	4	=	=	SYM
easat-10856	153	5	1	1	NUM
easat-10856	153	6	+	+	NUM
easat-10856	153	7	𝐸1.𝑥	𝐸1.𝑥	ADJ
easat-10856	153	8	2	2	NUM
easat-10856	153	9	2	2	NUM
easat-10856	153	10	!	!	PUNCT
easat-10856	154	1	+	+	CCONJ
easat-10856	154	2	𝐸2.𝑥	𝐸2.𝑥	X
easat-10856	154	3	4	4	NUM
easat-10856	154	4	4	4	NUM
easat-10856	154	5	!	!	PUNCT
easat-10856	155	1	+	+	X
easat-10856	155	2	𝐸3.𝑥	𝐸3.𝑥	NOUN
easat-10856	155	3	6	6	NUM
easat-10856	155	4	6	6	NUM
easat-10856	155	5	!	!	PUNCT
easat-10856	156	1	+	+	X
easat-10856	156	2	.	.	PUNCT
easat-10856	156	3	..	..	PUNCT
easat-10856	156	4	𝑠𝑒𝑐	𝑠𝑒𝑐	ADJ
easat-10856	156	5	ℎ	ℎ	PROPN
easat-10856	156	6	.	.	PUNCT
easat-10856	157	1	𝑥	𝑥	X
easat-10856	157	2	=	=	SYM
easat-10856	157	3	1	1	NUM
easat-10856	157	4	−	−	NOUN
easat-10856	157	5	𝐸1.𝑥	𝐸1.𝑥	VERB
easat-10856	157	6	2	2	NUM
easat-10856	157	7	2	2	NUM
easat-10856	157	8	!	!	PUNCT
easat-10856	158	1	+	+	CCONJ
easat-10856	158	2	𝐸2.𝑥	𝐸2.𝑥	X
easat-10856	158	3	4	4	NUM
easat-10856	158	4	4	4	NUM
easat-10856	158	5	!	!	PUNCT
easat-10856	159	1	−	−	NOUN
easat-10856	159	2	𝐸3.𝑥	𝐸3.𝑥	NOUN
easat-10856	159	3	6	6	NUM
easat-10856	159	4	6	6	NUM
easat-10856	159	5	!	!	PUNCT
easat-10856	160	1	+	+	ADJ
easat-10856	160	2	.	.	PUNCT
easat-10856	160	3	..	..	PUNCT
easat-10856	161	1	𝐸𝑛	𝐸𝑛	ADP
easat-10856	161	2	=	=	NOUN
easat-10856	161	3	22𝑛+2(2𝑛	22𝑛+2(2𝑛	NUM
easat-10856	161	4	)	)	PUNCT
easat-10856	161	5	!	!	PUNCT
easat-10856	162	1	𝜋2𝑛+1	𝜋2𝑛+1	PUNCT
easat-10856	162	2	(	(	PUNCT
easat-10856	162	3	1	1	NUM
easat-10856	162	4	−	−	PROPN
easat-10856	162	5	1	1	NUM
easat-10856	162	6	32𝑛+1	32𝑛+1	NUM
easat-10856	162	7	+	+	CCONJ
easat-10856	162	8	1	1	NUM
easat-10856	162	9	52𝑛+1	52𝑛+1	NUM
easat-10856	162	10	−	−	NOUN
easat-10856	162	11	1	1	NUM
easat-10856	162	12	72𝑛+1	72𝑛+1	NUM
easat-10856	162	13	+	+	CCONJ
easat-10856	162	14	1	1	NUM
easat-10856	162	15	92𝑛+1	92𝑛+1	NOUN
easat-10856	162	16	−.	−.	PROPN
easat-10856	162	17	.	.	PUNCT
easat-10856	162	18	.	.	PUNCT
easat-10856	162	19	)	)	PUNCT
easat-10856	163	1	𝐸𝑛	𝐸𝑛	ADP
easat-10856	163	2	=	=	PUNCT
easat-10856	164	1	|	|	ADV
easat-10856	164	2	|	|	ADV
easat-10856	164	3	|	|	ADV
easat-10856	164	4	1	1	NUM
easat-10856	164	5	2	2	NUM
easat-10856	164	6	!	!	NOUN
easat-10856	164	7	1	1	NUM
easat-10856	164	8	.	.	PUNCT
easat-10856	164	9	.	.	PUNCT
easat-10856	164	10	.	.	PUNCT
easat-10856	165	1	0	0	NUM
easat-10856	165	2	0	0	NUM
easat-10856	165	3	1	1	NUM
easat-10856	165	4	4	4	NUM
easat-10856	165	5	!	!	SYM
easat-10856	165	6	1	1	NUM
easat-10856	165	7	2	2	NUM
easat-10856	165	8	!	!	PUNCT
easat-10856	165	9	.	.	PUNCT
easat-10856	165	10	.	.	PUNCT
easat-10856	166	1	.	.	PUNCT
easat-10856	167	1	0	0	NUM
easat-10856	167	2	0	0	NUM
easat-10856	167	3	.	.	PUNCT
easat-10856	167	4	.	.	PUNCT
easat-10856	167	5	.	.	PUNCT
easat-10856	167	6	.	.	PUNCT
easat-10856	167	7	.	.	PUNCT
easat-10856	167	8	.	.	PUNCT
easat-10856	167	9	.	.	PUNCT
easat-10856	167	10	.	.	PUNCT
easat-10856	167	11	.	.	PUNCT
easat-10856	167	12	.	.	PUNCT
easat-10856	167	13	.	.	PUNCT
easat-10856	167	14	.	.	PUNCT
easat-10856	167	15	.	.	PUNCT
easat-10856	167	16	.	.	PUNCT
easat-10856	167	17	.	.	PUNCT
easat-10856	167	18	.	.	PUNCT
easat-10856	167	19	.	.	PUNCT
easat-10856	167	20	.	.	PUNCT
easat-10856	167	21	.	.	PUNCT
easat-10856	167	22	.	.	PUNCT
easat-10856	167	23	.	.	PUNCT
easat-10856	167	24	.	.	PUNCT
easat-10856	167	25	.	.	PUNCT
easat-10856	167	26	.	.	PUNCT
easat-10856	167	27	.	.	PUNCT
easat-10856	168	1	.	.	PUNCT
easat-10856	169	1	1	1	NUM
easat-10856	169	2	0	0	NUM
easat-10856	169	3	.	.	PUNCT
easat-10856	169	4	.	.	PUNCT
easat-10856	169	5	.	.	PUNCT
easat-10856	169	6	.	.	PUNCT
easat-10856	169	7	.	.	PUNCT
easat-10856	170	1	1	1	NUM
easat-10856	170	2	2	2	NUM
easat-10856	170	3	!	!	SYM
easat-10856	170	4	1	1	NUM
easat-10856	170	5	1	1	NUM
easat-10856	170	6	2𝑛	2𝑛	NUM
easat-10856	170	7	!	!	PUNCT
easat-10856	171	1	1	1	NUM
easat-10856	171	2	2𝑛−2	2𝑛−2	NUM
easat-10856	171	3	!	!	PUNCT
easat-10856	171	4	.	.	PUNCT
easat-10856	171	5	.	.	PUNCT
easat-10856	172	1	.	.	PUNCT
easat-10856	173	1	1	1	NUM
easat-10856	173	2	4	4	NUM
easat-10856	173	3	!	!	SYM
easat-10856	173	4	1	1	NUM
easat-10856	173	5	2	2	NUM
easat-10856	173	6	!	!	PUNCT
easat-10856	174	1	|	|	ADV
easat-10856	174	2	|	|	ADV
easat-10856	174	3	|	|	ADV
easat-10856	174	4	278	278	NUM
easat-10856	174	5	edelweiss	edelweiss	PROPN
easat-10856	174	6	applied	apply	VERB
easat-10856	174	7	science	science	NOUN
easat-10856	174	8	and	and	CCONJ
easat-10856	174	9	technology	technology	NOUN
easat-10856	174	10	issn	issn	PROPN
easat-10856	174	11	:	:	PUNCT
easat-10856	174	12	2576	2576	NUM
easat-10856	174	13	-	-	SYM
easat-10856	174	14	8484	8484	NUM
easat-10856	174	15	vol	vol	NOUN
easat-10856	174	16	.	.	PROPN
easat-10856	175	1	9	9	NUM
easat-10856	175	2	,	,	PUNCT
easat-10856	175	3	no	no	INTJ
easat-10856	175	4	.	.	NOUN
easat-10856	175	5	11	11	NUM
easat-10856	175	6	:	:	PUNCT
easat-10856	175	7	274	274	NUM
easat-10856	175	8	-	-	SYM
easat-10856	175	9	288	288	NUM
easat-10856	175	10	,	,	PUNCT
easat-10856	175	11	2025	2025	NUM
easat-10856	175	12	doi	doi	NOUN
easat-10856	175	13	:	:	PUNCT
easat-10856	175	14	10.55214/2576	10.55214/2576	NUM
easat-10856	175	15	-	-	PUNCT
easat-10856	175	16	8484.v9i11.10856	8484.v9i11.10856	NUM
easat-10856	175	17	©	©	PROPN
easat-10856	175	18	2025	2025	NUM
easat-10856	175	19	by	by	ADP
easat-10856	175	20	the	the	DET
easat-10856	175	21	authors	author	NOUN
easat-10856	175	22	;	;	PUNCT
easat-10856	175	23	licensee	licensee	NOUN
easat-10856	175	24	learning	learning	NOUN
easat-10856	175	25	gate	gate	NOUN
easat-10856	176	1	𝐸𝑛	𝐸𝑛	ADP
easat-10856	176	2	=	=	PUNCT
easat-10856	177	1	|	|	ADV
easat-10856	177	2	|	|	ADV
easat-10856	177	3	|	|	ADV
easat-10856	177	4	1	1	NUM
easat-10856	177	5	1	1	NUM
easat-10856	177	6	0	0	NUM
easat-10856	177	7	.	.	PUNCT
easat-10856	177	8	.	.	PUNCT
easat-10856	177	9	.	.	PUNCT
easat-10856	178	1	0	0	NUM
easat-10856	178	2	1	1	NUM
easat-10856	178	3	(	(	PUNCT
easat-10856	178	4	4	4	NUM
easat-10856	178	5	2	2	NUM
easat-10856	178	6	)	)	PUNCT
easat-10856	178	7	1	1	NUM
easat-10856	178	8	.	.	PUNCT
easat-10856	178	9	.	.	PUNCT
easat-10856	179	1	.	.	PUNCT
easat-10856	180	1	0	0	NUM
easat-10856	181	1	1	1	NUM
easat-10856	181	2	(	(	PUNCT
easat-10856	181	3	6	6	NUM
easat-10856	181	4	2	2	NUM
easat-10856	181	5	)	)	PUNCT
easat-10856	181	6	(	(	PUNCT
easat-10856	181	7	6	6	NUM
easat-10856	181	8	4	4	NUM
easat-10856	181	9	)	)	PUNCT
easat-10856	181	10	.	.	PUNCT
easat-10856	181	11	.	.	PUNCT
easat-10856	182	1	.	.	PUNCT
easat-10856	182	2	0	0	PUNCT
easat-10856	182	3	.	.	PUNCT
easat-10856	182	4	.	.	PUNCT
easat-10856	183	1	.	.	PUNCT
easat-10856	183	2	.	.	PUNCT
easat-10856	184	1	.	.	PUNCT
easat-10856	184	2	.	.	PUNCT
easat-10856	185	1	.	.	PUNCT
easat-10856	185	2	.	.	PUNCT
easat-10856	186	1	.	.	PUNCT
easat-10856	186	2	.	.	PUNCT
easat-10856	187	1	.	.	PUNCT
easat-10856	187	2	.	.	PUNCT
easat-10856	188	1	.	.	PUNCT
easat-10856	188	2	.	.	PUNCT
easat-10856	189	1	.	.	PUNCT
easat-10856	189	2	.	.	PUNCT
easat-10856	190	1	.	.	PUNCT
easat-10856	190	2	.	.	PUNCT
easat-10856	191	1	.	.	PUNCT
easat-10856	191	2	.	.	PUNCT
easat-10856	192	1	.	.	PUNCT
easat-10856	193	1	1	1	NUM
easat-10856	193	2	(	(	PUNCT
easat-10856	193	3	2𝑛	2𝑛	NOUN
easat-10856	193	4	−	−	PROPN
easat-10856	193	5	2	2	NUM
easat-10856	193	6	2	2	NUM
easat-10856	193	7	)	)	PUNCT
easat-10856	193	8	(	(	PUNCT
easat-10856	193	9	2𝑛	2𝑛	NOUN
easat-10856	193	10	−	−	PROPN
easat-10856	193	11	2	2	NUM
easat-10856	193	12	4	4	NUM
easat-10856	193	13	)	)	PUNCT
easat-10856	193	14	.	.	PUNCT
easat-10856	193	15	.	.	PUNCT
easat-10856	194	1	.	.	PUNCT
easat-10856	195	1	1	1	NUM
easat-10856	195	2	1	1	NUM
easat-10856	195	3	(	(	PUNCT
easat-10856	195	4	2𝑛	2𝑛	PROPN
easat-10856	195	5	2	2	NUM
easat-10856	195	6	)	)	PUNCT
easat-10856	195	7	(	(	PUNCT
easat-10856	195	8	2𝑛	2𝑛	PROPN
easat-10856	195	9	4	4	NUM
easat-10856	195	10	)	)	PUNCT
easat-10856	195	11	.	.	PUNCT
easat-10856	195	12	.	.	PUNCT
easat-10856	195	13	.	.	PUNCT
easat-10856	196	1	(	(	PUNCT
easat-10856	196	2	2𝑛	2𝑛	PROPN
easat-10856	196	3	2𝑛	2𝑛	PROPN
easat-10856	196	4	−	−	PROPN
easat-10856	196	5	2	2	X
easat-10856	196	6	)	)	PUNCT
easat-10856	197	1	|	|	ADV
easat-10856	197	2	|	|	ADV
easat-10856	197	3	|	|	ADV
easat-10856	197	4	2	2	NUM
easat-10856	197	5	.	.	PUNCT
easat-10856	197	6	materials	material	NOUN
easat-10856	197	7	y	y	PROPN
easat-10856	197	8	methods	method	NOUN
easat-10856	197	9	methodology	methodology	NOUN
easat-10856	197	10	.	.	PUNCT
easat-10856	198	1	the	the	DET
easat-10856	198	2	research	research	NOUN
easat-10856	198	3	has	have	AUX
easat-10856	198	4	been	be	AUX
easat-10856	198	5	divided	divide	VERB
easat-10856	198	6	into	into	ADP
easat-10856	198	7	two	two	NUM
easat-10856	198	8	parts	part	NOUN
easat-10856	198	9	.	.	PUNCT
easat-10856	199	1	in	in	ADP
easat-10856	199	2	the	the	DET
easat-10856	199	3	first	first	ADJ
easat-10856	199	4	part	part	NOUN
easat-10856	199	5	,	,	PUNCT
easat-10856	199	6	we	we	PRON
easat-10856	199	7	focused	focus	VERB
easat-10856	199	8	on	on	ADP
easat-10856	199	9	calculating	calculate	VERB
easat-10856	199	10	the	the	DET
easat-10856	199	11	first	first	ADJ
easat-10856	199	12	twenty	twenty	NUM
easat-10856	199	13	bernoulli	bernoulli	NOUN
easat-10856	199	14	numbers	number	NOUN
easat-10856	199	15	,	,	PUNCT
easat-10856	199	16	and	and	CCONJ
easat-10856	199	17	in	in	ADP
easat-10856	199	18	the	the	DET
easat-10856	199	19	second	second	ADJ
easat-10856	199	20	part	part	NOUN
easat-10856	199	21	,	,	PUNCT
easat-10856	199	22	we	we	PRON
easat-10856	199	23	focused	focus	VERB
easat-10856	199	24	on	on	ADP
easat-10856	199	25	calculating	calculate	VERB
easat-10856	199	26	the	the	DET
easat-10856	199	27	first	first	ADJ
easat-10856	199	28	twenty	twenty	NUM
easat-10856	199	29	euler	euler	NOUN
easat-10856	199	30	numbers	number	NOUN
easat-10856	199	31	.	.	PUNCT
easat-10856	200	1	the	the	DET
easat-10856	200	2	most	most	ADV
easat-10856	200	3	convenient	convenient	ADJ
easat-10856	200	4	,	,	PUNCT
easat-10856	200	5	suitable	suitable	ADJ
easat-10856	200	6	,	,	PUNCT
easat-10856	200	7	and	and	CCONJ
easat-10856	200	8	important	important	ADJ
easat-10856	200	9	expression	expression	NOUN
easat-10856	200	10	that	that	PRON
easat-10856	200	11	relates	relate	VERB
easat-10856	200	12	bernoulli	bernoulli	NOUN
easat-10856	200	13	numbers	number	NOUN
easat-10856	200	14	,	,	PUNCT
easat-10856	200	15	according	accord	VERB
easat-10856	200	16	to	to	ADP
easat-10856	200	17	tsuneo	tsuneo	NOUN
easat-10856	200	18	et	et	PROPN
easat-10856	200	19	al	al	PROPN
easat-10856	200	20	.	.	PUNCT
easat-10856	201	1	[	[	X
easat-10856	201	2	21	21	NUM
easat-10856	201	3	]	]	PUNCT
easat-10856	201	4	and	and	CCONJ
easat-10856	201	5	fernández	fernández	PROPN
easat-10856	201	6	[	[	X
easat-10856	201	7	5	5	NUM
easat-10856	201	8	]	]	PUNCT
easat-10856	201	9	,	,	PUNCT
easat-10856	201	10	which	which	PRON
easat-10856	201	11	has	have	AUX
easat-10856	201	12	been	be	AUX
easat-10856	201	13	used	use	VERB
easat-10856	201	14	in	in	ADP
easat-10856	201	15	this	this	DET
easat-10856	201	16	study	study	NOUN
easat-10856	201	17	,	,	PUNCT
easat-10856	201	18	is	be	AUX
easat-10856	201	19	:	:	PUNCT
easat-10856	201	20	(	(	PUNCT
easat-10856	201	21	2𝑛	2𝑛	NOUN
easat-10856	201	22	+	+	CCONJ
easat-10856	201	23	1	1	NUM
easat-10856	201	24	1	1	NUM
easat-10856	201	25	)	)	PUNCT
easat-10856	201	26	𝐵𝑛	𝐵𝑛	PROPN
easat-10856	201	27	−	−	PROPN
easat-10856	201	28	(	(	PUNCT
easat-10856	201	29	2𝑛	2𝑛	NOUN
easat-10856	201	30	+	+	CCONJ
easat-10856	201	31	1	1	NUM
easat-10856	201	32	3	3	NUM
easat-10856	201	33	)	)	PUNCT
easat-10856	201	34	𝐵𝑛−1	𝐵𝑛−1	PROPN
easat-10856	201	35	+	+	CCONJ
easat-10856	201	36	(	(	PUNCT
easat-10856	201	37	2𝑛	2𝑛	NUM
easat-10856	201	38	+	+	CCONJ
easat-10856	201	39	1	1	NUM
easat-10856	201	40	5	5	NUM
easat-10856	201	41	)	)	PUNCT
easat-10856	201	42	𝐵𝑛−2	𝐵𝑛−2	PROPN
easat-10856	201	43	+	+	CCONJ
easat-10856	201	44	(	(	PUNCT
easat-10856	201	45	−1)𝑛−1	−1)𝑛−1	INTJ
easat-10856	201	46	(	(	PUNCT
easat-10856	201	47	2𝑛	2𝑛	NOUN
easat-10856	201	48	+	+	CCONJ
easat-10856	201	49	1	1	NUM
easat-10856	201	50	2𝑛	2𝑛	NUM
easat-10856	201	51	−	−	NOUN
easat-10856	201	52	1	1	NUM
easat-10856	201	53	)	)	PUNCT
easat-10856	201	54	𝐵1	𝐵1	NOUN
easat-10856	201	55	+	+	CCONJ
easat-10856	201	56	(	(	PUNCT
easat-10856	201	57	−1)𝑛	−1)𝑛	X
easat-10856	201	58	(	(	PUNCT
easat-10856	201	59	𝑛	𝑛	PROPN
easat-10856	201	60	−	−	NUM
easat-10856	201	61	1	1	NUM
easat-10856	201	62	2	2	NUM
easat-10856	201	63	)	)	PUNCT
easat-10856	201	64	=	=	SYM
easat-10856	201	65	0	0	NUM
easat-10856	201	66	,	,	PUNCT
easat-10856	201	67	procedure	procedure	NOUN
easat-10856	201	68	:	:	PUNCT
easat-10856	201	69	calculation	calculation	NOUN
easat-10856	201	70	of	of	ADP
easat-10856	201	71	bernoulli	bernoulli	NOUN
easat-10856	201	72	numbers	number	NOUN
easat-10856	201	73	(	(	PUNCT
easat-10856	201	74	2𝑛	2𝑛	NOUN
easat-10856	201	75	+	+	CCONJ
easat-10856	201	76	1	1	NUM
easat-10856	201	77	1	1	NUM
easat-10856	201	78	)	)	PUNCT
easat-10856	201	79	𝐵𝑛	𝐵𝑛	PROPN
easat-10856	201	80	−	−	PROPN
easat-10856	201	81	(	(	PUNCT
easat-10856	201	82	2𝑛	2𝑛	NOUN
easat-10856	201	83	+	+	CCONJ
easat-10856	201	84	1	1	NUM
easat-10856	201	85	3	3	NUM
easat-10856	201	86	)	)	PUNCT
easat-10856	201	87	𝐵𝑛−1	𝐵𝑛−1	PROPN
easat-10856	201	88	+	+	CCONJ
easat-10856	201	89	(	(	PUNCT
easat-10856	201	90	2𝑛	2𝑛	NUM
easat-10856	201	91	+	+	CCONJ
easat-10856	201	92	1	1	NUM
easat-10856	201	93	5	5	NUM
easat-10856	201	94	)	)	PUNCT
easat-10856	201	95	𝐵𝑛−2	𝐵𝑛−2	PROPN
easat-10856	201	96	+	+	CCONJ
easat-10856	201	97	(	(	PUNCT
easat-10856	201	98	−1)𝑛−1	−1)𝑛−1	INTJ
easat-10856	201	99	(	(	PUNCT
easat-10856	201	100	2𝑛	2𝑛	NOUN
easat-10856	201	101	+	+	CCONJ
easat-10856	201	102	1	1	NUM
easat-10856	201	103	2𝑛	2𝑛	NUM
easat-10856	201	104	−	−	NOUN
easat-10856	201	105	1	1	NUM
easat-10856	201	106	)	)	PUNCT
easat-10856	201	107	𝐵1	𝐵1	NOUN
easat-10856	201	108	+	+	CCONJ
easat-10856	201	109	(	(	PUNCT
easat-10856	201	110	−1)𝑛	−1)𝑛	X
easat-10856	201	111	(	(	PUNCT
easat-10856	201	112	𝑛	𝑛	PROPN
easat-10856	201	113	−	−	NUM
easat-10856	201	114	1	1	NUM
easat-10856	201	115	2	2	NUM
easat-10856	201	116	)	)	PUNCT
easat-10856	201	117	=	=	SYM
easat-10856	201	118	0	0	NUM
easat-10856	201	119	,	,	PUNCT
easat-10856	201	120	the	the	DET
easat-10856	201	121	above	above	ADJ
easat-10856	201	122	expression	expression	NOUN
easat-10856	201	123	has	have	AUX
easat-10856	201	124	been	be	AUX
easat-10856	201	125	used	use	VERB
easat-10856	201	126	to	to	PART
easat-10856	201	127	evaluate	evaluate	VERB
easat-10856	201	128	the	the	DET
easat-10856	201	129	bernoulli	bernoulli	NOUN
easat-10856	201	130	numbers	number	NOUN
easat-10856	201	131	(	(	PUNCT
easat-10856	201	132	𝐵𝑛	𝐵𝑛	PROPN
easat-10856	201	133	)	)	PUNCT
easat-10856	201	134	;	;	PUNCT
easat-10856	201	135	whose	whose	DET
easat-10856	201	136	calculations	calculation	NOUN
easat-10856	201	137	are	be	AUX
easat-10856	201	138	presented	present	VERB
easat-10856	201	139	according	accord	VERB
easat-10856	201	140	to	to	ADP
easat-10856	201	141	the	the	DET
easat-10856	201	142	development	development	NOUN
easat-10856	201	143	outlined	outline	VERB
easat-10856	201	144	in	in	ADP
easat-10856	201	145	summarized	summarize	VERB
easat-10856	201	146	form	form	NOUN
easat-10856	201	147	below	below	ADV
easat-10856	201	148	:	:	PUNCT
easat-10856	201	149	calculation	calculation	NOUN
easat-10856	201	150	,	,	PUNCT
easat-10856	201	151	according	accord	VERB
easat-10856	201	152	to	to	ADP
easat-10856	201	153	the	the	DET
easat-10856	201	154	binomial	binomial	ADJ
easat-10856	201	155	formula	formula	NOUN
easat-10856	201	156	for	for	ADP
easat-10856	201	157	the	the	DET
easat-10856	201	158	bernoulli	bernoulli	NOUN
easat-10856	201	159	number	number	NOUN
easat-10856	201	160	,	,	PUNCT
easat-10856	201	161	of	of	ADP
easat-10856	201	162	𝐵1	𝐵1	NOUN
easat-10856	201	163	(	(	PUNCT
easat-10856	201	164	3	3	NUM
easat-10856	201	165	1	1	NUM
easat-10856	201	166	)	)	PUNCT
easat-10856	201	167	𝐵1	𝐵1	NOUN
easat-10856	201	168	−	−	PROPN
easat-10856	202	1	(	(	PUNCT
easat-10856	202	2	1	1	NUM
easat-10856	202	3	−	−	NUM
easat-10856	202	4	1	1	NUM
easat-10856	202	5	2	2	NUM
easat-10856	202	6	)	)	PUNCT
easat-10856	202	7	=	=	SYM
easat-10856	202	8	0	0	NUM
easat-10856	202	9	;	;	PUNCT
easat-10856	202	10	3	3	NUM
easat-10856	202	11	!	!	SYM
easat-10856	202	12	1!×2	1!×2	NUM
easat-10856	202	13	!	!	PUNCT
easat-10856	203	1	𝐵1	𝐵1	NOUN
easat-10856	203	2	=	=	NOUN
easat-10856	203	3	1	1	NUM
easat-10856	203	4	2	2	NUM
easat-10856	203	5	⇒	⇒	NOUN
easat-10856	203	6	𝐵1	𝐵1	NOUN
easat-10856	203	7	=	=	NOUN
easat-10856	203	8	1	1	NUM
easat-10856	203	9	6	6	NUM
easat-10856	203	10	calculation	calculation	NOUN
easat-10856	203	11	,	,	PUNCT
easat-10856	203	12	according	accord	VERB
easat-10856	203	13	to	to	ADP
easat-10856	203	14	the	the	DET
easat-10856	203	15	binomial	binomial	ADJ
easat-10856	203	16	formula	formula	NOUN
easat-10856	203	17	for	for	ADP
easat-10856	203	18	the	the	DET
easat-10856	203	19	bernoulli	bernoulli	NOUN
easat-10856	203	20	number	number	NOUN
easat-10856	203	21	,	,	PUNCT
easat-10856	203	22	of	of	ADP
easat-10856	203	23	𝐵2	𝐵2	NOUN
easat-10856	203	24	(	(	PUNCT
easat-10856	203	25	5	5	NUM
easat-10856	203	26	1	1	NUM
easat-10856	203	27	)	)	PUNCT
easat-10856	203	28	𝐵2	𝐵2	NOUN
easat-10856	203	29	−	−	PROPN
easat-10856	203	30	(	(	PUNCT
easat-10856	203	31	5	5	NUM
easat-10856	203	32	3	3	NUM
easat-10856	203	33	)	)	PUNCT
easat-10856	203	34	×	×	NOUN
easat-10856	203	35	1	1	NUM
easat-10856	203	36	6	6	NUM
easat-10856	203	37	+	+	CCONJ
easat-10856	203	38	(	(	PUNCT
easat-10856	203	39	2	2	NUM
easat-10856	203	40	−	−	NUM
easat-10856	203	41	1	1	NUM
easat-10856	203	42	2	2	NUM
easat-10856	203	43	)	)	PUNCT
easat-10856	203	44	=	=	SYM
easat-10856	203	45	0	0	NUM
easat-10856	203	46	;	;	PUNCT
easat-10856	203	47	5	5	NUM
easat-10856	203	48	!	!	SYM
easat-10856	203	49	1!×4	1!×4	NUM
easat-10856	203	50	!	!	PUNCT
easat-10856	204	1	𝐵2	𝐵2	NOUN
easat-10856	204	2	−	−	NOUN
easat-10856	204	3	5	5	NUM
easat-10856	204	4	!	!	SYM
easat-10856	204	5	3!×3	3!×3	NUM
easat-10856	204	6	!	!	PUNCT
easat-10856	205	1	×	×	NOUN
easat-10856	205	2	1	1	NUM
easat-10856	205	3	6	6	NUM
easat-10856	205	4	+	+	CCONJ
easat-10856	205	5	3	3	NUM
easat-10856	205	6	2	2	NUM
easat-10856	205	7	=	=	SYM
easat-10856	205	8	0	0	NUM
easat-10856	205	9	⇒	⇒	NOUN
easat-10856	205	10	𝐵2	𝐵2	NOUN
easat-10856	205	11	=	=	NOUN
easat-10856	205	12	1	1	NUM
easat-10856	205	13	30	30	NUM
easat-10856	205	14	calculation	calculation	NOUN
easat-10856	205	15	,	,	PUNCT
easat-10856	205	16	according	accord	VERB
easat-10856	205	17	to	to	ADP
easat-10856	205	18	the	the	DET
easat-10856	205	19	binomial	binomial	ADJ
easat-10856	205	20	formula	formula	NOUN
easat-10856	205	21	for	for	ADP
easat-10856	205	22	the	the	DET
easat-10856	205	23	bernoulli	bernoulli	NOUN
easat-10856	205	24	number	number	NOUN
easat-10856	205	25	,	,	PUNCT
easat-10856	205	26	of	of	ADP
easat-10856	205	27	𝐵3	𝐵3	NOUN
easat-10856	205	28	(	(	PUNCT
easat-10856	205	29	7	7	NUM
easat-10856	205	30	1	1	NUM
easat-10856	205	31	)	)	PUNCT
easat-10856	205	32	×	×	NOUN
easat-10856	205	33	𝐵3	𝐵3	NOUN
easat-10856	205	34	−	−	PROPN
easat-10856	206	1	(	(	PUNCT
easat-10856	206	2	7	7	NUM
easat-10856	206	3	3	3	NUM
easat-10856	206	4	)	)	PUNCT
easat-10856	206	5	×	×	NOUN
easat-10856	206	6	1	1	NUM
easat-10856	206	7	30	30	NUM
easat-10856	206	8	+	+	CCONJ
easat-10856	206	9	(	(	PUNCT
easat-10856	206	10	7	7	NUM
easat-10856	206	11	5	5	NUM
easat-10856	206	12	)	)	PUNCT
easat-10856	206	13	×	×	NOUN
easat-10856	206	14	1	1	NUM
easat-10856	206	15	6	6	NUM
easat-10856	206	16	−	−	PROPN
easat-10856	206	17	(	(	PUNCT
easat-10856	206	18	3	3	NUM
easat-10856	206	19	−	−	NUM
easat-10856	206	20	1	1	NUM
easat-10856	206	21	2	2	NUM
easat-10856	206	22	)	)	PUNCT
easat-10856	206	23	=	=	SYM
easat-10856	206	24	0	0	NUM
easat-10856	206	25	;	;	PUNCT
easat-10856	206	26	7	7	NUM
easat-10856	206	27	!	!	NOUN
easat-10856	206	28	1!×6	1!×6	NUM
easat-10856	206	29	!	!	PUNCT
easat-10856	207	1	×	×	PROPN
easat-10856	207	2	𝐵3	𝐵3	NOUN
easat-10856	207	3	−	−	PROPN
easat-10856	208	1	7	7	NUM
easat-10856	208	2	!	!	SYM
easat-10856	208	3	3!×4	3!×4	NUM
easat-10856	208	4	!	!	PUNCT
easat-10856	209	1	×	×	NOUN
easat-10856	209	2	1	1	NUM
easat-10856	209	3	30	30	NUM
easat-10856	209	4	+	+	CCONJ
easat-10856	209	5	7	7	NUM
easat-10856	209	6	!	!	NUM
easat-10856	209	7	5!×2	5!×2	NUM
easat-10856	209	8	!	!	PUNCT
easat-10856	210	1	×	×	NOUN
easat-10856	210	2	1	1	NUM
easat-10856	210	3	6	6	NUM
easat-10856	210	4	−	−	NUM
easat-10856	210	5	5	5	NUM
easat-10856	210	6	2	2	NUM
easat-10856	210	7	=	=	SYM
easat-10856	210	8	0	0	NUM
easat-10856	210	9	⇒	⇒	NOUN
easat-10856	210	10	𝐵3	𝐵3	NOUN
easat-10856	211	1	=	=	SYM
easat-10856	211	2	1	1	NUM
easat-10856	211	3	42	42	NUM
easat-10856	211	4	calculation	calculation	NOUN
easat-10856	211	5	,	,	PUNCT
easat-10856	211	6	according	accord	VERB
easat-10856	211	7	to	to	ADP
easat-10856	211	8	the	the	DET
easat-10856	211	9	binomial	binomial	ADJ
easat-10856	211	10	formula	formula	NOUN
easat-10856	211	11	for	for	ADP
easat-10856	211	12	the	the	DET
easat-10856	211	13	bernoulli	bernoulli	NOUN
easat-10856	211	14	number	number	NOUN
easat-10856	211	15	,	,	PUNCT
easat-10856	211	16	of	of	ADP
easat-10856	211	17	𝐵4	𝐵4	NOUN
easat-10856	211	18	(	(	PUNCT
easat-10856	211	19	9	9	NUM
easat-10856	211	20	1	1	NUM
easat-10856	211	21	)	)	PUNCT
easat-10856	211	22	×	×	NOUN
easat-10856	211	23	𝐵4	𝐵4	NOUN
easat-10856	211	24	−	−	PROPN
easat-10856	211	25	(	(	PUNCT
easat-10856	211	26	9	9	NUM
easat-10856	211	27	3	3	NUM
easat-10856	211	28	)	)	PUNCT
easat-10856	211	29	×	×	NOUN
easat-10856	211	30	1	1	NUM
easat-10856	211	31	42	42	NUM
easat-10856	211	32	+	+	CCONJ
easat-10856	211	33	(	(	PUNCT
easat-10856	211	34	9	9	NUM
easat-10856	211	35	5	5	NUM
easat-10856	211	36	)	)	PUNCT
easat-10856	211	37	×	×	NOUN
easat-10856	211	38	1	1	NUM
easat-10856	211	39	30	30	NUM
easat-10856	211	40	−	−	NOUN
easat-10856	211	41	(	(	PUNCT
easat-10856	211	42	9	9	NUM
easat-10856	211	43	7	7	NUM
easat-10856	211	44	)	)	PUNCT
easat-10856	211	45	×	×	NOUN
easat-10856	211	46	1	1	NUM
easat-10856	211	47	6	6	NUM
easat-10856	211	48	+	+	CCONJ
easat-10856	211	49	(	(	PUNCT
easat-10856	211	50	4	4	NUM
easat-10856	211	51	−	−	NUM
easat-10856	211	52	1	1	NUM
easat-10856	211	53	2	2	NUM
easat-10856	211	54	)	)	PUNCT
easat-10856	211	55	=	=	SYM
easat-10856	212	1	0	0	NUM
easat-10856	212	2	9	9	NUM
easat-10856	212	3	!	!	SYM
easat-10856	212	4	1!×8	1!×8	NUM
easat-10856	212	5	!	!	PUNCT
easat-10856	213	1	×	×	NOUN
easat-10856	213	2	𝐵4	𝐵4	NOUN
easat-10856	213	3	−	−	PROPN
easat-10856	213	4	9	9	NUM
easat-10856	213	5	!	!	SYM
easat-10856	213	6	3!×6	3!×6	NUM
easat-10856	213	7	!	!	PUNCT
easat-10856	214	1	×	×	NOUN
easat-10856	214	2	1	1	NUM
easat-10856	214	3	42	42	NUM
easat-10856	214	4	+	+	CCONJ
easat-10856	214	5	9	9	NUM
easat-10856	214	6	!	!	NOUN
easat-10856	214	7	5!×4	5!×4	NOUN
easat-10856	214	8	!	!	PUNCT
easat-10856	215	1	×	×	NOUN
easat-10856	215	2	1	1	NUM
easat-10856	215	3	30	30	NUM
easat-10856	215	4	−	−	NOUN
easat-10856	215	5	9	9	NUM
easat-10856	215	6	!	!	PUNCT
easat-10856	215	7	7!×2	7!×2	NUM
easat-10856	215	8	!	!	PUNCT
easat-10856	216	1	×	×	NOUN
easat-10856	216	2	1	1	NUM
easat-10856	216	3	6	6	NUM
easat-10856	216	4	+	+	CCONJ
easat-10856	216	5	7	7	NUM
easat-10856	216	6	2	2	NUM
easat-10856	216	7	=	=	SYM
easat-10856	216	8	0	0	NUM
easat-10856	216	9	⇒	⇒	NOUN
easat-10856	216	10	𝐵4	𝐵4	NOUN
easat-10856	216	11	=	=	SYM
easat-10856	216	12	1	1	NUM
easat-10856	216	13	30	30	NUM
easat-10856	216	14	calculation	calculation	NOUN
easat-10856	216	15	,	,	PUNCT
easat-10856	216	16	according	accord	VERB
easat-10856	216	17	to	to	ADP
easat-10856	216	18	the	the	DET
easat-10856	216	19	binomial	binomial	ADJ
easat-10856	216	20	formula	formula	NOUN
easat-10856	216	21	for	for	ADP
easat-10856	216	22	the	the	DET
easat-10856	216	23	bernoulli	bernoulli	NOUN
easat-10856	216	24	number	number	NOUN
easat-10856	216	25	,	,	PUNCT
easat-10856	216	26	of	of	ADP
easat-10856	216	27	𝐵5	𝐵5	NOUN
easat-10856	216	28	279	279	NUM
easat-10856	216	29	edelweiss	edelweiss	PROPN
easat-10856	216	30	applied	apply	VERB
easat-10856	216	31	science	science	NOUN
easat-10856	216	32	and	and	CCONJ
easat-10856	216	33	technology	technology	NOUN
easat-10856	216	34	issn	issn	PROPN
easat-10856	216	35	:	:	PUNCT
easat-10856	216	36	2576	2576	NUM
easat-10856	216	37	-	-	SYM
easat-10856	216	38	8484	8484	NUM
easat-10856	216	39	vol	vol	NOUN
easat-10856	216	40	.	.	PROPN
easat-10856	217	1	9	9	NUM
easat-10856	217	2	,	,	PUNCT
easat-10856	217	3	no	no	INTJ
easat-10856	217	4	.	.	NOUN
easat-10856	217	5	11	11	NUM
easat-10856	217	6	:	:	PUNCT
easat-10856	217	7	274	274	NUM
easat-10856	217	8	-	-	SYM
easat-10856	217	9	288	288	NUM
easat-10856	217	10	,	,	PUNCT
easat-10856	217	11	2025	2025	NUM
easat-10856	217	12	doi	doi	NOUN
easat-10856	217	13	:	:	PUNCT
easat-10856	217	14	10.55214/2576	10.55214/2576	NUM
easat-10856	217	15	-	-	PUNCT
easat-10856	217	16	8484.v9i11.10856	8484.v9i11.10856	NUM
easat-10856	217	17	©	©	PROPN
easat-10856	217	18	2025	2025	NUM
easat-10856	217	19	by	by	ADP
easat-10856	217	20	the	the	DET
easat-10856	217	21	authors	author	NOUN
easat-10856	217	22	;	;	PUNCT
easat-10856	217	23	licensee	licensee	PROPN
easat-10856	217	24	learning	learning	NOUN
easat-10856	217	25	gate	gate	NOUN
easat-10856	217	26	(	(	PUNCT
easat-10856	217	27	11	11	NUM
easat-10856	217	28	1	1	NUM
easat-10856	217	29	)	)	PUNCT
easat-10856	217	30	𝐵5	𝐵5	NOUN
easat-10856	217	31	−	−	NOUN
easat-10856	218	1	(	(	PUNCT
easat-10856	218	2	11	11	NUM
easat-10856	218	3	3	3	NUM
easat-10856	218	4	)	)	PUNCT
easat-10856	218	5	1	1	NUM
easat-10856	218	6	30	30	NUM
easat-10856	218	7	+	+	CCONJ
easat-10856	218	8	(	(	PUNCT
easat-10856	218	9	11	11	NUM
easat-10856	218	10	5	5	NUM
easat-10856	218	11	)	)	PUNCT
easat-10856	218	12	1	1	NUM
easat-10856	218	13	42	42	NUM
easat-10856	218	14	−	−	NOUN
easat-10856	218	15	(	(	PUNCT
easat-10856	218	16	11	11	NUM
easat-10856	218	17	7	7	NUM
easat-10856	218	18	)	)	PUNCT
easat-10856	218	19	1	1	NUM
easat-10856	218	20	30	30	NUM
easat-10856	218	21	+	+	CCONJ
easat-10856	218	22	(	(	PUNCT
easat-10856	218	23	11	11	NUM
easat-10856	218	24	9	9	NUM
easat-10856	218	25	)	)	PUNCT
easat-10856	218	26	1	1	NUM
easat-10856	218	27	6	6	NUM
easat-10856	218	28	−	−	NOUN
easat-10856	218	29	(	(	PUNCT
easat-10856	218	30	5	5	NUM
easat-10856	218	31	−	−	NUM
easat-10856	218	32	1	1	NUM
easat-10856	218	33	2	2	NUM
easat-10856	218	34	)	)	PUNCT
easat-10856	218	35	=	=	SYM
easat-10856	218	36	0	0	NUM
easat-10856	218	37	11	11	NUM
easat-10856	218	38	!	!	PUNCT
easat-10856	219	1	1!×10	1!×10	X
easat-10856	219	2	!	!	PUNCT
easat-10856	219	3	𝐵5	𝐵5	NOUN
easat-10856	219	4	−	−	PROPN
easat-10856	219	5	11	11	NUM
easat-10856	219	6	!	!	PUNCT
easat-10856	219	7	3!×8	3!×8	NUM
easat-10856	219	8	!	!	PUNCT
easat-10856	220	1	1	1	NUM
easat-10856	220	2	30	30	NUM
easat-10856	220	3	+	+	CCONJ
easat-10856	220	4	11	11	NUM
easat-10856	220	5	!	!	X
easat-10856	221	1	5!×6	5!×6	NUM
easat-10856	221	2	!	!	PUNCT
easat-10856	222	1	×	×	NOUN
easat-10856	222	2	1	1	NUM
easat-10856	222	3	42	42	NUM
easat-10856	222	4	−	−	NOUN
easat-10856	222	5	11	11	NUM
easat-10856	222	6	!	!	PUNCT
easat-10856	223	1	7!×4	7!×4	NUM
easat-10856	223	2	!	!	NOUN
easat-10856	223	3	1	1	NUM
easat-10856	223	4	30	30	NUM
easat-10856	223	5	+	+	CCONJ
easat-10856	223	6	11	11	NUM
easat-10856	223	7	!	!	PUNCT
easat-10856	224	1	9!×2	9!×2	NUM
easat-10856	224	2	!	!	PUNCT
easat-10856	225	1	−	−	NOUN
easat-10856	225	2	9	9	NUM
easat-10856	225	3	2	2	NUM
easat-10856	225	4	=	=	SYM
easat-10856	225	5	0	0	NUM
easat-10856	225	6	⇒	⇒	NOUN
easat-10856	225	7	𝐵5	𝐵5	NOUN
easat-10856	225	8	=	=	NOUN
easat-10856	225	9	5	5	NUM
easat-10856	225	10	66	66	NUM
easat-10856	225	11	calculation	calculation	NOUN
easat-10856	225	12	,	,	PUNCT
easat-10856	225	13	according	accord	VERB
easat-10856	225	14	to	to	ADP
easat-10856	225	15	the	the	DET
easat-10856	225	16	binomial	binomial	ADJ
easat-10856	225	17	formula	formula	NOUN
easat-10856	225	18	for	for	ADP
easat-10856	225	19	the	the	DET
easat-10856	225	20	bernoulli	bernoulli	NOUN
easat-10856	225	21	number	number	NOUN
easat-10856	225	22	,	,	PUNCT
easat-10856	225	23	of	of	ADP
easat-10856	225	24	𝐵6	𝐵6	NOUN
easat-10856	225	25	(	(	PUNCT
easat-10856	225	26	13	13	NUM
easat-10856	225	27	1	1	NUM
easat-10856	225	28	)	)	PUNCT
easat-10856	225	29	𝐵6	𝐵6	NOUN
easat-10856	225	30	−	−	PROPN
easat-10856	225	31	(	(	PUNCT
easat-10856	225	32	13	13	NUM
easat-10856	225	33	3	3	NUM
easat-10856	225	34	)	)	PUNCT
easat-10856	225	35	5	5	NUM
easat-10856	225	36	66	66	NUM
easat-10856	225	37	+	+	CCONJ
easat-10856	225	38	(	(	PUNCT
easat-10856	225	39	13	13	NUM
easat-10856	225	40	5	5	NUM
easat-10856	225	41	)	)	PUNCT
easat-10856	225	42	1	1	NUM
easat-10856	225	43	30	30	NUM
easat-10856	225	44	−	−	NOUN
easat-10856	225	45	(	(	PUNCT
easat-10856	225	46	13	13	NUM
easat-10856	225	47	7	7	NUM
easat-10856	225	48	)	)	PUNCT
easat-10856	225	49	1	1	NUM
easat-10856	225	50	42	42	NUM
easat-10856	225	51	+	+	CCONJ
easat-10856	225	52	(	(	PUNCT
easat-10856	225	53	13	13	NUM
easat-10856	225	54	9	9	NUM
easat-10856	225	55	)	)	PUNCT
easat-10856	225	56	1	1	NUM
easat-10856	225	57	30	30	NUM
easat-10856	225	58	−	−	NOUN
easat-10856	225	59	(	(	PUNCT
easat-10856	225	60	13	13	NUM
easat-10856	225	61	11	11	NUM
easat-10856	225	62	)	)	PUNCT
easat-10856	225	63	1	1	NUM
easat-10856	225	64	6	6	NUM
easat-10856	225	65	+	+	CCONJ
easat-10856	225	66	(	(	PUNCT
easat-10856	225	67	6	6	NUM
easat-10856	225	68	−	−	NUM
easat-10856	225	69	1	1	NUM
easat-10856	225	70	2	2	NUM
easat-10856	225	71	)	)	PUNCT
easat-10856	225	72	=	=	SYM
easat-10856	225	73	0	0	NUM
easat-10856	225	74	13	13	NUM
easat-10856	225	75	!	!	PUNCT
easat-10856	226	1	1!×12	1!×12	NUM
easat-10856	226	2	!	!	PUNCT
easat-10856	226	3	𝐵6	𝐵6	PROPN
easat-10856	226	4	−	−	PROPN
easat-10856	226	5	13	13	NUM
easat-10856	226	6	!	!	SYM
easat-10856	226	7	3!×10	3!×10	NUM
easat-10856	226	8	!	!	PUNCT
easat-10856	226	9	5	5	NUM
easat-10856	226	10	66	66	NUM
easat-10856	226	11	+	+	CCONJ
easat-10856	226	12	13	13	NUM
easat-10856	226	13	!	!	X
easat-10856	226	14	5!×8	5!×8	NUM
easat-10856	226	15	!	!	NOUN
easat-10856	227	1	1	1	NUM
easat-10856	227	2	30	30	NUM
easat-10856	227	3	−	−	NOUN
easat-10856	227	4	13	13	NUM
easat-10856	227	5	!	!	PUNCT
easat-10856	228	1	7!×6	7!×6	NUM
easat-10856	228	2	!	!	NOUN
easat-10856	228	3	1	1	NUM
easat-10856	228	4	42	42	NUM
easat-10856	228	5	+	+	NOUN
easat-10856	228	6	13	13	NUM
easat-10856	228	7	!	!	SYM
easat-10856	228	8	9!×4	9!×4	NUM
easat-10856	228	9	!	!	NOUN
easat-10856	229	1	1	1	NUM
easat-10856	229	2	30	30	NUM
easat-10856	229	3	−	−	NOUN
easat-10856	229	4	13	13	NUM
easat-10856	229	5	!	!	PUNCT
easat-10856	229	6	11!×2	11!×2	NUM
easat-10856	229	7	!	!	NOUN
easat-10856	230	1	1	1	NUM
easat-10856	230	2	6	6	NUM
easat-10856	230	3	+	+	CCONJ
easat-10856	230	4	11	11	NUM
easat-10856	230	5	2	2	NUM
easat-10856	230	6	=	=	SYM
easat-10856	230	7	0	0	NUM
easat-10856	230	8	⇒	⇒	NOUN
easat-10856	230	9	𝐵6	𝐵6	NOUN
easat-10856	230	10	=	=	PUNCT
easat-10856	230	11	691	691	NUM
easat-10856	230	12	2730	2730	NUM
easat-10856	230	13	calculation	calculation	NOUN
easat-10856	230	14	,	,	PUNCT
easat-10856	230	15	according	accord	VERB
easat-10856	230	16	to	to	ADP
easat-10856	230	17	the	the	DET
easat-10856	230	18	binomial	binomial	ADJ
easat-10856	230	19	formula	formula	NOUN
easat-10856	230	20	for	for	ADP
easat-10856	230	21	the	the	DET
easat-10856	230	22	bernoulli	bernoulli	NOUN
easat-10856	230	23	number	number	NOUN
easat-10856	230	24	,	,	PUNCT
easat-10856	230	25	of	of	ADP
easat-10856	230	26	𝐵7	𝐵7	PROPN
easat-10856	230	27	(	(	PUNCT
easat-10856	230	28	15	15	NUM
easat-10856	230	29	1	1	NUM
easat-10856	230	30	)	)	PUNCT
easat-10856	230	31	𝐵8	𝐵8	PROPN
easat-10856	230	32	−	−	PROPN
easat-10856	230	33	(	(	PUNCT
easat-10856	230	34	15	15	NUM
easat-10856	230	35	3	3	NUM
easat-10856	230	36	)	)	PUNCT
easat-10856	230	37	691	691	NUM
easat-10856	230	38	2730	2730	NUM
easat-10856	231	1	+	+	CCONJ
easat-10856	231	2	(	(	PUNCT
easat-10856	231	3	15	15	NUM
easat-10856	231	4	5	5	NUM
easat-10856	231	5	)	)	PUNCT
easat-10856	231	6	5	5	NUM
easat-10856	231	7	66	66	NUM
easat-10856	231	8	−	−	NOUN
easat-10856	231	9	(	(	PUNCT
easat-10856	231	10	15	15	NUM
easat-10856	231	11	7	7	NUM
easat-10856	231	12	)	)	PUNCT
easat-10856	231	13	1	1	NUM
easat-10856	231	14	30	30	NUM
easat-10856	231	15	+	+	CCONJ
easat-10856	231	16	(	(	PUNCT
easat-10856	231	17	15	15	NUM
easat-10856	231	18	9	9	NUM
easat-10856	231	19	)	)	PUNCT
easat-10856	231	20	1	1	NUM
easat-10856	231	21	42	42	NUM
easat-10856	231	22	−	−	NOUN
easat-10856	231	23	(	(	PUNCT
easat-10856	231	24	15	15	NUM
easat-10856	231	25	11	11	NUM
easat-10856	231	26	)	)	PUNCT
easat-10856	231	27	1	1	NUM
easat-10856	231	28	30	30	NUM
easat-10856	231	29	+	+	CCONJ
easat-10856	231	30	(	(	PUNCT
easat-10856	231	31	15	15	NUM
easat-10856	231	32	13	13	NUM
easat-10856	231	33	)	)	PUNCT
easat-10856	231	34	1	1	NUM
easat-10856	231	35	6	6	NUM
easat-10856	231	36	−	−	NOUN
easat-10856	231	37	(	(	PUNCT
easat-10856	231	38	7	7	NUM
easat-10856	231	39	−	−	NUM
easat-10856	231	40	1	1	NUM
easat-10856	231	41	2	2	NUM
easat-10856	231	42	)	)	PUNCT
easat-10856	231	43	=	=	SYM
easat-10856	232	1	0	0	NUM
easat-10856	232	2	15	15	NUM
easat-10856	232	3	!	!	PUNCT
easat-10856	232	4	1!×14	1!×14	NUM
easat-10856	232	5	!	!	PUNCT
easat-10856	232	6	𝐵7	𝐵7	PROPN
easat-10856	233	1	−	−	PROPN
easat-10856	233	2	15	15	NUM
easat-10856	233	3	!	!	PUNCT
easat-10856	234	1	3!×12	3!×12	NUM
easat-10856	234	2	!	!	PUNCT
easat-10856	235	1	691	691	NUM
easat-10856	235	2	2730	2730	NUM
easat-10856	235	3	+	+	CCONJ
easat-10856	235	4	15	15	NUM
easat-10856	235	5	!	!	X
easat-10856	235	6	5!×10	5!×10	NUM
easat-10856	235	7	!	!	PUNCT
easat-10856	235	8	5	5	NUM
easat-10856	235	9	66	66	NUM
easat-10856	235	10	−	−	NUM
easat-10856	235	11	15	15	NUM
easat-10856	235	12	!	!	PUNCT
easat-10856	236	1	7!×8	7!×8	NUM
easat-10856	236	2	!	!	NOUN
easat-10856	237	1	1	1	NUM
easat-10856	237	2	30	30	NUM
easat-10856	237	3	+	+	NUM
easat-10856	237	4	15	15	NUM
easat-10856	237	5	!	!	NOUN
easat-10856	237	6	9!×6	9!×6	NUM
easat-10856	237	7	!	!	PUNCT
easat-10856	238	1	−	−	NOUN
easat-10856	239	1	15	15	NUM
easat-10856	239	2	!	!	PUNCT
easat-10856	240	1	11!×4	11!×4	NUM
easat-10856	240	2	!	!	NOUN
easat-10856	240	3	1	1	NUM
easat-10856	240	4	30	30	NUM
easat-10856	240	5	+	+	NUM
easat-10856	240	6	15	15	NUM
easat-10856	240	7	!	!	PUNCT
easat-10856	240	8	13!×2	13!×2	ADV
easat-10856	240	9	!	!	PUNCT
easat-10856	241	1	1	1	NUM
easat-10856	241	2	6	6	NUM
easat-10856	241	3	−	−	NUM
easat-10856	241	4	13	13	NUM
easat-10856	241	5	2	2	NUM
easat-10856	241	6	=	=	SYM
easat-10856	241	7	0	0	PROPN
easat-10856	241	8	⇒	⇒	NOUN
easat-10856	241	9	𝐵7	𝐵7	NOUN
easat-10856	241	10	=	=	SYM
easat-10856	241	11	7	7	NUM
easat-10856	241	12	6	6	NUM
easat-10856	241	13	calculation	calculation	NOUN
easat-10856	241	14	,	,	PUNCT
easat-10856	241	15	according	accord	VERB
easat-10856	241	16	to	to	ADP
easat-10856	241	17	the	the	DET
easat-10856	241	18	binomial	binomial	ADJ
easat-10856	241	19	formula	formula	NOUN
easat-10856	241	20	for	for	ADP
easat-10856	241	21	the	the	DET
easat-10856	241	22	bernoulli	bernoulli	NOUN
easat-10856	241	23	number	number	NOUN
easat-10856	241	24	,	,	PUNCT
easat-10856	241	25	of	of	ADP
easat-10856	241	26	𝐵8	𝐵8	PROPN
easat-10856	241	27	(	(	PUNCT
easat-10856	241	28	17	17	NUM
easat-10856	241	29	1	1	NUM
easat-10856	241	30	)	)	PUNCT
easat-10856	241	31	𝐵8	𝐵8	PROPN
easat-10856	241	32	−	−	PROPN
easat-10856	241	33	(	(	PUNCT
easat-10856	241	34	17	17	NUM
easat-10856	241	35	3	3	NUM
easat-10856	241	36	)	)	PUNCT
easat-10856	241	37	7	7	NUM
easat-10856	241	38	6	6	NUM
easat-10856	241	39	+	+	CCONJ
easat-10856	241	40	(	(	PUNCT
easat-10856	241	41	17	17	NUM
easat-10856	241	42	5	5	NUM
easat-10856	241	43	)	)	PUNCT
easat-10856	241	44	691	691	NUM
easat-10856	241	45	2730	2730	NUM
easat-10856	241	46	−	−	NOUN
easat-10856	241	47	(	(	PUNCT
easat-10856	241	48	17	17	NUM
easat-10856	241	49	7	7	NUM
easat-10856	241	50	)	)	PUNCT
easat-10856	241	51	5	5	NUM
easat-10856	241	52	66	66	NUM
easat-10856	241	53	+	+	CCONJ
easat-10856	241	54	(	(	PUNCT
easat-10856	241	55	17	17	NUM
easat-10856	241	56	9	9	NUM
easat-10856	241	57	)	)	PUNCT
easat-10856	241	58	1	1	NUM
easat-10856	241	59	30	30	NUM
easat-10856	241	60	−	−	NOUN
easat-10856	241	61	(	(	PUNCT
easat-10856	241	62	17	17	NUM
easat-10856	241	63	11	11	NUM
easat-10856	241	64	)	)	PUNCT
easat-10856	241	65	1	1	NUM
easat-10856	241	66	42	42	NUM
easat-10856	242	1	+	+	CCONJ
easat-10856	242	2	(	(	PUNCT
easat-10856	242	3	17	17	NUM
easat-10856	242	4	13	13	NUM
easat-10856	242	5	)	)	PUNCT
easat-10856	242	6	1	1	NUM
easat-10856	242	7	30	30	NUM
easat-10856	242	8	−	−	NOUN
easat-10856	242	9	(	(	PUNCT
easat-10856	242	10	17	17	NUM
easat-10856	242	11	15	15	NUM
easat-10856	242	12	)	)	PUNCT
easat-10856	242	13	1	1	NUM
easat-10856	242	14	6	6	NUM
easat-10856	242	15	+	+	CCONJ
easat-10856	242	16	(	(	PUNCT
easat-10856	242	17	8	8	NUM
easat-10856	242	18	−	−	NUM
easat-10856	242	19	1	1	NUM
easat-10856	242	20	2	2	NUM
easat-10856	242	21	)	)	PUNCT
easat-10856	242	22	=	=	SYM
easat-10856	242	23	0	0	NUM
easat-10856	242	24	17	17	NUM
easat-10856	242	25	!	!	PUNCT
easat-10856	243	1	1!×16	1!×16	NUM
easat-10856	243	2	!	!	PUNCT
easat-10856	244	1	𝐵8	𝐵8	PROPN
easat-10856	244	2	−	−	PROPN
easat-10856	244	3	17	17	NUM
easat-10856	244	4	!	!	PUNCT
easat-10856	245	1	3!×14	3!×14	NUM
easat-10856	245	2	!	!	PUNCT
easat-10856	245	3	7	7	NUM
easat-10856	245	4	6	6	NUM
easat-10856	245	5	+	+	NUM
easat-10856	245	6	17	17	NUM
easat-10856	245	7	!	!	PUNCT
easat-10856	245	8	5!×12	5!×12	NUM
easat-10856	245	9	!	!	PUNCT
easat-10856	246	1	691	691	NUM
easat-10856	246	2	2730	2730	NUM
easat-10856	246	3	−	−	NOUN
easat-10856	246	4	17	17	NUM
easat-10856	246	5	!	!	PUNCT
easat-10856	247	1	7!×10	7!×10	NUM
easat-10856	247	2	!	!	NOUN
easat-10856	247	3	5	5	NUM
easat-10856	247	4	66	66	NUM
easat-10856	247	5	+	+	CCONJ
easat-10856	247	6	17	17	NUM
easat-10856	247	7	!	!	PUNCT
easat-10856	248	1	9!×8	9!×8	NUM
easat-10856	248	2	!	!	NOUN
easat-10856	249	1	1	1	NUM
easat-10856	249	2	30	30	NUM
easat-10856	249	3	−	−	NUM
easat-10856	249	4	17	17	NUM
easat-10856	249	5	!	!	PUNCT
easat-10856	250	1	11!×6	11!×6	NUM
easat-10856	250	2	!	!	PUNCT
easat-10856	251	1	1	1	NUM
easat-10856	251	2	42	42	NUM
easat-10856	251	3	+	+	NOUN
easat-10856	251	4	17	17	NUM
easat-10856	251	5	!	!	PUNCT
easat-10856	252	1	13!×4	13!×4	X
easat-10856	252	2	!	!	NOUN
easat-10856	252	3	1	1	NUM
easat-10856	252	4	30	30	NUM
easat-10856	252	5	−	−	NUM
easat-10856	252	6	17	17	NUM
easat-10856	252	7	!	!	PUNCT
easat-10856	253	1	15!×2	15!×2	ADJ
easat-10856	253	2	!	!	PUNCT
easat-10856	254	1	1	1	NUM
easat-10856	254	2	6	6	NUM
easat-10856	254	3	+	+	CCONJ
easat-10856	254	4	15	15	NUM
easat-10856	254	5	2	2	NUM
easat-10856	254	6	=	=	SYM
easat-10856	254	7	0	0	NUM
easat-10856	254	8	⇒	⇒	NOUN
easat-10856	254	9	𝐵8	𝐵8	PROPN
easat-10856	254	10	=	=	SYM
easat-10856	254	11	3617	3617	NUM
easat-10856	254	12	510	510	NUM
easat-10856	254	13	calculation	calculation	NOUN
easat-10856	254	14	,	,	PUNCT
easat-10856	254	15	according	accord	VERB
easat-10856	254	16	to	to	ADP
easat-10856	254	17	the	the	DET
easat-10856	254	18	binomial	binomial	ADJ
easat-10856	254	19	formula	formula	NOUN
easat-10856	254	20	for	for	ADP
easat-10856	254	21	the	the	DET
easat-10856	254	22	bernoulli	bernoulli	NOUN
easat-10856	254	23	number	number	NOUN
easat-10856	254	24	,	,	PUNCT
easat-10856	254	25	of	of	ADP
easat-10856	254	26	𝐵9	𝐵9	NOUN
easat-10856	254	27	(	(	PUNCT
easat-10856	254	28	19	19	NUM
easat-10856	254	29	1	1	NUM
easat-10856	254	30	)	)	PUNCT
easat-10856	254	31	𝐵9	𝐵9	NOUN
easat-10856	254	32	−	−	PROPN
easat-10856	254	33	(	(	PUNCT
easat-10856	254	34	19	19	NUM
easat-10856	254	35	3	3	NUM
easat-10856	254	36	)	)	PUNCT
easat-10856	254	37	3617	3617	NUM
easat-10856	254	38	510	510	NUM
easat-10856	255	1	+	+	CCONJ
easat-10856	255	2	(	(	PUNCT
easat-10856	255	3	19	19	NUM
easat-10856	255	4	5	5	NUM
easat-10856	255	5	)	)	PUNCT
easat-10856	255	6	7	7	NUM
easat-10856	255	7	6	6	NUM
easat-10856	255	8	−	−	NOUN
easat-10856	255	9	(	(	PUNCT
easat-10856	255	10	19	19	NUM
easat-10856	255	11	7	7	NUM
easat-10856	255	12	)	)	PUNCT
easat-10856	255	13	691	691	NUM
easat-10856	255	14	2730	2730	NUM
easat-10856	256	1	+	+	CCONJ
easat-10856	256	2	(	(	PUNCT
easat-10856	256	3	19	19	NUM
easat-10856	256	4	9	9	NUM
easat-10856	256	5	)	)	PUNCT
easat-10856	256	6	5	5	NUM
easat-10856	256	7	66	66	NUM
easat-10856	256	8	−	−	NOUN
easat-10856	256	9	(	(	PUNCT
easat-10856	256	10	19	19	NUM
easat-10856	256	11	11	11	NUM
easat-10856	256	12	)	)	PUNCT
easat-10856	256	13	1	1	NUM
easat-10856	256	14	30	30	NUM
easat-10856	256	15	+	+	CCONJ
easat-10856	256	16	(	(	PUNCT
easat-10856	256	17	19	19	NUM
easat-10856	256	18	13	13	NUM
easat-10856	256	19	)	)	PUNCT
easat-10856	256	20	1	1	NUM
easat-10856	256	21	42	42	NUM
easat-10856	256	22	−	−	NOUN
easat-10856	256	23	(	(	PUNCT
easat-10856	256	24	19	19	NUM
easat-10856	256	25	15	15	NUM
easat-10856	256	26	)	)	PUNCT
easat-10856	256	27	1	1	NUM
easat-10856	256	28	30	30	NUM
easat-10856	256	29	+	+	CCONJ
easat-10856	256	30	(	(	PUNCT
easat-10856	256	31	19	19	NUM
easat-10856	256	32	17	17	NUM
easat-10856	256	33	)	)	PUNCT
easat-10856	256	34	1	1	NUM
easat-10856	256	35	6	6	NUM
easat-10856	256	36	−	−	NOUN
easat-10856	256	37	(	(	PUNCT
easat-10856	256	38	9	9	NUM
easat-10856	256	39	−	−	NUM
easat-10856	256	40	1	1	NUM
easat-10856	256	41	2	2	NUM
easat-10856	256	42	)	)	PUNCT
easat-10856	256	43	=	=	SYM
easat-10856	256	44	0	0	NUM
easat-10856	256	45	19	19	NUM
easat-10856	256	46	!	!	PUNCT
easat-10856	257	1	1!×18	1!×18	NUM
easat-10856	257	2	!	!	PUNCT
easat-10856	258	1	𝐵9	𝐵9	PROPN
easat-10856	258	2	−	−	PROPN
easat-10856	258	3	19	19	NUM
easat-10856	258	4	!	!	PUNCT
easat-10856	258	5	3!×16	3!×16	NUM
easat-10856	258	6	!	!	PUNCT
easat-10856	259	1	3617	3617	NUM
easat-10856	259	2	510	510	NUM
easat-10856	259	3	+	+	NUM
easat-10856	259	4	19	19	NUM
easat-10856	259	5	!	!	PUNCT
easat-10856	259	6	5!×14	5!×14	NUM
easat-10856	259	7	!	!	PUNCT
easat-10856	260	1	7	7	NUM
easat-10856	260	2	6	6	NUM
easat-10856	260	3	−	−	NUM
easat-10856	260	4	19	19	NUM
easat-10856	260	5	!	!	PUNCT
easat-10856	260	6	7!×12	7!×12	NUM
easat-10856	260	7	!	!	PUNCT
easat-10856	261	1	691	691	NUM
easat-10856	261	2	2730	2730	NUM
easat-10856	261	3	+	+	CCONJ
easat-10856	261	4	19	19	NUM
easat-10856	261	5	!	!	NOUN
easat-10856	261	6	9!×10	9!×10	NOUN
easat-10856	261	7	!	!	PUNCT
easat-10856	262	1	5	5	NUM
easat-10856	262	2	66	66	NUM
easat-10856	262	3	−	−	NUM
easat-10856	262	4	19	19	NUM
easat-10856	262	5	!	!	PUNCT
easat-10856	262	6	11!×8	11!×8	NUM
easat-10856	262	7	!	!	PUNCT
easat-10856	263	1	1	1	NUM
easat-10856	263	2	30	30	NUM
easat-10856	263	3	+	+	NUM
easat-10856	263	4	19	19	NUM
easat-10856	263	5	!	!	PUNCT
easat-10856	263	6	13!×6	13!×6	X
easat-10856	263	7	!	!	PUNCT
easat-10856	264	1	1	1	NUM
easat-10856	264	2	42	42	NUM
easat-10856	264	3	−	−	NUM
easat-10856	264	4	19	19	NUM
easat-10856	264	5	!	!	PUNCT
easat-10856	264	6	15!×4	15!×4	NUM
easat-10856	264	7	!	!	PROPN
easat-10856	265	1	1	1	NUM
easat-10856	265	2	30	30	NUM
easat-10856	265	3	+	+	NUM
easat-10856	265	4	19	19	NUM
easat-10856	265	5	!	!	PUNCT
easat-10856	265	6	17!×2	17!×2	NUM
easat-10856	265	7	!	!	PUNCT
easat-10856	266	1	1	1	NUM
easat-10856	266	2	6	6	NUM
easat-10856	266	3	−	−	NUM
easat-10856	266	4	17	17	NUM
easat-10856	266	5	2	2	NUM
easat-10856	266	6	=	=	SYM
easat-10856	266	7	0	0	NUM
easat-10856	266	8	⇒	⇒	NOUN
easat-10856	266	9	𝐵9	𝐵9	NOUN
easat-10856	266	10	=	=	SYM
easat-10856	266	11	43867	43867	NUM
easat-10856	266	12	798	798	NUM
easat-10856	266	13	calculation	calculation	NOUN
easat-10856	266	14	,	,	PUNCT
easat-10856	266	15	according	accord	VERB
easat-10856	266	16	to	to	ADP
easat-10856	266	17	the	the	DET
easat-10856	266	18	binomial	binomial	ADJ
easat-10856	266	19	formula	formula	NOUN
easat-10856	266	20	for	for	ADP
easat-10856	266	21	the	the	DET
easat-10856	266	22	bernoulli	bernoulli	NOUN
easat-10856	266	23	number	number	NOUN
easat-10856	266	24	,	,	PUNCT
easat-10856	266	25	of	of	ADP
easat-10856	266	26	𝐵10	𝐵10	PROPN
easat-10856	266	27	(	(	PUNCT
easat-10856	266	28	21	21	NUM
easat-10856	266	29	1	1	NUM
easat-10856	266	30	)	)	PUNCT
easat-10856	266	31	𝐵10	𝐵10	PROPN
easat-10856	266	32	−	−	PROPN
easat-10856	266	33	(	(	PUNCT
easat-10856	266	34	21	21	NUM
easat-10856	266	35	3	3	NUM
easat-10856	266	36	)	)	PUNCT
easat-10856	266	37	43867	43867	NUM
easat-10856	267	1	798	798	NUM
easat-10856	268	1	+	+	CCONJ
easat-10856	268	2	(	(	PUNCT
easat-10856	268	3	25	25	NUM
easat-10856	268	4	5	5	NUM
easat-10856	268	5	)	)	PUNCT
easat-10856	268	6	3617	3617	NUM
easat-10856	268	7	510	510	NUM
easat-10856	268	8	−	−	PROPN
easat-10856	268	9	(	(	PUNCT
easat-10856	268	10	25	25	NUM
easat-10856	268	11	7	7	NUM
easat-10856	268	12	)	)	PUNCT
easat-10856	268	13	7	7	NUM
easat-10856	268	14	6	6	NUM
easat-10856	268	15	+	+	CCONJ
easat-10856	268	16	(	(	PUNCT
easat-10856	268	17	21	21	NUM
easat-10856	268	18	9	9	NUM
easat-10856	268	19	)	)	PUNCT
easat-10856	268	20	691	691	NUM
easat-10856	268	21	2730	2730	NUM
easat-10856	268	22	−	−	NOUN
easat-10856	268	23	(	(	PUNCT
easat-10856	268	24	21	21	NUM
easat-10856	268	25	11	11	NUM
easat-10856	268	26	)	)	PUNCT
easat-10856	268	27	5	5	NUM
easat-10856	268	28	66	66	NUM
easat-10856	268	29	+	+	CCONJ
easat-10856	268	30	(	(	PUNCT
easat-10856	268	31	21	21	NUM
easat-10856	268	32	13	13	NUM
easat-10856	268	33	)	)	PUNCT
easat-10856	268	34	1	1	NUM
easat-10856	268	35	30	30	NUM
easat-10856	268	36	−	−	NOUN
easat-10856	268	37	(	(	PUNCT
easat-10856	268	38	21	21	NUM
easat-10856	268	39	15	15	NUM
easat-10856	268	40	)	)	PUNCT
easat-10856	268	41	1	1	NUM
easat-10856	268	42	42	42	NUM
easat-10856	269	1	+	+	CCONJ
easat-10856	269	2	+	+	ADJ
easat-10856	269	3	(	(	PUNCT
easat-10856	269	4	21	21	NUM
easat-10856	269	5	17	17	NUM
easat-10856	269	6	)	)	PUNCT
easat-10856	269	7	1	1	NUM
easat-10856	269	8	30	30	NUM
easat-10856	269	9	−	−	NOUN
easat-10856	269	10	(	(	PUNCT
easat-10856	269	11	21	21	NUM
easat-10856	269	12	19	19	NUM
easat-10856	269	13	)	)	PUNCT
easat-10856	269	14	1	1	NUM
easat-10856	269	15	6	6	NUM
easat-10856	269	16	+	+	CCONJ
easat-10856	269	17	(	(	PUNCT
easat-10856	269	18	10	10	NUM
easat-10856	269	19	−	−	NUM
easat-10856	269	20	1	1	NUM
easat-10856	269	21	2	2	NUM
easat-10856	269	22	)	)	PUNCT
easat-10856	269	23	=	=	SYM
easat-10856	269	24	0	0	NUM
easat-10856	269	25	21	21	NUM
easat-10856	269	26	!	!	PUNCT
easat-10856	269	27	1!×20	1!×20	NUM
easat-10856	269	28	!	!	PUNCT
easat-10856	270	1	𝐵10	𝐵10	PROPN
easat-10856	271	1	−	−	NOUN
easat-10856	271	2	21	21	NUM
easat-10856	271	3	!	!	PUNCT
easat-10856	272	1	3!×18	3!×18	NUM
easat-10856	272	2	!	!	PUNCT
easat-10856	273	1	43867	43867	NUM
easat-10856	273	2	798	798	NUM
easat-10856	274	1	+	+	CCONJ
easat-10856	274	2	21	21	NUM
easat-10856	274	3	!	!	PUNCT
easat-10856	275	1	5!×16	5!×16	NUM
easat-10856	275	2	!	!	PUNCT
easat-10856	275	3	3617	3617	NUM
easat-10856	275	4	510	510	NUM
easat-10856	275	5	−	−	PROPN
easat-10856	275	6	21	21	NUM
easat-10856	275	7	!	!	PUNCT
easat-10856	275	8	7!×14	7!×14	NUM
easat-10856	275	9	!	!	PUNCT
easat-10856	276	1	7	7	NUM
easat-10856	276	2	6	6	NUM
easat-10856	276	3	+	+	SYM
easat-10856	276	4	21	21	NUM
easat-10856	276	5	!	!	PUNCT
easat-10856	276	6	9!×12	9!×12	NUM
easat-10856	276	7	!	!	PUNCT
easat-10856	277	1	691	691	NUM
easat-10856	277	2	2730	2730	NUM
easat-10856	277	3	−	−	NOUN
easat-10856	277	4	21	21	NUM
easat-10856	277	5	!	!	PUNCT
easat-10856	278	1	11!×10	11!×10	NUM
easat-10856	278	2	!	!	NOUN
easat-10856	279	1	5	5	NUM
easat-10856	279	2	66	66	NUM
easat-10856	279	3	+	+	CCONJ
easat-10856	279	4	21	21	NUM
easat-10856	279	5	!	!	PUNCT
easat-10856	279	6	13!×8	13!×8	NUM
easat-10856	279	7	!	!	PUNCT
easat-10856	280	1	1	1	NUM
easat-10856	280	2	30	30	NUM
easat-10856	280	3	−	−	NOUN
easat-10856	280	4	21	21	NUM
easat-10856	280	5	!	!	PUNCT
easat-10856	280	6	15!×6	15!×6	NUM
easat-10856	280	7	!	!	PUNCT
easat-10856	281	1	1	1	NUM
easat-10856	281	2	42	42	NUM
easat-10856	281	3	+	+	SYM
easat-10856	281	4	21	21	NUM
easat-10856	281	5	!	!	PUNCT
easat-10856	282	1	17!×4	17!×4	NUM
easat-10856	282	2	!	!	X
easat-10856	282	3	1	1	NUM
easat-10856	282	4	30	30	NUM
easat-10856	282	5	−	−	NUM
easat-10856	282	6	21	21	NUM
easat-10856	282	7	!	!	PUNCT
easat-10856	283	1	19!×2	19!×2	NOUN
easat-10856	283	2	!	!	PUNCT
easat-10856	284	1	1	1	NUM
easat-10856	284	2	6	6	NUM
easat-10856	284	3	+	+	SYM
easat-10856	284	4	19	19	NUM
easat-10856	284	5	2	2	NUM
easat-10856	284	6	=	=	SYM
easat-10856	284	7	0	0	NUM
easat-10856	284	8	⇒	⇒	NOUN
easat-10856	284	9	𝐵10	𝐵10	PROPN
easat-10856	284	10	=	=	PUNCT
easat-10856	284	11	174611	174611	NUM
easat-10856	284	12	330	330	NUM
easat-10856	284	13	calculation	calculation	NOUN
easat-10856	284	14	,	,	PUNCT
easat-10856	284	15	according	accord	VERB
easat-10856	284	16	to	to	ADP
easat-10856	284	17	the	the	DET
easat-10856	284	18	binomial	binomial	ADJ
easat-10856	284	19	formula	formula	NOUN
easat-10856	284	20	for	for	ADP
easat-10856	284	21	the	the	DET
easat-10856	284	22	bernoulli	bernoulli	NOUN
easat-10856	284	23	number	number	NOUN
easat-10856	284	24	,	,	PUNCT
easat-10856	284	25	of	of	ADP
easat-10856	284	26	𝐵11	𝐵11	PROPN
easat-10856	284	27	(	(	PUNCT
easat-10856	284	28	23	23	NUM
easat-10856	284	29	1	1	NUM
easat-10856	284	30	)	)	PUNCT
easat-10856	284	31	𝐵11	𝐵11	PROPN
easat-10856	285	1	−	−	PROPN
easat-10856	285	2	(	(	PUNCT
easat-10856	285	3	23	23	NUM
easat-10856	285	4	3	3	NUM
easat-10856	285	5	)	)	PUNCT
easat-10856	285	6	174611	174611	NUM
easat-10856	285	7	330	330	NUM
easat-10856	285	8	+	+	CCONJ
easat-10856	285	9	(	(	PUNCT
easat-10856	285	10	23	23	NUM
easat-10856	285	11	5	5	NUM
easat-10856	285	12	)	)	PUNCT
easat-10856	285	13	43867	43867	NUM
easat-10856	285	14	798	798	NUM
easat-10856	285	15	−	−	NOUN
easat-10856	285	16	(	(	PUNCT
easat-10856	285	17	23	23	NUM
easat-10856	285	18	7	7	NUM
easat-10856	285	19	)	)	PUNCT
easat-10856	285	20	3617	3617	NUM
easat-10856	285	21	510	510	NUM
easat-10856	286	1	+	+	CCONJ
easat-10856	286	2	(	(	PUNCT
easat-10856	286	3	23	23	NUM
easat-10856	286	4	9	9	NUM
easat-10856	286	5	)	)	PUNCT
easat-10856	286	6	7	7	NUM
easat-10856	286	7	6	6	NUM
easat-10856	286	8	−	−	PROPN
easat-10856	286	9	(	(	PUNCT
easat-10856	286	10	23	23	NUM
easat-10856	286	11	11	11	NUM
easat-10856	286	12	)	)	PUNCT
easat-10856	286	13	691	691	NUM
easat-10856	286	14	2730	2730	NUM
easat-10856	287	1	+	+	CCONJ
easat-10856	287	2	(	(	PUNCT
easat-10856	287	3	23	23	NUM
easat-10856	287	4	13	13	NUM
easat-10856	287	5	)	)	PUNCT
easat-10856	287	6	5	5	NUM
easat-10856	287	7	66	66	NUM
easat-10856	287	8	−	−	PROPN
easat-10856	287	9	(	(	PUNCT
easat-10856	287	10	23	23	NUM
easat-10856	287	11	15	15	NUM
easat-10856	287	12	)	)	PUNCT
easat-10856	287	13	1	1	NUM
easat-10856	287	14	30	30	NUM
easat-10856	287	15	+	+	CCONJ
easat-10856	287	16	(	(	PUNCT
easat-10856	287	17	23	23	NUM
easat-10856	287	18	17	17	NUM
easat-10856	287	19	)	)	PUNCT
easat-10856	287	20	1	1	NUM
easat-10856	287	21	42	42	NUM
easat-10856	287	22	−	−	NOUN
easat-10856	287	23	(	(	PUNCT
easat-10856	287	24	23	23	NUM
easat-10856	287	25	19	19	NUM
easat-10856	287	26	)	)	PUNCT
easat-10856	287	27	1	1	NUM
easat-10856	287	28	30	30	NUM
easat-10856	287	29	+	+	CCONJ
easat-10856	287	30	(	(	PUNCT
easat-10856	287	31	23	23	NUM
easat-10856	287	32	21	21	NUM
easat-10856	287	33	)	)	PUNCT
easat-10856	287	34	1	1	NUM
easat-10856	287	35	6	6	NUM
easat-10856	287	36	−	−	NOUN
easat-10856	287	37	(	(	PUNCT
easat-10856	287	38	11	11	NUM
easat-10856	287	39	−	−	NUM
easat-10856	287	40	1	1	NUM
easat-10856	287	41	2	2	NUM
easat-10856	287	42	)	)	PUNCT
easat-10856	287	43	=	=	SYM
easat-10856	287	44	0	0	NUM
easat-10856	287	45	280	280	NUM
easat-10856	287	46	edelweiss	edelweiss	PROPN
easat-10856	287	47	applied	apply	VERB
easat-10856	287	48	science	science	NOUN
easat-10856	287	49	and	and	CCONJ
easat-10856	287	50	technology	technology	NOUN
easat-10856	287	51	issn	issn	PROPN
easat-10856	287	52	:	:	PUNCT
easat-10856	287	53	2576	2576	NUM
easat-10856	287	54	-	-	SYM
easat-10856	287	55	8484	8484	NUM
easat-10856	287	56	vol	vol	NOUN
easat-10856	287	57	.	.	PROPN
easat-10856	288	1	9	9	NUM
easat-10856	288	2	,	,	PUNCT
easat-10856	288	3	no	no	INTJ
easat-10856	288	4	.	.	NOUN
easat-10856	288	5	11	11	NUM
easat-10856	288	6	:	:	PUNCT
easat-10856	288	7	274	274	NUM
easat-10856	288	8	-	-	SYM
easat-10856	288	9	288	288	NUM
easat-10856	288	10	,	,	PUNCT
easat-10856	288	11	2025	2025	NUM
easat-10856	288	12	doi	doi	NOUN
easat-10856	288	13	:	:	PUNCT
easat-10856	288	14	10.55214/2576	10.55214/2576	NUM
easat-10856	288	15	-	-	PUNCT
easat-10856	288	16	8484.v9i11.10856	8484.v9i11.10856	NUM
easat-10856	288	17	©	©	PROPN
easat-10856	288	18	2025	2025	NUM
easat-10856	288	19	by	by	ADP
easat-10856	288	20	the	the	DET
easat-10856	288	21	authors	author	NOUN
easat-10856	288	22	;	;	PUNCT
easat-10856	288	23	licensee	licensee	PROPN
easat-10856	288	24	learning	learning	NOUN
easat-10856	288	25	gate	gate	NOUN
easat-10856	288	26	23	23	NUM
easat-10856	288	27	!	!	PUNCT
easat-10856	288	28	1!×22	1!×22	NUM
easat-10856	288	29	!	!	PUNCT
easat-10856	289	1	𝐵11	𝐵11	PROPN
easat-10856	290	1	−	−	NOUN
easat-10856	290	2	23	23	NUM
easat-10856	290	3	!	!	PUNCT
easat-10856	291	1	3!×20	3!×20	NUM
easat-10856	291	2	!	!	PUNCT
easat-10856	292	1	174611	174611	NUM
easat-10856	292	2	330	330	NUM
easat-10856	292	3	+	+	SYM
easat-10856	292	4	23	23	NUM
easat-10856	292	5	!	!	PUNCT
easat-10856	293	1	5!×18	5!×18	NUM
easat-10856	293	2	!	!	PUNCT
easat-10856	294	1	43867	43867	NUM
easat-10856	294	2	798	798	NUM
easat-10856	295	1	−	−	NOUN
easat-10856	295	2	23	23	NUM
easat-10856	295	3	!	!	PUNCT
easat-10856	296	1	7!×16	7!×16	NUM
easat-10856	296	2	!	!	PUNCT
easat-10856	296	3	3617	3617	NUM
easat-10856	296	4	510	510	NUM
easat-10856	296	5	+	+	CCONJ
easat-10856	296	6	23	23	NUM
easat-10856	296	7	!	!	PUNCT
easat-10856	297	1	9!×14	9!×14	NUM
easat-10856	297	2	!	!	NOUN
easat-10856	298	1	7	7	NUM
easat-10856	298	2	6	6	NUM
easat-10856	298	3	−	−	NUM
easat-10856	298	4	23	23	NUM
easat-10856	298	5	!	!	PUNCT
easat-10856	299	1	11!×12	11!×12	NUM
easat-10856	299	2	!	!	PUNCT
easat-10856	300	1	691	691	NUM
easat-10856	300	2	2730	2730	NUM
easat-10856	300	3	+	+	CCONJ
easat-10856	300	4	23	23	NUM
easat-10856	300	5	!	!	PUNCT
easat-10856	301	1	13!×10	13!×10	X
easat-10856	301	2	!	!	NOUN
easat-10856	301	3	5	5	NUM
easat-10856	301	4	66	66	NUM
easat-10856	301	5	−	−	NUM
easat-10856	301	6	23	23	NUM
easat-10856	301	7	!	!	PUNCT
easat-10856	302	1	15!×8	15!×8	NUM
easat-10856	302	2	!	!	PROPN
easat-10856	302	3	1	1	NUM
easat-10856	302	4	30	30	NUM
easat-10856	302	5	+	+	CCONJ
easat-10856	302	6	23	23	NUM
easat-10856	302	7	!	!	PUNCT
easat-10856	303	1	17!×6	17!×6	X
easat-10856	303	2	!	!	PUNCT
easat-10856	304	1	1	1	NUM
easat-10856	304	2	42	42	NUM
easat-10856	304	3	−	−	NOUN
easat-10856	304	4	23	23	NUM
easat-10856	304	5	!	!	PUNCT
easat-10856	305	1	19!×4	19!×4	X
easat-10856	305	2	!	!	NOUN
easat-10856	305	3	1	1	NUM
easat-10856	305	4	30	30	NUM
easat-10856	305	5	+	+	CCONJ
easat-10856	305	6	23	23	NUM
easat-10856	305	7	!	!	PUNCT
easat-10856	306	1	21!×2	21!×2	NUM
easat-10856	306	2	!	!	NOUN
easat-10856	306	3	1	1	NUM
easat-10856	306	4	6	6	NUM
easat-10856	306	5	−	−	NUM
easat-10856	306	6	21	21	NUM
easat-10856	306	7	2	2	NUM
easat-10856	306	8	=	=	SYM
easat-10856	306	9	0	0	NUM
easat-10856	306	10	⇒	⇒	NOUN
easat-10856	306	11	𝐵11	𝐵11	PROPN
easat-10856	307	1	=	=	SYM
easat-10856	307	2	854513	854513	NUM
easat-10856	307	3	138	138	NUM
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easat-10856	307	5	,	,	PUNCT
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easat-10856	307	7	to	to	ADP
easat-10856	307	8	the	the	DET
easat-10856	307	9	binomial	binomial	ADJ
easat-10856	307	10	formula	formula	NOUN
easat-10856	307	11	for	for	ADP
easat-10856	307	12	the	the	DET
easat-10856	307	13	bernoulli	bernoulli	NOUN
easat-10856	307	14	number	number	NOUN
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easat-10856	307	17	𝐵12	𝐵12	PROPN
easat-10856	307	18	(	(	PUNCT
easat-10856	307	19	25	25	NUM
easat-10856	307	20	1	1	NUM
easat-10856	307	21	)	)	PUNCT
easat-10856	307	22	𝐵12	𝐵12	PROPN
easat-10856	307	23	−	−	PROPN
easat-10856	307	24	(	(	PUNCT
easat-10856	307	25	25	25	NUM
easat-10856	307	26	3	3	NUM
easat-10856	307	27	)	)	PUNCT
easat-10856	307	28	854513	854513	NUM
easat-10856	307	29	138	138	NUM
easat-10856	308	1	+	+	CCONJ
easat-10856	308	2	(	(	PUNCT
easat-10856	308	3	25	25	NUM
easat-10856	308	4	5	5	NUM
easat-10856	308	5	)	)	PUNCT
easat-10856	308	6	174611	174611	NUM
easat-10856	308	7	330	330	NUM
easat-10856	308	8	−	−	NOUN
easat-10856	308	9	(	(	PUNCT
easat-10856	308	10	25	25	NUM
easat-10856	308	11	7	7	NUM
easat-10856	308	12	)	)	PUNCT
easat-10856	308	13	43867	43867	NUM
easat-10856	308	14	798	798	NUM
easat-10856	309	1	+	+	CCONJ
easat-10856	309	2	(	(	PUNCT
easat-10856	309	3	25	25	NUM
easat-10856	309	4	9	9	NUM
easat-10856	309	5	)	)	PUNCT
easat-10856	309	6	3617	3617	NUM
easat-10856	309	7	510	510	NUM
easat-10856	309	8	−	−	PROPN
easat-10856	309	9	(	(	PUNCT
easat-10856	309	10	25	25	NUM
easat-10856	309	11	11	11	NUM
easat-10856	309	12	)	)	PUNCT
easat-10856	309	13	7	7	NUM
easat-10856	309	14	6	6	NUM
easat-10856	309	15	+	+	CCONJ
easat-10856	309	16	+	+	ADJ
easat-10856	309	17	(	(	PUNCT
easat-10856	309	18	25	25	NUM
easat-10856	309	19	13	13	NUM
easat-10856	309	20	)	)	PUNCT
easat-10856	309	21	691	691	NUM
easat-10856	309	22	2730	2730	NUM
easat-10856	309	23	−	−	NOUN
easat-10856	309	24	(	(	PUNCT
easat-10856	309	25	25	25	NUM
easat-10856	309	26	15	15	NUM
easat-10856	309	27	)	)	PUNCT
easat-10856	309	28	5	5	NUM
easat-10856	309	29	66	66	NUM
easat-10856	309	30	+	+	CCONJ
easat-10856	309	31	(	(	PUNCT
easat-10856	309	32	25	25	NUM
easat-10856	309	33	17	17	NUM
easat-10856	309	34	)	)	PUNCT
easat-10856	309	35	1	1	NUM
easat-10856	309	36	30	30	NUM
easat-10856	309	37	−	−	NOUN
easat-10856	309	38	(	(	PUNCT
easat-10856	309	39	25	25	NUM
easat-10856	309	40	19	19	NUM
easat-10856	309	41	)	)	PUNCT
easat-10856	309	42	1	1	NUM
easat-10856	309	43	42	42	NUM
easat-10856	309	44	+	+	CCONJ
easat-10856	309	45	(	(	PUNCT
easat-10856	309	46	25	25	NUM
easat-10856	309	47	21	21	NUM
easat-10856	309	48	)	)	PUNCT
easat-10856	309	49	1	1	NUM
easat-10856	309	50	30	30	NUM
easat-10856	309	51	−	−	NOUN
easat-10856	309	52	(	(	PUNCT
easat-10856	309	53	25	25	NUM
easat-10856	309	54	23	23	NUM
easat-10856	309	55	)	)	PUNCT
easat-10856	309	56	1	1	NUM
easat-10856	309	57	6	6	NUM
easat-10856	309	58	+	+	CCONJ
easat-10856	309	59	(	(	PUNCT
easat-10856	309	60	12	12	NUM
easat-10856	309	61	−	−	NUM
easat-10856	309	62	1	1	NUM
easat-10856	309	63	2	2	NUM
easat-10856	309	64	)	)	PUNCT
easat-10856	309	65	=	=	SYM
easat-10856	309	66	0	0	NUM
easat-10856	309	67	25	25	NUM
easat-10856	309	68	!	!	PUNCT
easat-10856	309	69	1!×24	1!×24	NUM
easat-10856	309	70	!	!	PUNCT
easat-10856	310	1	𝐵12	𝐵12	NOUN
easat-10856	310	2	−	−	PROPN
easat-10856	311	1	25	25	NUM
easat-10856	311	2	!	!	PUNCT
easat-10856	311	3	3!×22	3!×22	NUM
easat-10856	311	4	!	!	PUNCT
easat-10856	312	1	854513	854513	NUM
easat-10856	312	2	138	138	NUM
easat-10856	313	1	+	+	CCONJ
easat-10856	313	2	25	25	NUM
easat-10856	313	3	!	!	NUM
easat-10856	313	4	5!×20	5!×20	NUM
easat-10856	313	5	!	!	PUNCT
easat-10856	314	1	174611	174611	NUM
easat-10856	314	2	330	330	NUM
easat-10856	314	3	−	−	NUM
easat-10856	314	4	25	25	NUM
easat-10856	314	5	!	!	PUNCT
easat-10856	315	1	7!×18	7!×18	VERB
easat-10856	315	2	!	!	PUNCT
easat-10856	316	1	43867	43867	NUM
easat-10856	316	2	798	798	NUM
easat-10856	317	1	+	+	CCONJ
easat-10856	317	2	25	25	NUM
easat-10856	317	3	!	!	PUNCT
easat-10856	318	1	9!×16	9!×16	NUM
easat-10856	318	2	!	!	PUNCT
easat-10856	319	1	3617	3617	NUM
easat-10856	319	2	510	510	NUM
easat-10856	319	3	−	−	PROPN
easat-10856	319	4	25	25	NUM
easat-10856	319	5	!	!	PUNCT
easat-10856	320	1	11!×14	11!×14	NUM
easat-10856	320	2	!	!	NOUN
easat-10856	320	3	7	7	NUM
easat-10856	320	4	6	6	NUM
easat-10856	320	5	+	+	NUM
easat-10856	320	6	25	25	NUM
easat-10856	320	7	!	!	PUNCT
easat-10856	321	1	13!×12	13!×12	NUM
easat-10856	321	2	!	!	PUNCT
easat-10856	322	1	691	691	NUM
easat-10856	322	2	2730	2730	NUM
easat-10856	322	3	−	−	NOUN
easat-10856	322	4	25	25	NUM
easat-10856	322	5	!	!	PUNCT
easat-10856	323	1	15!×10	15!×10	X
easat-10856	323	2	!	!	NOUN
easat-10856	323	3	5	5	NUM
easat-10856	323	4	66	66	NUM
easat-10856	323	5	+	+	CCONJ
easat-10856	323	6	25	25	NUM
easat-10856	323	7	!	!	PUNCT
easat-10856	324	1	17!×8	17!×8	NUM
easat-10856	324	2	!	!	PUNCT
easat-10856	325	1	1	1	NUM
easat-10856	325	2	30	30	NUM
easat-10856	325	3	−	−	NOUN
easat-10856	325	4	25	25	NUM
easat-10856	325	5	!	!	PUNCT
easat-10856	325	6	19!×6	19!×6	NUM
easat-10856	325	7	!	!	PUNCT
easat-10856	326	1	1	1	NUM
easat-10856	326	2	42	42	NUM
easat-10856	326	3	+	+	NUM
easat-10856	326	4	25	25	NUM
easat-10856	326	5	!	!	PUNCT
easat-10856	327	1	21!×4	21!×4	X
easat-10856	327	2	!	!	NOUN
easat-10856	327	3	1	1	NUM
easat-10856	327	4	30	30	NUM
easat-10856	327	5	−	−	NOUN
easat-10856	327	6	25	25	NUM
easat-10856	327	7	!	!	PUNCT
easat-10856	328	1	23!×2	23!×2	ADJ
easat-10856	328	2	!	!	NOUN
easat-10856	328	3	1	1	NUM
easat-10856	328	4	6	6	NUM
easat-10856	328	5	+	+	CCONJ
easat-10856	328	6	23	23	NUM
easat-10856	328	7	2	2	NUM
easat-10856	328	8	=	=	SYM
easat-10856	328	9	0	0	NUM
easat-10856	328	10	⇒	⇒	NOUN
easat-10856	328	11	𝐵12	𝐵12	PROPN
easat-10856	328	12	=	=	SYM
easat-10856	328	13	236364091	236364091	NUM
easat-10856	328	14	2730	2730	NUM
easat-10856	328	15	calculation	calculation	NOUN
easat-10856	328	16	,	,	PUNCT
easat-10856	328	17	according	accord	VERB
easat-10856	328	18	to	to	ADP
easat-10856	328	19	the	the	DET
easat-10856	328	20	binomial	binomial	ADJ
easat-10856	328	21	formula	formula	NOUN
easat-10856	328	22	for	for	ADP
easat-10856	328	23	the	the	DET
easat-10856	328	24	bernoulli	bernoulli	NOUN
easat-10856	328	25	number	number	NOUN
easat-10856	328	26	,	,	PUNCT
easat-10856	328	27	of	of	ADP
easat-10856	328	28	𝐵13	𝐵13	PROPN
easat-10856	328	29	(	(	PUNCT
easat-10856	328	30	27	27	NUM
easat-10856	328	31	1	1	NUM
easat-10856	328	32	)	)	PUNCT
easat-10856	328	33	𝐵13	𝐵13	PROPN
easat-10856	328	34	−	−	PROPN
easat-10856	328	35	(	(	PUNCT
easat-10856	328	36	27	27	NUM
easat-10856	328	37	3	3	NUM
easat-10856	328	38	)	)	PUNCT
easat-10856	328	39	236364091	236364091	NUM
easat-10856	328	40	2730	2730	NUM
easat-10856	329	1	+	+	CCONJ
easat-10856	329	2	(	(	PUNCT
easat-10856	329	3	27	27	NUM
easat-10856	329	4	5	5	NUM
easat-10856	329	5	)	)	PUNCT
easat-10856	329	6	854513	854513	NUM
easat-10856	329	7	138	138	NUM
easat-10856	329	8	−	−	PROPN
easat-10856	329	9	(	(	PUNCT
easat-10856	329	10	27	27	NUM
easat-10856	329	11	7	7	NUM
easat-10856	329	12	)	)	PUNCT
easat-10856	329	13	174611	174611	NUM
easat-10856	329	14	330	330	NUM
easat-10856	329	15	+	+	CCONJ
easat-10856	329	16	(	(	PUNCT
easat-10856	329	17	27	27	NUM
easat-10856	329	18	9	9	NUM
easat-10856	329	19	)	)	PUNCT
easat-10856	329	20	43867	43867	NUM
easat-10856	329	21	798	798	NUM
easat-10856	329	22	−	−	NOUN
easat-10856	329	23	(	(	PUNCT
easat-10856	329	24	27	27	NUM
easat-10856	329	25	11	11	NUM
easat-10856	329	26	)	)	PUNCT
easat-10856	329	27	3617	3617	NUM
easat-10856	329	28	510	510	NUM
easat-10856	330	1	+	+	CCONJ
easat-10856	330	2	(	(	PUNCT
easat-10856	330	3	27	27	NUM
easat-10856	330	4	13	13	NUM
easat-10856	330	5	)	)	PUNCT
easat-10856	330	6	7	7	NUM
easat-10856	330	7	6	6	NUM
easat-10856	330	8	−	−	PROPN
easat-10856	330	9	(	(	PUNCT
easat-10856	330	10	27	27	NUM
easat-10856	330	11	15	15	NUM
easat-10856	330	12	)	)	PUNCT
easat-10856	330	13	691	691	NUM
easat-10856	330	14	2730	2730	NUM
easat-10856	330	15	+	+	CCONJ
easat-10856	330	16	(	(	PUNCT
easat-10856	330	17	27	27	NUM
easat-10856	330	18	17	17	NUM
easat-10856	330	19	)	)	PUNCT
easat-10856	330	20	5	5	NUM
easat-10856	330	21	66	66	NUM
easat-10856	330	22	−	−	NOUN
easat-10856	330	23	(	(	PUNCT
easat-10856	330	24	27	27	NUM
easat-10856	330	25	19	19	NUM
easat-10856	330	26	)	)	PUNCT
easat-10856	330	27	1	1	NUM
easat-10856	330	28	30	30	NUM
easat-10856	330	29	+	+	CCONJ
easat-10856	330	30	(	(	PUNCT
easat-10856	330	31	27	27	NUM
easat-10856	330	32	21	21	NUM
easat-10856	330	33	)	)	PUNCT
easat-10856	330	34	1	1	NUM
easat-10856	330	35	42	42	NUM
easat-10856	330	36	−	−	NOUN
easat-10856	330	37	(	(	PUNCT
easat-10856	330	38	27	27	NUM
easat-10856	330	39	23	23	NUM
easat-10856	330	40	)	)	PUNCT
easat-10856	330	41	1	1	NUM
easat-10856	330	42	30	30	NUM
easat-10856	330	43	+	+	CCONJ
easat-10856	330	44	(	(	PUNCT
easat-10856	330	45	23	23	NUM
easat-10856	330	46	25	25	NUM
easat-10856	330	47	)	)	PUNCT
easat-10856	330	48	1	1	NUM
easat-10856	330	49	6	6	NUM
easat-10856	330	50	−	−	NOUN
easat-10856	330	51	(	(	PUNCT
easat-10856	330	52	13	13	NUM
easat-10856	330	53	−	−	NUM
easat-10856	330	54	1	1	NUM
easat-10856	330	55	2	2	NUM
easat-10856	330	56	)	)	PUNCT
easat-10856	330	57	=	=	SYM
easat-10856	330	58	0	0	NUM
easat-10856	330	59	27	27	NUM
easat-10856	330	60	!	!	PUNCT
easat-10856	330	61	1!×26	1!×26	NUM
easat-10856	330	62	!	!	PUNCT
easat-10856	331	1	𝐵13	𝐵13	PROPN
easat-10856	331	2	−	−	PROPN
easat-10856	332	1	27	27	NUM
easat-10856	332	2	!	!	PUNCT
easat-10856	333	1	3!×24	3!×24	NUM
easat-10856	333	2	!	!	PUNCT
easat-10856	334	1	236364091	236364091	NUM
easat-10856	334	2	2730	2730	NUM
easat-10856	335	1	+	+	CCONJ
easat-10856	335	2	27	27	NUM
easat-10856	335	3	!	!	PUNCT
easat-10856	336	1	5!×22	5!×22	NUM
easat-10856	336	2	!	!	PUNCT
easat-10856	336	3	854513	854513	NUM
easat-10856	336	4	138	138	NUM
easat-10856	336	5	−	−	NOUN
easat-10856	336	6	27	27	NUM
easat-10856	336	7	!	!	PUNCT
easat-10856	337	1	7!×20	7!×20	NUM
easat-10856	337	2	!	!	PUNCT
easat-10856	338	1	174611	174611	NUM
easat-10856	338	2	330	330	NUM
easat-10856	338	3	+	+	SYM
easat-10856	338	4	27	27	NUM
easat-10856	338	5	!	!	PUNCT
easat-10856	339	1	9!×18	9!×18	VERB
easat-10856	339	2	!	!	PUNCT
easat-10856	340	1	43867	43867	NUM
easat-10856	340	2	798	798	NUM
easat-10856	341	1	−	−	NUM
easat-10856	341	2	27	27	NUM
easat-10856	341	3	!	!	PUNCT
easat-10856	342	1	11!×16	11!×16	NUM
easat-10856	342	2	!	!	NOUN
easat-10856	342	3	3617	3617	NUM
easat-10856	342	4	510	510	NUM
easat-10856	342	5	+	+	CCONJ
easat-10856	342	6	27	27	NUM
easat-10856	342	7	!	!	PUNCT
easat-10856	343	1	13!×14	13!×14	NUM
easat-10856	343	2	!	!	NOUN
easat-10856	343	3	7	7	NUM
easat-10856	343	4	6	6	NUM
easat-10856	343	5	−	−	NUM
easat-10856	343	6	27	27	NUM
easat-10856	343	7	!	!	PUNCT
easat-10856	344	1	15!×12	15!×12	NUM
easat-10856	344	2	!	!	PUNCT
easat-10856	345	1	691	691	NUM
easat-10856	345	2	2730	2730	NUM
easat-10856	345	3	+	+	CCONJ
easat-10856	345	4	27	27	NUM
easat-10856	345	5	!	!	PUNCT
easat-10856	346	1	17!×10	17!×10	NUM
easat-10856	346	2	!	!	NOUN
easat-10856	346	3	5	5	NUM
easat-10856	346	4	66	66	NUM
easat-10856	346	5	−	−	NUM
easat-10856	346	6	27	27	NUM
easat-10856	346	7	!	!	PUNCT
easat-10856	347	1	19!×8	19!×8	NUM
easat-10856	347	2	!	!	PUNCT
easat-10856	348	1	1	1	NUM
easat-10856	348	2	30	30	NUM
easat-10856	348	3	+	+	NUM
easat-10856	348	4	27	27	NUM
easat-10856	348	5	!	!	PUNCT
easat-10856	349	1	21!×6	21!×6	NUM
easat-10856	349	2	!	!	NOUN
easat-10856	349	3	1	1	NUM
easat-10856	349	4	42	42	NUM
easat-10856	349	5	−	−	NUM
easat-10856	349	6	27	27	NUM
easat-10856	349	7	!	!	PUNCT
easat-10856	350	1	23!×4	23!×4	X
easat-10856	350	2	!	!	NOUN
easat-10856	350	3	1	1	NUM
easat-10856	350	4	30	30	NUM
easat-10856	350	5	+	+	NUM
easat-10856	350	6	27	27	NUM
easat-10856	350	7	!	!	PUNCT
easat-10856	351	1	25!×2	25!×2	ADJ
easat-10856	351	2	!	!	PUNCT
easat-10856	352	1	1	1	NUM
easat-10856	352	2	6	6	NUM
easat-10856	352	3	−	−	NUM
easat-10856	352	4	25	25	NUM
easat-10856	352	5	2	2	NUM
easat-10856	352	6	=	=	SYM
easat-10856	352	7	0	0	NUM
easat-10856	352	8	⇒	⇒	NOUN
easat-10856	352	9	𝐵13	𝐵13	PROPN
easat-10856	352	10	=	=	SYM
easat-10856	352	11	8553103	8553103	NUM
easat-10856	352	12	6	6	NUM
easat-10856	352	13	calculation	calculation	NOUN
easat-10856	352	14	,	,	PUNCT
easat-10856	352	15	according	accord	VERB
easat-10856	352	16	to	to	ADP
easat-10856	352	17	the	the	DET
easat-10856	352	18	binomial	binomial	ADJ
easat-10856	352	19	formula	formula	NOUN
easat-10856	352	20	for	for	ADP
easat-10856	352	21	the	the	DET
easat-10856	352	22	bernoulli	bernoulli	NOUN
easat-10856	352	23	number	number	NOUN
easat-10856	352	24	,	,	PUNCT
easat-10856	352	25	of	of	ADP
easat-10856	352	26	𝐵14	𝐵14	PROPN
easat-10856	352	27	(	(	PUNCT
easat-10856	352	28	29	29	NUM
easat-10856	352	29	1	1	NUM
easat-10856	352	30	)	)	PUNCT
easat-10856	352	31	𝐵14	𝐵14	PROPN
easat-10856	353	1	−	−	PROPN
easat-10856	353	2	(	(	PUNCT
easat-10856	353	3	29	29	NUM
easat-10856	353	4	3	3	NUM
easat-10856	353	5	)	)	PUNCT
easat-10856	353	6	8553103	8553103	NUM
easat-10856	353	7	6	6	NUM
easat-10856	354	1	+	+	CCONJ
easat-10856	354	2	(	(	PUNCT
easat-10856	354	3	29	29	NUM
easat-10856	354	4	5	5	NUM
easat-10856	354	5	)	)	PUNCT
easat-10856	354	6	236364091	236364091	NUM
easat-10856	354	7	2730	2730	NUM
easat-10856	354	8	−	−	NOUN
easat-10856	354	9	(	(	PUNCT
easat-10856	354	10	29	29	NUM
easat-10856	354	11	7	7	NUM
easat-10856	354	12	)	)	PUNCT
easat-10856	354	13	854513	854513	NUM
easat-10856	354	14	138	138	NUM
easat-10856	355	1	+	+	CCONJ
easat-10856	355	2	(	(	PUNCT
easat-10856	355	3	29	29	NUM
easat-10856	355	4	9	9	NUM
easat-10856	355	5	)	)	PUNCT
easat-10856	355	6	174611	174611	NUM
easat-10856	355	7	330	330	NUM
easat-10856	355	8	−	−	NOUN
easat-10856	355	9	(	(	PUNCT
easat-10856	355	10	29	29	NUM
easat-10856	355	11	11	11	NUM
easat-10856	355	12	)	)	PUNCT
easat-10856	355	13	43867	43867	NUM
easat-10856	355	14	798	798	NUM
easat-10856	356	1	+	+	CCONJ
easat-10856	356	2	(	(	PUNCT
easat-10856	356	3	29	29	NUM
easat-10856	356	4	13	13	NUM
easat-10856	356	5	)	)	PUNCT
easat-10856	356	6	3617	3617	NUM
easat-10856	356	7	510	510	NUM
easat-10856	356	8	−	−	PROPN
easat-10856	356	9	(	(	PUNCT
easat-10856	356	10	29	29	NUM
easat-10856	356	11	15	15	NUM
easat-10856	356	12	)	)	PUNCT
easat-10856	356	13	7	7	NUM
easat-10856	356	14	6	6	NUM
easat-10856	356	15	+	+	CCONJ
easat-10856	356	16	(	(	PUNCT
easat-10856	356	17	29	29	NUM
easat-10856	356	18	17	17	NUM
easat-10856	356	19	)	)	PUNCT
easat-10856	356	20	691	691	NUM
easat-10856	356	21	2730	2730	NUM
easat-10856	356	22	−	−	NOUN
easat-10856	356	23	(	(	PUNCT
easat-10856	356	24	29	29	NUM
easat-10856	356	25	19	19	NUM
easat-10856	356	26	)	)	PUNCT
easat-10856	356	27	5	5	NUM
easat-10856	356	28	66	66	NUM
easat-10856	356	29	+	+	CCONJ
easat-10856	356	30	(	(	PUNCT
easat-10856	356	31	29	29	NUM
easat-10856	356	32	21	21	NUM
easat-10856	356	33	)	)	PUNCT
easat-10856	356	34	1	1	NUM
easat-10856	356	35	30	30	NUM
easat-10856	356	36	−	−	NOUN
easat-10856	356	37	(	(	PUNCT
easat-10856	356	38	29	29	NUM
easat-10856	356	39	23	23	NUM
easat-10856	356	40	)	)	PUNCT
easat-10856	356	41	1	1	NUM
easat-10856	356	42	42	42	NUM
easat-10856	356	43	+	+	CCONJ
easat-10856	356	44	(	(	PUNCT
easat-10856	356	45	29	29	NUM
easat-10856	356	46	25	25	NUM
easat-10856	356	47	)	)	PUNCT
easat-10856	356	48	1	1	NUM
easat-10856	356	49	30	30	NUM
easat-10856	356	50	−	−	NOUN
easat-10856	356	51	(	(	PUNCT
easat-10856	356	52	29	29	NUM
easat-10856	356	53	27	27	NUM
easat-10856	356	54	)	)	PUNCT
easat-10856	356	55	1	1	NUM
easat-10856	356	56	6	6	NUM
easat-10856	356	57	+	+	CCONJ
easat-10856	356	58	(	(	PUNCT
easat-10856	356	59	14	14	NUM
easat-10856	356	60	−	−	NUM
easat-10856	356	61	1	1	NUM
easat-10856	356	62	2	2	NUM
easat-10856	356	63	)	)	PUNCT
easat-10856	356	64	=	=	SYM
easat-10856	356	65	0	0	NUM
easat-10856	356	66	29	29	NUM
easat-10856	356	67	!	!	PUNCT
easat-10856	356	68	1!×28	1!×28	NUM
easat-10856	356	69	!	!	PUNCT
easat-10856	357	1	𝐵14	𝐵14	PROPN
easat-10856	358	1	−	−	NOUN
easat-10856	359	1	29	29	NUM
easat-10856	359	2	!	!	PUNCT
easat-10856	360	1	3!×26	3!×26	NUM
easat-10856	360	2	!	!	NOUN
easat-10856	360	3	8553103	8553103	NUM
easat-10856	360	4	6	6	NUM
easat-10856	360	5	+	+	CCONJ
easat-10856	360	6	29	29	NUM
easat-10856	360	7	!	!	X
easat-10856	361	1	5!×24	5!×24	NUM
easat-10856	361	2	!	!	PUNCT
easat-10856	361	3	236364091	236364091	NUM
easat-10856	362	1	2730	2730	NUM
easat-10856	362	2	−	−	ADP
easat-10856	363	1	29	29	NUM
easat-10856	363	2	!	!	PUNCT
easat-10856	364	1	7!×22	7!×22	NUM
easat-10856	364	2	!	!	PROPN
easat-10856	364	3	854513	854513	NUM
easat-10856	364	4	138	138	NUM
easat-10856	365	1	+	+	CCONJ
easat-10856	365	2	29	29	NUM
easat-10856	365	3	!	!	PUNCT
easat-10856	366	1	9!×20	9!×20	NUM
easat-10856	366	2	!	!	PUNCT
easat-10856	367	1	174611	174611	NUM
easat-10856	367	2	330	330	NUM
easat-10856	367	3	−	−	NUM
easat-10856	367	4	29	29	NUM
easat-10856	367	5	!	!	PUNCT
easat-10856	368	1	11!×18	11!×18	NUM
easat-10856	368	2	!	!	PUNCT
easat-10856	369	1	43867	43867	NUM
easat-10856	369	2	798	798	NUM
easat-10856	370	1	+	+	CCONJ
easat-10856	370	2	29	29	NUM
easat-10856	370	3	!	!	PUNCT
easat-10856	371	1	13!×16	13!×16	NUM
easat-10856	371	2	!	!	PROPN
easat-10856	371	3	3617	3617	NUM
easat-10856	371	4	510	510	NUM
easat-10856	371	5	−	−	PROPN
easat-10856	371	6	29	29	NUM
easat-10856	371	7	!	!	PUNCT
easat-10856	371	8	15!×14	15!×14	NUM
easat-10856	371	9	!	!	NOUN
easat-10856	371	10	7	7	NUM
easat-10856	371	11	6	6	NUM
easat-10856	371	12	+	+	SYM
easat-10856	371	13	29	29	NUM
easat-10856	371	14	!	!	PUNCT
easat-10856	372	1	17!×12	17!×12	NUM
easat-10856	372	2	!	!	NOUN
easat-10856	373	1	691	691	NUM
easat-10856	373	2	2730	2730	NUM
easat-10856	373	3	−	−	NOUN
easat-10856	373	4	29	29	NUM
easat-10856	373	5	!	!	SYM
easat-10856	373	6	19!×10	19!×10	NUM
easat-10856	373	7	!	!	NOUN
easat-10856	373	8	5	5	NUM
easat-10856	373	9	66	66	NUM
easat-10856	373	10	+	+	CCONJ
easat-10856	373	11	29	29	NUM
easat-10856	373	12	!	!	PUNCT
easat-10856	374	1	21!×8	21!×8	NUM
easat-10856	374	2	!	!	PUNCT
easat-10856	375	1	1	1	NUM
easat-10856	375	2	30	30	NUM
easat-10856	375	3	−	−	NOUN
easat-10856	375	4	29	29	NUM
easat-10856	375	5	!	!	PUNCT
easat-10856	376	1	23!×6	23!×6	NUM
easat-10856	376	2	!	!	NOUN
easat-10856	376	3	1	1	NUM
easat-10856	376	4	42	42	NUM
easat-10856	376	5	+	+	CCONJ
easat-10856	376	6	29	29	NUM
easat-10856	376	7	!	!	PUNCT
easat-10856	377	1	25!×4	25!×4	X
easat-10856	377	2	!	!	NOUN
easat-10856	377	3	1	1	NUM
easat-10856	377	4	30	30	NUM
easat-10856	377	5	−	−	NOUN
easat-10856	377	6	29	29	NUM
easat-10856	377	7	!	!	PUNCT
easat-10856	378	1	27!×2	27!×2	ADJ
easat-10856	378	2	!	!	PUNCT
easat-10856	379	1	1	1	NUM
easat-10856	379	2	6	6	NUM
easat-10856	379	3	+	+	CCONJ
easat-10856	379	4	27	27	NUM
easat-10856	379	5	2	2	NUM
easat-10856	379	6	=	=	SYM
easat-10856	379	7	0	0	NUM
easat-10856	379	8	⇒	⇒	NOUN
easat-10856	379	9	𝐵14	𝐵14	PROPN
easat-10856	380	1	=	=	PUNCT
easat-10856	380	2	23749461029	23749461029	NUM
easat-10856	380	3	870	870	NUM
easat-10856	380	4	calculation	calculation	NOUN
easat-10856	380	5	,	,	PUNCT
easat-10856	380	6	according	accord	VERB
easat-10856	380	7	to	to	ADP
easat-10856	380	8	the	the	DET
easat-10856	380	9	binomial	binomial	ADJ
easat-10856	380	10	formula	formula	NOUN
easat-10856	380	11	for	for	ADP
easat-10856	380	12	the	the	DET
easat-10856	380	13	bernoulli	bernoulli	NOUN
easat-10856	380	14	number	number	NOUN
easat-10856	380	15	,	,	PUNCT
easat-10856	380	16	of	of	ADP
easat-10856	380	17	𝐵15	𝐵15	NOUN
easat-10856	380	18	(	(	PUNCT
easat-10856	380	19	31	31	NUM
easat-10856	380	20	1	1	NUM
easat-10856	380	21	)	)	PUNCT
easat-10856	380	22	𝐵15	𝐵15	NOUN
easat-10856	380	23	−	−	NOUN
easat-10856	380	24	(	(	PUNCT
easat-10856	380	25	31	31	NUM
easat-10856	380	26	3	3	NUM
easat-10856	380	27	)	)	PUNCT
easat-10856	380	28	23749461029	23749461029	NUM
easat-10856	380	29	870	870	NUM
easat-10856	381	1	+	+	CCONJ
easat-10856	381	2	(	(	PUNCT
easat-10856	381	3	31	31	NUM
easat-10856	381	4	5	5	NUM
easat-10856	381	5	)	)	PUNCT
easat-10856	381	6	8553103	8553103	NUM
easat-10856	381	7	6	6	NUM
easat-10856	381	8	−	−	PROPN
easat-10856	381	9	(	(	PUNCT
easat-10856	381	10	31	31	NUM
easat-10856	381	11	7	7	NUM
easat-10856	381	12	)	)	PUNCT
easat-10856	381	13	236364091	236364091	NUM
easat-10856	381	14	2730	2730	NUM
easat-10856	382	1	+	+	CCONJ
easat-10856	382	2	(	(	PUNCT
easat-10856	382	3	31	31	NUM
easat-10856	382	4	9	9	NUM
easat-10856	382	5	)	)	PUNCT
easat-10856	382	6	854513	854513	NUM
easat-10856	382	7	138	138	NUM
easat-10856	382	8	−	−	PROPN
easat-10856	382	9	(	(	PUNCT
easat-10856	382	10	31	31	NUM
easat-10856	382	11	11	11	NUM
easat-10856	382	12	)	)	PUNCT
easat-10856	382	13	174611	174611	NUM
easat-10856	382	14	330	330	NUM
easat-10856	382	15	+	+	CCONJ
easat-10856	382	16	(	(	PUNCT
easat-10856	382	17	31	31	NUM
easat-10856	382	18	13	13	NUM
easat-10856	382	19	)	)	PUNCT
easat-10856	382	20	43867	43867	NUM
easat-10856	382	21	798	798	NUM
easat-10856	382	22	−	−	NOUN
easat-10856	382	23	(	(	PUNCT
easat-10856	382	24	31	31	NUM
easat-10856	382	25	15	15	NUM
easat-10856	382	26	)	)	PUNCT
easat-10856	382	27	3617	3617	NUM
easat-10856	382	28	510	510	NUM
easat-10856	383	1	+	+	CCONJ
easat-10856	383	2	(	(	PUNCT
easat-10856	383	3	31	31	NUM
easat-10856	383	4	17	17	NUM
easat-10856	383	5	)	)	PUNCT
easat-10856	383	6	7	7	NUM
easat-10856	383	7	6	6	NUM
easat-10856	383	8	−	−	NOUN
easat-10856	383	9	(	(	PUNCT
easat-10856	383	10	31	31	NUM
easat-10856	383	11	19	19	NUM
easat-10856	383	12	)	)	PUNCT
easat-10856	383	13	691	691	NUM
easat-10856	383	14	2730	2730	NUM
easat-10856	384	1	+	+	CCONJ
easat-10856	384	2	(	(	PUNCT
easat-10856	384	3	31	31	NUM
easat-10856	384	4	21	21	NUM
easat-10856	384	5	)	)	PUNCT
easat-10856	384	6	5	5	NUM
easat-10856	384	7	66	66	NUM
easat-10856	384	8	−	−	NOUN
easat-10856	384	9	(	(	PUNCT
easat-10856	384	10	31	31	NUM
easat-10856	384	11	23	23	NUM
easat-10856	384	12	)	)	PUNCT
easat-10856	384	13	1	1	NUM
easat-10856	384	14	30	30	NUM
easat-10856	384	15	+	+	CCONJ
easat-10856	384	16	(	(	PUNCT
easat-10856	384	17	31	31	NUM
easat-10856	384	18	25	25	NUM
easat-10856	384	19	)	)	PUNCT
easat-10856	384	20	1	1	NUM
easat-10856	384	21	42	42	NUM
easat-10856	384	22	−	−	NOUN
easat-10856	384	23	(	(	PUNCT
easat-10856	384	24	31	31	NUM
easat-10856	384	25	27	27	NUM
easat-10856	384	26	)	)	PUNCT
easat-10856	384	27	1	1	NUM
easat-10856	384	28	30	30	NUM
easat-10856	384	29	+	+	CCONJ
easat-10856	384	30	(	(	PUNCT
easat-10856	384	31	31	31	NUM
easat-10856	384	32	29	29	NUM
easat-10856	384	33	)	)	PUNCT
easat-10856	384	34	1	1	NUM
easat-10856	384	35	6	6	NUM
easat-10856	384	36	−	−	NOUN
easat-10856	384	37	(	(	PUNCT
easat-10856	384	38	15	15	NUM
easat-10856	384	39	−	−	NUM
easat-10856	384	40	1	1	NUM
easat-10856	384	41	2	2	NUM
easat-10856	384	42	)	)	PUNCT
easat-10856	384	43	=	=	SYM
easat-10856	384	44	0	0	NUM
easat-10856	385	1	31	31	NUM
easat-10856	385	2	!	!	PUNCT
easat-10856	385	3	1!×30	1!×30	NUM
easat-10856	385	4	!	!	PUNCT
easat-10856	386	1	𝐵15	𝐵15	NOUN
easat-10856	386	2	−	−	NOUN
easat-10856	386	3	31	31	NUM
easat-10856	386	4	!	!	PUNCT
easat-10856	387	1	3!×28	3!×28	ADV
easat-10856	387	2	!	!	PUNCT
easat-10856	388	1	23749461029	23749461029	NUM
easat-10856	388	2	870	870	NUM
easat-10856	389	1	+	+	CCONJ
easat-10856	389	2	31	31	NUM
easat-10856	389	3	!	!	PUNCT
easat-10856	389	4	5!×26	5!×26	NOUN
easat-10856	389	5	!	!	PUNCT
easat-10856	389	6	8553103	8553103	NUM
easat-10856	390	1	6	6	NUM
easat-10856	390	2	−	−	NOUN
easat-10856	390	3	31	31	NUM
easat-10856	390	4	!	!	PUNCT
easat-10856	391	1	7!×24	7!×24	NUM
easat-10856	391	2	!	!	PUNCT
easat-10856	391	3	236364091	236364091	NUM
easat-10856	391	4	2730	2730	NUM
easat-10856	392	1	+	+	CCONJ
easat-10856	392	2	31	31	NUM
easat-10856	392	3	!	!	PUNCT
easat-10856	393	1	9!×22	9!×22	NUM
easat-10856	393	2	!	!	PUNCT
easat-10856	393	3	854513	854513	NUM
easat-10856	393	4	138	138	NUM
easat-10856	393	5	−	−	NOUN
easat-10856	393	6	31	31	NUM
easat-10856	393	7	!	!	PUNCT
easat-10856	394	1	11!×20	11!×20	X
easat-10856	394	2	!	!	PUNCT
easat-10856	395	1	174611	174611	NUM
easat-10856	395	2	330	330	NUM
easat-10856	395	3	+	+	SYM
easat-10856	395	4	31	31	NUM
easat-10856	395	5	!	!	PUNCT
easat-10856	396	1	13!×18	13!×18	NUM
easat-10856	396	2	!	!	PUNCT
easat-10856	397	1	43867	43867	NUM
easat-10856	397	2	798	798	NUM
easat-10856	398	1	−	−	NUM
easat-10856	398	2	31	31	NUM
easat-10856	398	3	!	!	PUNCT
easat-10856	399	1	15!×16	15!×16	NUM
easat-10856	399	2	!	!	NOUN
easat-10856	399	3	3617	3617	NUM
easat-10856	399	4	510	510	NUM
easat-10856	399	5	+	+	CCONJ
easat-10856	399	6	31	31	NUM
easat-10856	399	7	!	!	PUNCT
easat-10856	399	8	17!×14	17!×14	NUM
easat-10856	399	9	!	!	NOUN
easat-10856	399	10	7	7	NUM
easat-10856	399	11	6	6	NUM
easat-10856	399	12	−	−	NUM
easat-10856	399	13	31	31	NUM
easat-10856	399	14	!	!	PUNCT
easat-10856	400	1	19!×12	19!×12	NUM
easat-10856	400	2	!	!	PUNCT
easat-10856	401	1	691	691	NUM
easat-10856	401	2	2730	2730	NUM
easat-10856	401	3	+	+	CCONJ
easat-10856	401	4	31	31	NUM
easat-10856	401	5	!	!	PUNCT
easat-10856	402	1	21!×10	21!×10	X
easat-10856	402	2	!	!	NOUN
easat-10856	402	3	5	5	NUM
easat-10856	402	4	66	66	NUM
easat-10856	402	5	−	−	NUM
easat-10856	402	6	31	31	NUM
easat-10856	402	7	!	!	PUNCT
easat-10856	403	1	23!×8	23!×8	NUM
easat-10856	403	2	!	!	PUNCT
easat-10856	404	1	1	1	NUM
easat-10856	404	2	30	30	NUM
easat-10856	404	3	+	+	SYM
easat-10856	404	4	31	31	NUM
easat-10856	404	5	!	!	PUNCT
easat-10856	405	1	25!×6	25!×6	NUM
easat-10856	405	2	!	!	PUNCT
easat-10856	406	1	1	1	NUM
easat-10856	406	2	42	42	NUM
easat-10856	406	3	−	−	NUM
easat-10856	406	4	31	31	NUM
easat-10856	406	5	!	!	PUNCT
easat-10856	407	1	27!×4	27!×4	PROPN
easat-10856	407	2	!	!	PROPN
easat-10856	407	3	1	1	NUM
easat-10856	407	4	30	30	NUM
easat-10856	407	5	+	+	NUM
easat-10856	407	6	31	31	NUM
easat-10856	407	7	!	!	PUNCT
easat-10856	408	1	29!×2	29!×2	NUM
easat-10856	408	2	!	!	NOUN
easat-10856	408	3	1	1	NUM
easat-10856	408	4	6	6	NUM
easat-10856	408	5	−	−	NUM
easat-10856	408	6	29	29	NUM
easat-10856	408	7	2	2	NUM
easat-10856	408	8	=	=	SYM
easat-10856	408	9	0	0	NUM
easat-10856	408	10	⇒	⇒	NOUN
easat-10856	408	11	𝐵15	𝐵15	NOUN
easat-10856	408	12	=	=	SYM
easat-10856	408	13	8615841276005	8615841276005	NUM
easat-10856	408	14	14322	14322	NUM
easat-10856	408	15	281	281	NUM
easat-10856	408	16	edelweiss	edelweiss	PROPN
easat-10856	408	17	applied	apply	VERB
easat-10856	408	18	science	science	NOUN
easat-10856	408	19	and	and	CCONJ
easat-10856	408	20	technology	technology	NOUN
easat-10856	408	21	issn	issn	PROPN
easat-10856	408	22	:	:	PUNCT
easat-10856	408	23	2576	2576	NUM
easat-10856	408	24	-	-	SYM
easat-10856	408	25	8484	8484	NUM
easat-10856	408	26	vol	vol	NOUN
easat-10856	408	27	.	.	PROPN
easat-10856	409	1	9	9	NUM
easat-10856	409	2	,	,	PUNCT
easat-10856	409	3	no	no	INTJ
easat-10856	409	4	.	.	NOUN
easat-10856	409	5	11	11	NUM
easat-10856	409	6	:	:	PUNCT
easat-10856	409	7	274	274	NUM
easat-10856	409	8	-	-	SYM
easat-10856	409	9	288	288	NUM
easat-10856	409	10	,	,	PUNCT
easat-10856	409	11	2025	2025	NUM
easat-10856	409	12	doi	doi	NOUN
easat-10856	409	13	:	:	PUNCT
easat-10856	409	14	10.55214/2576	10.55214/2576	NUM
easat-10856	409	15	-	-	PUNCT
easat-10856	409	16	8484.v9i11.10856	8484.v9i11.10856	NUM
easat-10856	409	17	©	©	PROPN
easat-10856	409	18	2025	2025	NUM
easat-10856	409	19	by	by	ADP
easat-10856	409	20	the	the	DET
easat-10856	409	21	authors	author	NOUN
easat-10856	409	22	;	;	PUNCT
easat-10856	409	23	licensee	licensee	PROPN
easat-10856	409	24	learning	learning	NOUN
easat-10856	409	25	gate	gate	NOUN
easat-10856	409	26	with	with	ADP
easat-10856	409	27	respect	respect	NOUN
easat-10856	409	28	to	to	ADP
easat-10856	409	29	the	the	DET
easat-10856	409	30	euler	euler	NOUN
easat-10856	409	31	numbers	number	NOUN
easat-10856	409	32	,	,	PUNCT
easat-10856	409	33	the	the	DET
easat-10856	409	34	most	most	ADV
easat-10856	409	35	important	important	ADJ
easat-10856	409	36	,	,	PUNCT
easat-10856	409	37	convenient	convenient	ADJ
easat-10856	409	38	,	,	PUNCT
easat-10856	409	39	and	and	CCONJ
easat-10856	409	40	appropriate	appropriate	ADJ
easat-10856	409	41	expression	expression	NOUN
easat-10856	409	42	that	that	PRON
easat-10856	409	43	relates	relate	VERB
easat-10856	409	44	euler	euler	NOUN
easat-10856	409	45	numbers	number	NOUN
easat-10856	409	46	according	accord	VERB
easat-10856	409	47	to	to	ADP
easat-10856	409	48	varadarajan	varadarajan	NOUN
easat-10856	409	49	[	[	X
easat-10856	409	50	20	20	NUM
easat-10856	409	51	]	]	PUNCT
easat-10856	409	52	and	and	CCONJ
easat-10856	409	53	murray	murray	VERB
easat-10856	410	1	[	[	X
easat-10856	410	2	22	22	NUM
easat-10856	410	3	]	]	PUNCT
easat-10856	410	4	and	and	CCONJ
easat-10856	410	5	which	which	PRON
easat-10856	410	6	was	be	AUX
easat-10856	410	7	used	use	VERB
easat-10856	410	8	to	to	PART
easat-10856	410	9	calculate	calculate	VERB
easat-10856	410	10	the	the	DET
easat-10856	410	11	euler	euler	NOUN
easat-10856	410	12	numbers	number	NOUN
easat-10856	410	13	on	on	ADP
easat-10856	410	14	this	this	DET
easat-10856	410	15	occasion	occasion	NOUN
easat-10856	410	16	,	,	PUNCT
easat-10856	410	17	is	be	AUX
easat-10856	410	18	:	:	PUNCT
easat-10856	411	1	𝐸𝑛	𝐸𝑛	ADP
easat-10856	411	2	=	=	PUNCT
easat-10856	411	3	(	(	PUNCT
easat-10856	411	4	2𝑛	2𝑛	PROPN
easat-10856	411	5	2	2	NUM
easat-10856	411	6	)	)	PUNCT
easat-10856	411	7	×	×	NOUN
easat-10856	411	8	𝐸𝑛−1	𝐸𝑛−1	NOUN
easat-10856	411	9	−	−	PROPN
easat-10856	411	10	(	(	PUNCT
easat-10856	411	11	2𝑛	2𝑛	PROPN
easat-10856	411	12	4	4	NUM
easat-10856	411	13	)	)	PUNCT
easat-10856	411	14	×	×	NOUN
easat-10856	411	15	𝐸𝑛−2	𝐸𝑛−2	NOUN
easat-10856	411	16	+	+	CCONJ
easat-10856	411	17	(	(	PUNCT
easat-10856	411	18	2𝑛	2𝑛	NUM
easat-10856	411	19	6	6	NUM
easat-10856	411	20	)	)	PUNCT
easat-10856	411	21	×	×	NOUN
easat-10856	411	22	𝐸𝑛−3	𝐸𝑛−3	NOUN
easat-10856	412	1	−	−	PROPN
easat-10856	413	1	(	(	PUNCT
easat-10856	413	2	2𝑛	2𝑛	PROPN
easat-10856	413	3	8	8	NUM
easat-10856	413	4	)	)	PUNCT
easat-10856	413	5	𝐸𝑛−4	𝐸𝑛−4	PROPN
easat-10856	413	6	+	+	PROPN
easat-10856	413	7	.	.	PUNCT
easat-10856	413	8	.	.	PUNCT
easat-10856	413	9	.	.	PUNCT
easat-10856	414	1	(	(	PUNCT
easat-10856	414	2	−1	−1	NOUN
easat-10856	414	3	)	)	PUNCT
easat-10856	414	4	𝑛	𝑛	DET
easat-10856	414	5	the	the	DET
easat-10856	414	6	above	above	ADJ
easat-10856	414	7	expression	expression	NOUN
easat-10856	414	8	has	have	AUX
easat-10856	414	9	been	be	AUX
easat-10856	414	10	used	use	VERB
easat-10856	414	11	to	to	PART
easat-10856	414	12	evaluate	evaluate	VERB
easat-10856	414	13	the	the	DET
easat-10856	414	14	euler	euler	NOUN
easat-10856	414	15	numbers	number	NOUN
easat-10856	414	16	(	(	PUNCT
easat-10856	414	17	𝐸𝑛	𝐸𝑛	PROPN
easat-10856	414	18	)	)	PUNCT
easat-10856	414	19	;	;	PUNCT
easat-10856	414	20	whose	whose	DET
easat-10856	414	21	calculations	calculation	NOUN
easat-10856	414	22	are	be	AUX
easat-10856	414	23	presented	present	VERB
easat-10856	414	24	in	in	ADP
easat-10856	414	25	the	the	DET
easat-10856	414	26	development	development	NOUN
easat-10856	414	27	detailed	detail	VERB
easat-10856	414	28	below	below	ADV
easat-10856	414	29	:	:	PUNCT
easat-10856	414	30	calculation	calculation	NOUN
easat-10856	414	31	,	,	PUNCT
easat-10856	414	32	according	accord	VERB
easat-10856	414	33	to	to	ADP
easat-10856	414	34	the	the	DET
easat-10856	414	35	binomial	binomial	ADJ
easat-10856	414	36	formula	formula	NOUN
easat-10856	414	37	for	for	ADP
easat-10856	414	38	the	the	DET
easat-10856	414	39	euler	euler	NOUN
easat-10856	414	40	number	number	NOUN
easat-10856	414	41	,	,	PUNCT
easat-10856	414	42	of	of	ADP
easat-10856	414	43	𝐸1	𝐸1	NOUN
easat-10856	414	44	𝐸1	𝐸1	NOUN
easat-10856	414	45	=	=	PUNCT
easat-10856	414	46	−(−1)1	−(−1)1	NOUN
easat-10856	414	47	⇒	⇒	NOUN
easat-10856	414	48	𝐸1	𝐸1	NOUN
easat-10856	414	49	=	=	SYM
easat-10856	414	50	1	1	NUM
easat-10856	414	51	calculation	calculation	NOUN
easat-10856	414	52	,	,	PUNCT
easat-10856	414	53	according	accord	VERB
easat-10856	414	54	to	to	ADP
easat-10856	414	55	the	the	DET
easat-10856	414	56	binomial	binomial	ADJ
easat-10856	414	57	formula	formula	NOUN
easat-10856	414	58	for	for	ADP
easat-10856	414	59	the	the	DET
easat-10856	414	60	euler	euler	NOUN
easat-10856	414	61	number	number	NOUN
easat-10856	414	62	,	,	PUNCT
easat-10856	414	63	of	of	ADP
easat-10856	414	64	𝐸2	𝐸2	PROPN
easat-10856	414	65	𝐸2	𝐸2	PROPN
easat-10856	414	66	=	=	PUNCT
easat-10856	414	67	(	(	PUNCT
easat-10856	414	68	4	4	NUM
easat-10856	414	69	2	2	NUM
easat-10856	414	70	)	)	PUNCT
easat-10856	414	71	×	×	NOUN
easat-10856	414	72	1	1	NUM
easat-10856	414	73	−	−	NOUN
easat-10856	414	74	(	(	PUNCT
easat-10856	414	75	−1)2	−1)2	X
easat-10856	414	76	=	=	SYM
easat-10856	414	77	4	4	NUM
easat-10856	414	78	!	!	NOUN
easat-10856	415	1	2!×2	2!×2	NUM
easat-10856	415	2	!	!	PUNCT
easat-10856	416	1	×	×	NOUN
easat-10856	416	2	1	1	NUM
easat-10856	416	3	−	−	NUM
easat-10856	416	4	1	1	NUM
easat-10856	416	5	⇒	⇒	NOUN
easat-10856	416	6	𝐸2	𝐸2	NOUN
easat-10856	417	1	=	=	SYM
easat-10856	417	2	5	5	NUM
easat-10856	417	3	calculation	calculation	NOUN
easat-10856	417	4	,	,	PUNCT
easat-10856	417	5	according	accord	VERB
easat-10856	417	6	to	to	ADP
easat-10856	417	7	the	the	DET
easat-10856	417	8	binomial	binomial	ADJ
easat-10856	417	9	formula	formula	NOUN
easat-10856	417	10	for	for	ADP
easat-10856	417	11	the	the	DET
easat-10856	417	12	euler	euler	NOUN
easat-10856	417	13	number	number	NOUN
easat-10856	417	14	,	,	PUNCT
easat-10856	417	15	of	of	ADP
easat-10856	417	16	𝐸3	𝐸3	PROPN
easat-10856	417	17	𝐸3	𝐸3	PROPN
easat-10856	417	18	=	=	PUNCT
easat-10856	417	19	(	(	PUNCT
easat-10856	417	20	6	6	NUM
easat-10856	417	21	2	2	NUM
easat-10856	417	22	)	)	PUNCT
easat-10856	417	23	×	×	NOUN
easat-10856	417	24	5	5	NUM
easat-10856	417	25	−	−	NOUN
easat-10856	417	26	(	(	PUNCT
easat-10856	417	27	6	6	NUM
easat-10856	417	28	4	4	NUM
easat-10856	417	29	)	)	PUNCT
easat-10856	417	30	×	×	NOUN
easat-10856	417	31	1	1	NUM
easat-10856	417	32	−	−	NOUN
easat-10856	417	33	(	(	PUNCT
easat-10856	417	34	−1)3	−1)3	NOUN
easat-10856	417	35	=	=	SYM
easat-10856	417	36	6	6	NUM
easat-10856	417	37	!	!	X
easat-10856	417	38	4!×21	4!×21	NUM
easat-10856	417	39	×	×	NOUN
easat-10856	417	40	5	5	NUM
easat-10856	417	41	−	−	NOUN
easat-10856	417	42	6	6	NUM
easat-10856	417	43	!	!	SYM
easat-10856	417	44	2!×4	2!×4	NUM
easat-10856	417	45	!	!	PUNCT
easat-10856	418	1	×	×	NOUN
easat-10856	418	2	1	1	NUM
easat-10856	418	3	+	+	SYM
easat-10856	418	4	1	1	NUM
easat-10856	418	5	⇒	⇒	NOUN
easat-10856	418	6	𝐸3	𝐸3	NOUN
easat-10856	418	7	=	=	NOUN
easat-10856	418	8	61	61	NUM
easat-10856	418	9	calculation	calculation	NOUN
easat-10856	418	10	,	,	PUNCT
easat-10856	418	11	according	accord	VERB
easat-10856	418	12	to	to	ADP
easat-10856	418	13	the	the	DET
easat-10856	418	14	binomial	binomial	ADJ
easat-10856	418	15	formula	formula	NOUN
easat-10856	418	16	for	for	ADP
easat-10856	418	17	the	the	DET
easat-10856	418	18	euler	euler	NOUN
easat-10856	418	19	number	number	NOUN
easat-10856	418	20	,	,	PUNCT
easat-10856	418	21	of	of	ADP
easat-10856	418	22	𝐸4	𝐸4	NOUN
easat-10856	418	23	𝐸4	𝐸4	NOUN
easat-10856	418	24	=	=	PUNCT
easat-10856	419	1	(	(	PUNCT
easat-10856	419	2	8	8	NUM
easat-10856	419	3	2	2	NUM
easat-10856	419	4	)	)	PUNCT
easat-10856	419	5	61	61	NUM
easat-10856	419	6	−	−	NOUN
easat-10856	419	7	(	(	PUNCT
easat-10856	419	8	8	8	NUM
easat-10856	419	9	4	4	NUM
easat-10856	419	10	)	)	PUNCT
easat-10856	419	11	5	5	NUM
easat-10856	420	1	+	+	CCONJ
easat-10856	420	2	(	(	PUNCT
easat-10856	420	3	8	8	NUM
easat-10856	420	4	6	6	NUM
easat-10856	420	5	)	)	PUNCT
easat-10856	420	6	1	1	NUM
easat-10856	420	7	−	−	NOUN
easat-10856	420	8	(	(	PUNCT
easat-10856	420	9	−1)4	−1)4	NOUN
easat-10856	420	10	;	;	PUNCT
easat-10856	420	11	𝐸4	𝐸4	NOUN
easat-10856	420	12	=	=	NOUN
easat-10856	420	13	8	8	NUM
easat-10856	420	14	!	!	NUM
easat-10856	420	15	6!×2	6!×2	NUM
easat-10856	420	16	!	!	PUNCT
easat-10856	421	1	61	61	NUM
easat-10856	421	2	−	−	NUM
easat-10856	421	3	8	8	NUM
easat-10856	421	4	!	!	SYM
easat-10856	421	5	4!×4	4!×4	NUM
easat-10856	421	6	!	!	NOUN
easat-10856	421	7	5	5	NUM
easat-10856	421	8	+	+	CCONJ
easat-10856	421	9	8	8	NUM
easat-10856	421	10	!	!	NOUN
easat-10856	421	11	2!×6	2!×6	NUM
easat-10856	421	12	!	!	NOUN
easat-10856	421	13	1	1	NUM
easat-10856	421	14	−	−	NUM
easat-10856	421	15	1	1	NUM
easat-10856	421	16	⇒	⇒	NOUN
easat-10856	421	17	𝐸4	𝐸4	NOUN
easat-10856	421	18	=	=	NOUN
easat-10856	421	19	1385	1385	NUM
easat-10856	421	20	calculation	calculation	NOUN
easat-10856	421	21	,	,	PUNCT
easat-10856	421	22	according	accord	VERB
easat-10856	421	23	to	to	ADP
easat-10856	421	24	the	the	DET
easat-10856	421	25	binomial	binomial	ADJ
easat-10856	421	26	formula	formula	NOUN
easat-10856	421	27	for	for	ADP
easat-10856	421	28	the	the	DET
easat-10856	421	29	euler	euler	NOUN
easat-10856	421	30	number	number	NOUN
easat-10856	421	31	,	,	PUNCT
easat-10856	421	32	of	of	ADP
easat-10856	421	33	𝐸5	𝐸5	NOUN
easat-10856	421	34	𝐸5	𝐸5	NOUN
easat-10856	421	35	=	=	PUNCT
easat-10856	421	36	(	(	PUNCT
easat-10856	421	37	10	10	NUM
easat-10856	421	38	2	2	NUM
easat-10856	421	39	)	)	PUNCT
easat-10856	421	40	1385	1385	NUM
easat-10856	421	41	−	−	NOUN
easat-10856	421	42	(	(	PUNCT
easat-10856	421	43	10	10	NUM
easat-10856	421	44	4	4	NUM
easat-10856	421	45	)	)	PUNCT
easat-10856	421	46	61	61	NUM
easat-10856	421	47	+	+	CCONJ
easat-10856	421	48	(	(	PUNCT
easat-10856	421	49	10	10	NUM
easat-10856	421	50	6	6	NUM
easat-10856	421	51	)	)	PUNCT
easat-10856	421	52	5	5	NUM
easat-10856	421	53	−	−	PROPN
easat-10856	421	54	(	(	PUNCT
easat-10856	421	55	10	10	NUM
easat-10856	421	56	8	8	NUM
easat-10856	421	57	)	)	PUNCT
easat-10856	421	58	1	1	NUM
easat-10856	421	59	+	+	CCONJ
easat-10856	421	60	(	(	PUNCT
easat-10856	421	61	−1)5	−1)5	NOUN
easat-10856	421	62	𝐸5	𝐸5	NOUN
easat-10856	421	63	=	=	NOUN
easat-10856	421	64	10	10	NUM
easat-10856	421	65	!	!	PUNCT
easat-10856	421	66	8!×2	8!×2	NUM
easat-10856	421	67	!	!	PUNCT
easat-10856	421	68	1385	1385	NUM
easat-10856	422	1	−	−	NOUN
easat-10856	422	2	10	10	NUM
easat-10856	422	3	!	!	PUNCT
easat-10856	422	4	6!×4	6!×4	NUM
easat-10856	422	5	!	!	PUNCT
easat-10856	423	1	61	61	NUM
easat-10856	424	1	+	+	NUM
easat-10856	424	2	10	10	NUM
easat-10856	424	3	!	!	PUNCT
easat-10856	425	1	4!×6	4!×6	NUM
easat-10856	425	2	!	!	PUNCT
easat-10856	426	1	5	5	NUM
easat-10856	426	2	−	−	NOUN
easat-10856	426	3	10	10	NUM
easat-10856	426	4	!	!	SYM
easat-10856	426	5	2!×8	2!×8	NUM
easat-10856	426	6	!	!	PUNCT
easat-10856	426	7	1	1	NUM
easat-10856	426	8	+	+	NUM
easat-10856	426	9	1	1	NUM
easat-10856	426	10	𝐸5	𝐸5	NOUN
easat-10856	426	11	=	=	SYM
easat-10856	426	12	50521	50521	NUM
easat-10856	426	13	calculation	calculation	NOUN
easat-10856	426	14	,	,	PUNCT
easat-10856	426	15	according	accord	VERB
easat-10856	426	16	to	to	ADP
easat-10856	426	17	the	the	DET
easat-10856	426	18	binomial	binomial	ADJ
easat-10856	426	19	formula	formula	NOUN
easat-10856	426	20	for	for	ADP
easat-10856	426	21	the	the	DET
easat-10856	426	22	euler	euler	NOUN
easat-10856	426	23	number	number	NOUN
easat-10856	426	24	,	,	PUNCT
easat-10856	426	25	of	of	ADP
easat-10856	426	26	𝐸6	𝐸6	PROPN
easat-10856	426	27	𝐸6	𝐸6	PROPN
easat-10856	426	28	=	=	PUNCT
easat-10856	426	29	(	(	PUNCT
easat-10856	426	30	12	12	NUM
easat-10856	426	31	2	2	NUM
easat-10856	426	32	)	)	PUNCT
easat-10856	426	33	50521	50521	NUM
easat-10856	426	34	−	−	PROPN
easat-10856	426	35	(	(	PUNCT
easat-10856	426	36	12	12	NUM
easat-10856	426	37	4	4	NUM
easat-10856	426	38	)	)	PUNCT
easat-10856	426	39	1385	1385	NUM
easat-10856	427	1	+	+	CCONJ
easat-10856	427	2	(	(	PUNCT
easat-10856	427	3	12	12	NUM
easat-10856	427	4	6	6	NUM
easat-10856	427	5	)	)	PUNCT
easat-10856	427	6	61	61	NUM
easat-10856	427	7	−	−	NOUN
easat-10856	427	8	(	(	PUNCT
easat-10856	427	9	12	12	NUM
easat-10856	427	10	8	8	NUM
easat-10856	427	11	)	)	PUNCT
easat-10856	427	12	5	5	NUM
easat-10856	428	1	+	+	CCONJ
easat-10856	428	2	(	(	PUNCT
easat-10856	428	3	12	12	NUM
easat-10856	428	4	10	10	NUM
easat-10856	428	5	)	)	PUNCT
easat-10856	428	6	1	1	NUM
easat-10856	428	7	−	−	NOUN
easat-10856	428	8	(	(	PUNCT
easat-10856	428	9	−1)6	−1)6	X
easat-10856	428	10	𝐸6	𝐸6	NOUN
easat-10856	428	11	=	=	NOUN
easat-10856	428	12	12	12	NUM
easat-10856	428	13	!	!	PUNCT
easat-10856	429	1	10!×2	10!×2	NUM
easat-10856	429	2	!	!	PUNCT
easat-10856	430	1	50521	50521	NUM
easat-10856	431	1	−	−	NOUN
easat-10856	431	2	12	12	NUM
easat-10856	431	3	!	!	PUNCT
easat-10856	432	1	8!×4	8!×4	NUM
easat-10856	432	2	!	!	PUNCT
easat-10856	432	3	1385	1385	NUM
easat-10856	433	1	+	+	CCONJ
easat-10856	434	1	12	12	NUM
easat-10856	434	2	!	!	PUNCT
easat-10856	435	1	6!×6	6!×6	NUM
easat-10856	435	2	!	!	X
easat-10856	436	1	61	61	NUM
easat-10856	436	2	−	−	NUM
easat-10856	436	3	12	12	NUM
easat-10856	436	4	!	!	PUNCT
easat-10856	436	5	4!×8	4!×8	NUM
easat-10856	436	6	!	!	PUNCT
easat-10856	436	7	5	5	NUM
easat-10856	437	1	+	+	SYM
easat-10856	437	2	12	12	NUM
easat-10856	437	3	!	!	PUNCT
easat-10856	438	1	2!×10	2!×10	NUM
easat-10856	438	2	!	!	PUNCT
easat-10856	439	1	1	1	NUM
easat-10856	439	2	−	−	NUM
easat-10856	439	3	1	1	NUM
easat-10856	439	4	𝐸6	𝐸6	NOUN
easat-10856	439	5	=	=	SYM
easat-10856	439	6	2702765	2702765	NUM
easat-10856	439	7	calculation	calculation	NOUN
easat-10856	439	8	,	,	PUNCT
easat-10856	439	9	according	accord	VERB
easat-10856	439	10	to	to	ADP
easat-10856	439	11	the	the	DET
easat-10856	439	12	binomial	binomial	ADJ
easat-10856	439	13	formula	formula	NOUN
easat-10856	439	14	for	for	ADP
easat-10856	439	15	the	the	DET
easat-10856	439	16	euler	euler	NOUN
easat-10856	439	17	number	number	NOUN
easat-10856	439	18	,	,	PUNCT
easat-10856	439	19	of	of	ADP
easat-10856	439	20	𝐸7	𝐸7	NOUN
easat-10856	439	21	𝐸7	𝐸7	NOUN
easat-10856	439	22	=	=	PUNCT
easat-10856	439	23	(	(	PUNCT
easat-10856	439	24	14	14	NUM
easat-10856	439	25	2	2	NUM
easat-10856	439	26	)	)	PUNCT
easat-10856	439	27	2702765	2702765	NUM
easat-10856	439	28	−	−	PROPN
easat-10856	439	29	(	(	PUNCT
easat-10856	439	30	14	14	NUM
easat-10856	439	31	4	4	NUM
easat-10856	439	32	)	)	PUNCT
easat-10856	439	33	50521	50521	NUM
easat-10856	440	1	+	+	CCONJ
easat-10856	440	2	(	(	PUNCT
easat-10856	440	3	14	14	NUM
easat-10856	440	4	6	6	NUM
easat-10856	440	5	)	)	PUNCT
easat-10856	440	6	1385	1385	NUM
easat-10856	440	7	−	−	PROPN
easat-10856	440	8	(	(	PUNCT
easat-10856	440	9	14	14	NUM
easat-10856	440	10	8	8	NUM
easat-10856	440	11	)	)	PUNCT
easat-10856	440	12	61	61	NUM
easat-10856	441	1	+	+	CCONJ
easat-10856	441	2	(	(	PUNCT
easat-10856	441	3	14	14	NUM
easat-10856	441	4	10	10	NUM
easat-10856	441	5	)	)	PUNCT
easat-10856	441	6	5	5	NUM
easat-10856	441	7	−	−	PROPN
easat-10856	441	8	(	(	PUNCT
easat-10856	441	9	14	14	NUM
easat-10856	441	10	12	12	NUM
easat-10856	441	11	)	)	PUNCT
easat-10856	441	12	1	1	NUM
easat-10856	441	13	−	−	NOUN
easat-10856	441	14	(	(	PUNCT
easat-10856	441	15	−1)7	−1)7	NOUN
easat-10856	441	16	𝐸7	𝐸7	NOUN
easat-10856	441	17	=	=	SYM
easat-10856	441	18	14	14	NUM
easat-10856	441	19	!	!	PUNCT
easat-10856	442	1	12!×2	12!×2	NOUN
easat-10856	442	2	!	!	PUNCT
easat-10856	442	3	2702765	2702765	NUM
easat-10856	443	1	−	−	NOUN
easat-10856	443	2	14	14	NUM
easat-10856	443	3	!	!	PUNCT
easat-10856	444	1	10!×4	10!×4	NUM
easat-10856	444	2	!	!	NOUN
easat-10856	444	3	50521	50521	NUM
easat-10856	445	1	+	+	CCONJ
easat-10856	446	1	14	14	NUM
easat-10856	446	2	!	!	NUM
easat-10856	447	1	8!×6	8!×6	NUM
easat-10856	447	2	!	!	PUNCT
easat-10856	448	1	1385	1385	NUM
easat-10856	448	2	−	−	NOUN
easat-10856	448	3	14	14	NUM
easat-10856	448	4	!	!	SYM
easat-10856	448	5	6!×8	6!×8	NUM
easat-10856	448	6	!	!	PUNCT
easat-10856	449	1	61	61	NUM
easat-10856	449	2	+	+	NUM
easat-10856	449	3	14	14	NUM
easat-10856	449	4	!	!	PUNCT
easat-10856	449	5	4!×10	4!×10	NUM
easat-10856	449	6	!	!	NOUN
easat-10856	450	1	5	5	NUM
easat-10856	450	2	−	−	NOUN
easat-10856	450	3	14	14	NUM
easat-10856	450	4	!	!	PUNCT
easat-10856	450	5	2!×12	2!×12	NUM
easat-10856	450	6	!	!	PUNCT
easat-10856	451	1	+	+	CCONJ
easat-10856	451	2	1	1	NUM
easat-10856	451	3	⇒	⇒	NOUN
easat-10856	451	4	𝐸7	𝐸7	NOUN
easat-10856	451	5	=	=	SYM
easat-10856	451	6	199360981	199360981	NUM
easat-10856	451	7	calculation	calculation	NOUN
easat-10856	451	8	,	,	PUNCT
easat-10856	451	9	according	accord	VERB
easat-10856	451	10	to	to	ADP
easat-10856	451	11	the	the	DET
easat-10856	451	12	binomial	binomial	ADJ
easat-10856	451	13	formula	formula	NOUN
easat-10856	451	14	for	for	ADP
easat-10856	451	15	the	the	DET
easat-10856	451	16	euler	euler	NOUN
easat-10856	451	17	number	number	NOUN
easat-10856	451	18	,	,	PUNCT
easat-10856	451	19	of	of	ADP
easat-10856	451	20	𝐸8	𝐸8	NOUN
easat-10856	451	21	𝐸8	𝐸8	NOUN
easat-10856	451	22	=	=	SYM
easat-10856	451	23	(	(	PUNCT
easat-10856	451	24	16	16	NUM
easat-10856	451	25	2	2	NUM
easat-10856	451	26	)	)	PUNCT
easat-10856	451	27	199360981	199360981	NUM
easat-10856	451	28	−	−	PROPN
easat-10856	451	29	(	(	PUNCT
easat-10856	451	30	16	16	NUM
easat-10856	451	31	4	4	NUM
easat-10856	451	32	)	)	PUNCT
easat-10856	451	33	2702765	2702765	NUM
easat-10856	452	1	+	+	CCONJ
easat-10856	452	2	(	(	PUNCT
easat-10856	452	3	16	16	NUM
easat-10856	452	4	6	6	NUM
easat-10856	452	5	)	)	PUNCT
easat-10856	452	6	50521	50521	NUM
easat-10856	452	7	−	−	PROPN
easat-10856	452	8	(	(	PUNCT
easat-10856	452	9	16	16	NUM
easat-10856	452	10	8	8	NUM
easat-10856	452	11	)	)	PUNCT
easat-10856	452	12	1385	1385	NUM
easat-10856	453	1	+	+	CCONJ
easat-10856	453	2	(	(	PUNCT
easat-10856	453	3	16	16	NUM
easat-10856	453	4	10	10	NUM
easat-10856	453	5	)	)	PUNCT
easat-10856	453	6	61	61	NUM
easat-10856	453	7	−	−	PROPN
easat-10856	453	8	(	(	PUNCT
easat-10856	453	9	16	16	NUM
easat-10856	453	10	12	12	NUM
easat-10856	453	11	)	)	PUNCT
easat-10856	453	12	5	5	NUM
easat-10856	454	1	+	+	CCONJ
easat-10856	454	2	(	(	PUNCT
easat-10856	454	3	16	16	NUM
easat-10856	454	4	14	14	NUM
easat-10856	454	5	)	)	PUNCT
easat-10856	454	6	1	1	NUM
easat-10856	454	7	−	−	NOUN
easat-10856	454	8	(	(	PUNCT
easat-10856	454	9	−1)8	−1)8	X
easat-10856	454	10	𝐸8	𝐸8	NOUN
easat-10856	454	11	=	=	SYM
easat-10856	454	12	16	16	NUM
easat-10856	454	13	!	!	PUNCT
easat-10856	455	1	14!×2	14!×2	NUM
easat-10856	455	2	!	!	PUNCT
easat-10856	455	3	199360981	199360981	NUM
easat-10856	455	4	−	−	NOUN
easat-10856	455	5	16	16	NUM
easat-10856	455	6	!	!	PUNCT
easat-10856	456	1	12!×4	12!×4	X
easat-10856	456	2	!	!	PUNCT
easat-10856	456	3	2702765	2702765	NUM
easat-10856	457	1	+	+	CCONJ
easat-10856	457	2	16	16	NUM
easat-10856	457	3	!	!	PUNCT
easat-10856	458	1	10!×6	10!×6	X
easat-10856	458	2	!	!	PUNCT
easat-10856	459	1	50521	50521	NUM
easat-10856	459	2	−	−	NOUN
easat-10856	459	3	16	16	NUM
easat-10856	459	4	!	!	PUNCT
easat-10856	459	5	8!×8	8!×8	NUM
easat-10856	459	6	!	!	PUNCT
easat-10856	460	1	1385	1385	NUM
easat-10856	461	1	+	+	CCONJ
easat-10856	462	1	16	16	NUM
easat-10856	462	2	!	!	PUNCT
easat-10856	462	3	6!×10	6!×10	NOUN
easat-10856	462	4	!	!	PUNCT
easat-10856	463	1	61	61	NUM
easat-10856	463	2	−	−	NUM
easat-10856	463	3	16	16	NUM
easat-10856	463	4	!	!	PUNCT
easat-10856	463	5	4!×12	4!×12	PROPN
easat-10856	463	6	!	!	PUNCT
easat-10856	463	7	5	5	NUM
easat-10856	463	8	+	+	SYM
easat-10856	463	9	16	16	NUM
easat-10856	463	10	!	!	PUNCT
easat-10856	463	11	2!×14	2!×14	NUM
easat-10856	463	12	!	!	PUNCT
easat-10856	464	1	−	−	NOUN
easat-10856	464	2	1	1	NUM
easat-10856	464	3	⇒	⇒	NOUN
easat-10856	464	4	𝐸8	𝐸8	ADJ
easat-10856	464	5	=	=	SYM
easat-10856	464	6	19391512145	19391512145	NUM
easat-10856	464	7	calculation	calculation	NOUN
easat-10856	464	8	,	,	PUNCT
easat-10856	464	9	according	accord	VERB
easat-10856	464	10	to	to	ADP
easat-10856	464	11	the	the	DET
easat-10856	464	12	binomial	binomial	ADJ
easat-10856	464	13	formula	formula	NOUN
easat-10856	464	14	for	for	ADP
easat-10856	464	15	the	the	DET
easat-10856	464	16	euler	euler	NOUN
easat-10856	464	17	number	number	NOUN
easat-10856	464	18	,	,	PUNCT
easat-10856	464	19	of	of	ADP
easat-10856	464	20	𝐸9	𝐸9	PROPN
easat-10856	464	21	𝐸9	𝐸9	NOUN
easat-10856	464	22	=	=	PUNCT
easat-10856	464	23	(	(	PUNCT
easat-10856	464	24	18	18	NUM
easat-10856	464	25	2	2	NUM
easat-10856	464	26	)	)	PUNCT
easat-10856	464	27	19391512145	19391512145	NUM
easat-10856	464	28	−	−	PROPN
easat-10856	464	29	(	(	PUNCT
easat-10856	464	30	18	18	NUM
easat-10856	464	31	4	4	NUM
easat-10856	464	32	)	)	PUNCT
easat-10856	464	33	199360981	199360981	NUM
easat-10856	465	1	+	+	CCONJ
easat-10856	465	2	(	(	PUNCT
easat-10856	465	3	18	18	NUM
easat-10856	465	4	6	6	NUM
easat-10856	465	5	)	)	PUNCT
easat-10856	465	6	2702765	2702765	NUM
easat-10856	465	7	−	−	PROPN
easat-10856	465	8	(	(	PUNCT
easat-10856	465	9	18	18	NUM
easat-10856	465	10	8	8	NUM
easat-10856	465	11	)	)	PUNCT
easat-10856	465	12	50521	50521	NUM
easat-10856	466	1	+	+	CCONJ
easat-10856	466	2	(	(	PUNCT
easat-10856	466	3	18	18	NUM
easat-10856	466	4	10	10	NUM
easat-10856	466	5	)	)	PUNCT
easat-10856	466	6	1385	1385	NUM
easat-10856	466	7	−	−	PROPN
easat-10856	466	8	(	(	PUNCT
easat-10856	466	9	18	18	NUM
easat-10856	466	10	12	12	NUM
easat-10856	466	11	)	)	PUNCT
easat-10856	466	12	61	61	NUM
easat-10856	466	13	+	+	CCONJ
easat-10856	466	14	(	(	PUNCT
easat-10856	466	15	18	18	NUM
easat-10856	466	16	14	14	NUM
easat-10856	466	17	)	)	PUNCT
easat-10856	466	18	5	5	NUM
easat-10856	466	19	−	−	PROPN
easat-10856	466	20	(	(	PUNCT
easat-10856	466	21	18	18	NUM
easat-10856	466	22	16	16	NUM
easat-10856	466	23	)	)	PUNCT
easat-10856	466	24	1	1	NUM
easat-10856	466	25	−	−	NOUN
easat-10856	466	26	(	(	PUNCT
easat-10856	466	27	−1)9	−1)9	NUM
easat-10856	466	28	282	282	NUM
easat-10856	466	29	edelweiss	edelweiss	PROPN
easat-10856	466	30	applied	apply	VERB
easat-10856	466	31	science	science	NOUN
easat-10856	466	32	and	and	CCONJ
easat-10856	466	33	technology	technology	NOUN
easat-10856	466	34	issn	issn	PROPN
easat-10856	466	35	:	:	PUNCT
easat-10856	466	36	2576	2576	NUM
easat-10856	466	37	-	-	SYM
easat-10856	466	38	8484	8484	NUM
easat-10856	466	39	vol	vol	NOUN
easat-10856	466	40	.	.	PROPN
easat-10856	467	1	9	9	NUM
easat-10856	467	2	,	,	PUNCT
easat-10856	467	3	no	no	INTJ
easat-10856	467	4	.	.	NOUN
easat-10856	467	5	11	11	NUM
easat-10856	467	6	:	:	PUNCT
easat-10856	467	7	274	274	NUM
easat-10856	467	8	-	-	SYM
easat-10856	467	9	288	288	NUM
easat-10856	467	10	,	,	PUNCT
easat-10856	467	11	2025	2025	NUM
easat-10856	467	12	doi	doi	NOUN
easat-10856	467	13	:	:	PUNCT
easat-10856	467	14	10.55214/2576	10.55214/2576	NUM
easat-10856	467	15	-	-	PUNCT
easat-10856	467	16	8484.v9i11.10856	8484.v9i11.10856	NUM
easat-10856	467	17	©	©	PROPN
easat-10856	467	18	2025	2025	NUM
easat-10856	467	19	by	by	ADP
easat-10856	467	20	the	the	DET
easat-10856	467	21	authors	author	NOUN
easat-10856	467	22	;	;	PUNCT
easat-10856	468	1	licensee	licensee	PROPN
easat-10856	468	2	learning	learn	VERB
easat-10856	468	3	gate	gate	PROPN
easat-10856	468	4	𝐸9	𝐸9	PROPN
easat-10856	468	5	=	=	NUM
easat-10856	468	6	18	18	NUM
easat-10856	468	7	!	!	PUNCT
easat-10856	469	1	16!×2	16!×2	ADJ
easat-10856	469	2	!	!	PUNCT
easat-10856	470	1	19391512145	19391512145	NUM
easat-10856	470	2	−	−	NOUN
easat-10856	470	3	18	18	NUM
easat-10856	470	4	!	!	PUNCT
easat-10856	471	1	14!×4	14!×4	NUM
easat-10856	471	2	!	!	NOUN
easat-10856	471	3	199360981	199360981	NUM
easat-10856	471	4	+	+	SYM
easat-10856	471	5	18	18	NUM
easat-10856	471	6	!	!	PUNCT
easat-10856	471	7	12!×6	12!×6	NOUN
easat-10856	471	8	!	!	PUNCT
easat-10856	472	1	2702765	2702765	NUM
easat-10856	473	1	−	−	NOUN
easat-10856	473	2	18	18	NUM
easat-10856	473	3	!	!	PUNCT
easat-10856	474	1	10!×8	10!×8	NUM
easat-10856	474	2	!	!	PUNCT
easat-10856	475	1	50521	50521	NUM
easat-10856	475	2	+	+	CCONJ
easat-10856	475	3	18	18	NUM
easat-10856	475	4	!	!	NUM
easat-10856	475	5	8!×10	8!×10	NUM
easat-10856	475	6	!	!	PUNCT
easat-10856	476	1	1385	1385	NUM
easat-10856	476	2	−	−	NOUN
easat-10856	476	3	18	18	NUM
easat-10856	476	4	!	!	PUNCT
easat-10856	477	1	6!×12	6!×12	NUM
easat-10856	477	2	!	!	PUNCT
easat-10856	478	1	61	61	NUM
easat-10856	478	2	+	+	SYM
easat-10856	478	3	18	18	NUM
easat-10856	478	4	!	!	PUNCT
easat-10856	478	5	4!×14	4!×14	NUM
easat-10856	478	6	!	!	PUNCT
easat-10856	479	1	5	5	NUM
easat-10856	479	2	−	−	NOUN
easat-10856	479	3	18	18	NUM
easat-10856	479	4	!	!	PUNCT
easat-10856	480	1	2!×16	2!×16	NUM
easat-10856	480	2	!	!	NOUN
easat-10856	480	3	1	1	NUM
easat-10856	480	4	+	+	SYM
easat-10856	480	5	1	1	NUM
easat-10856	480	6	⇒	⇒	NOUN
easat-10856	480	7	𝐸9	𝐸9	NOUN
easat-10856	480	8	=	=	SYM
easat-10856	480	9	2404879675441	2404879675441	NUM
easat-10856	480	10	calculation	calculation	NOUN
easat-10856	480	11	,	,	PUNCT
easat-10856	480	12	according	accord	VERB
easat-10856	480	13	to	to	ADP
easat-10856	480	14	the	the	DET
easat-10856	480	15	binomial	binomial	ADJ
easat-10856	480	16	formula	formula	NOUN
easat-10856	480	17	for	for	ADP
easat-10856	480	18	the	the	DET
easat-10856	480	19	euler	euler	NOUN
easat-10856	480	20	number	number	NOUN
easat-10856	480	21	,	,	PUNCT
easat-10856	480	22	of	of	ADP
easat-10856	480	23	𝐸10	𝐸10	PROPN
easat-10856	480	24	𝐸10	𝐸10	PROPN
easat-10856	480	25	=	=	SYM
easat-10856	480	26	(	(	PUNCT
easat-10856	480	27	20	20	NUM
easat-10856	480	28	2	2	NUM
easat-10856	480	29	)	)	PUNCT
easat-10856	480	30	2404879675441	2404879675441	NUM
easat-10856	480	31	−	−	NOUN
easat-10856	480	32	(	(	PUNCT
easat-10856	480	33	20	20	NUM
easat-10856	480	34	4	4	NUM
easat-10856	480	35	)	)	PUNCT
easat-10856	480	36	19391512145	19391512145	NUM
easat-10856	480	37	+	+	CCONJ
easat-10856	480	38	(	(	PUNCT
easat-10856	480	39	20	20	NUM
easat-10856	480	40	6	6	NUM
easat-10856	480	41	)	)	PUNCT
easat-10856	480	42	199360981	199360981	NUM
easat-10856	480	43	−	−	PROPN
easat-10856	480	44	(	(	PUNCT
easat-10856	480	45	20	20	NUM
easat-10856	480	46	8	8	NUM
easat-10856	480	47	)	)	PUNCT
easat-10856	480	48	2702765	2702765	NUM
easat-10856	480	49	+	+	CCONJ
easat-10856	480	50	(	(	PUNCT
easat-10856	480	51	20	20	NUM
easat-10856	480	52	10	10	NUM
easat-10856	480	53	)	)	PUNCT
easat-10856	480	54	50521	50521	NUM
easat-10856	480	55	−	−	NOUN
easat-10856	480	56	(	(	PUNCT
easat-10856	480	57	20	20	NUM
easat-10856	480	58	12	12	NUM
easat-10856	480	59	)	)	PUNCT
easat-10856	480	60	1385	1385	NUM
easat-10856	481	1	+	+	CCONJ
easat-10856	481	2	(	(	PUNCT
easat-10856	481	3	20	20	NUM
easat-10856	481	4	14	14	NUM
easat-10856	481	5	)	)	PUNCT
easat-10856	481	6	61	61	NUM
easat-10856	481	7	−	−	PROPN
easat-10856	481	8	(	(	PUNCT
easat-10856	481	9	20	20	NUM
easat-10856	481	10	16	16	NUM
easat-10856	481	11	)	)	PUNCT
easat-10856	481	12	5	5	NUM
easat-10856	482	1	+	+	CCONJ
easat-10856	482	2	(	(	PUNCT
easat-10856	482	3	20	20	NUM
easat-10856	482	4	18	18	NUM
easat-10856	482	5	)	)	PUNCT
easat-10856	482	6	1	1	NUM
easat-10856	482	7	−	−	PROPN
easat-10856	482	8	(	(	PUNCT
easat-10856	482	9	−1)10	−1)10	PROPN
easat-10856	482	10	𝐸10	𝐸10	PROPN
easat-10856	482	11	=	=	SYM
easat-10856	482	12	20	20	NUM
easat-10856	482	13	!	!	PUNCT
easat-10856	483	1	18!×2	18!×2	NUM
easat-10856	483	2	!	!	PUNCT
easat-10856	484	1	2404879675441	2404879675441	NUM
easat-10856	485	1	−	−	NOUN
easat-10856	485	2	20	20	NUM
easat-10856	485	3	!	!	PUNCT
easat-10856	486	1	16!×4	16!×4	NUM
easat-10856	486	2	!	!	NOUN
easat-10856	486	3	1939151214	1939151214	NUM
easat-10856	487	1	+	+	CCONJ
easat-10856	488	1	20	20	NUM
easat-10856	488	2	!	!	PUNCT
easat-10856	488	3	14!×6	14!×6	NUM
easat-10856	488	4	!	!	PUNCT
easat-10856	489	1	199360981	199360981	NUM
easat-10856	489	2	−	−	NOUN
easat-10856	489	3	20	20	NUM
easat-10856	489	4	!	!	PUNCT
easat-10856	490	1	12!×8	12!×8	NUM
easat-10856	490	2	!	!	PUNCT
easat-10856	490	3	2702765	2702765	NUM
easat-10856	491	1	+	+	CCONJ
easat-10856	491	2	20	20	NUM
easat-10856	491	3	!	!	PUNCT
easat-10856	492	1	10!×10	10!×10	X
easat-10856	492	2	!	!	NOUN
easat-10856	492	3	50521	50521	NUM
easat-10856	493	1	−	−	NOUN
easat-10856	493	2	20	20	NUM
easat-10856	493	3	!	!	PUNCT
easat-10856	493	4	8!×12	8!×12	NUM
easat-10856	493	5	!	!	PUNCT
easat-10856	494	1	1385	1385	NUM
easat-10856	495	1	+	+	CCONJ
easat-10856	495	2	20	20	NUM
easat-10856	495	3	!	!	X
easat-10856	495	4	6!×14	6!×14	NUM
easat-10856	495	5	!	!	PUNCT
easat-10856	496	1	61	61	NUM
easat-10856	496	2	−	−	NUM
easat-10856	496	3	20	20	NUM
easat-10856	496	4	!	!	PUNCT
easat-10856	497	1	4!×16	4!×16	NUM
easat-10856	497	2	!	!	PUNCT
easat-10856	498	1	5	5	NUM
easat-10856	498	2	+	+	SYM
easat-10856	498	3	20	20	NUM
easat-10856	498	4	!	!	PUNCT
easat-10856	499	1	2!×18	2!×18	NUM
easat-10856	499	2	!	!	PUNCT
easat-10856	500	1	1	1	NUM
easat-10856	500	2	−	−	NUM
easat-10856	500	3	1	1	NUM
easat-10856	500	4	⇒	⇒	NOUN
easat-10856	500	5	𝐸10	𝐸10	PROPN
easat-10856	500	6	=	=	SYM
easat-10856	500	7	370371188237525	370371188237525	NUM
easat-10856	500	8	calculation	calculation	NOUN
easat-10856	500	9	,	,	PUNCT
easat-10856	500	10	according	accord	VERB
easat-10856	500	11	to	to	ADP
easat-10856	500	12	the	the	DET
easat-10856	500	13	binomial	binomial	ADJ
easat-10856	500	14	formula	formula	NOUN
easat-10856	500	15	for	for	ADP
easat-10856	500	16	the	the	DET
easat-10856	500	17	euler	euler	NOUN
easat-10856	500	18	number	number	NOUN
easat-10856	500	19	,	,	PUNCT
easat-10856	500	20	of	of	ADP
easat-10856	500	21	𝐸11	𝐸11	PROPN
easat-10856	500	22	𝐸11	𝐸11	PROPN
easat-10856	500	23	=	=	PUNCT
easat-10856	500	24	(	(	PUNCT
easat-10856	500	25	22	22	NUM
easat-10856	500	26	2	2	NUM
easat-10856	500	27	)	)	PUNCT
easat-10856	500	28	370371188237525	370371188237525	NUM
easat-10856	500	29	−	−	PROPN
easat-10856	500	30	(	(	PUNCT
easat-10856	500	31	22	22	NUM
easat-10856	500	32	4	4	NUM
easat-10856	500	33	)	)	PUNCT
easat-10856	500	34	2404879675441	2404879675441	NUM
easat-10856	500	35	+	+	CCONJ
easat-10856	500	36	(	(	PUNCT
easat-10856	500	37	22	22	NUM
easat-10856	500	38	6	6	NUM
easat-10856	500	39	)	)	PUNCT
easat-10856	500	40	19391512145	19391512145	NUM
easat-10856	500	41	−	−	PROPN
easat-10856	500	42	(	(	PUNCT
easat-10856	500	43	22	22	NUM
easat-10856	500	44	8	8	NUM
easat-10856	500	45	)	)	PUNCT
easat-10856	500	46	199360981	199360981	NUM
easat-10856	500	47	+	+	CCONJ
easat-10856	500	48	(	(	PUNCT
easat-10856	500	49	22	22	NUM
easat-10856	500	50	10	10	NUM
easat-10856	500	51	)	)	PUNCT
easat-10856	500	52	2702765	2702765	NUM
easat-10856	500	53	−	−	PROPN
easat-10856	501	1	(	(	PUNCT
easat-10856	501	2	22	22	NUM
easat-10856	501	3	12	12	NUM
easat-10856	501	4	)	)	PUNCT
easat-10856	501	5	50521	50521	NUM
easat-10856	502	1	+	+	CCONJ
easat-10856	502	2	(	(	PUNCT
easat-10856	502	3	22	22	NUM
easat-10856	502	4	14	14	NUM
easat-10856	502	5	)	)	PUNCT
easat-10856	502	6	1385	1385	NUM
easat-10856	502	7	−	−	PROPN
easat-10856	502	8	(	(	PUNCT
easat-10856	502	9	22	22	NUM
easat-10856	502	10	16	16	NUM
easat-10856	502	11	)	)	PUNCT
easat-10856	502	12	61	61	NUM
easat-10856	503	1	+	+	CCONJ
easat-10856	503	2	(	(	PUNCT
easat-10856	503	3	22	22	NUM
easat-10856	503	4	18	18	NUM
easat-10856	503	5	)	)	PUNCT
easat-10856	503	6	5	5	NUM
easat-10856	503	7	−	−	PROPN
easat-10856	503	8	(	(	PUNCT
easat-10856	503	9	22	22	NUM
easat-10856	503	10	20	20	NUM
easat-10856	503	11	)	)	PUNCT
easat-10856	503	12	1	1	NUM
easat-10856	503	13	−	−	PROPN
easat-10856	503	14	(	(	PUNCT
easat-10856	503	15	−1)11	−1)11	PROPN
easat-10856	503	16	𝐸11	𝐸11	PROPN
easat-10856	503	17	=	=	PUNCT
easat-10856	503	18	22	22	NUM
easat-10856	503	19	!	!	PUNCT
easat-10856	504	1	20!×2	20!×2	NUM
easat-10856	504	2	!	!	PUNCT
easat-10856	505	1	370371188237525	370371188237525	NUM
easat-10856	506	1	−	−	NOUN
easat-10856	506	2	22	22	NUM
easat-10856	506	3	!	!	PUNCT
easat-10856	507	1	18!×4	18!×4	NUM
easat-10856	507	2	!	!	PUNCT
easat-10856	507	3	2404879675441	2404879675441	NUM
easat-10856	508	1	+	+	CCONJ
easat-10856	509	1	22	22	NUM
easat-10856	509	2	!	!	PUNCT
easat-10856	510	1	16!×6	16!×6	X
easat-10856	510	2	!	!	PUNCT
easat-10856	511	1	19391512145	19391512145	NUM
easat-10856	512	1	−	−	NOUN
easat-10856	513	1	22	22	NUM
easat-10856	513	2	!	!	PUNCT
easat-10856	513	3	14!×8	14!×8	NUM
easat-10856	513	4	!	!	PUNCT
easat-10856	514	1	199360981	199360981	NUM
easat-10856	515	1	+	+	CCONJ
easat-10856	515	2	22	22	NUM
easat-10856	515	3	!	!	PUNCT
easat-10856	516	1	12!×10	12!×10	X
easat-10856	516	2	!	!	NOUN
easat-10856	516	3	2702765	2702765	NUM
easat-10856	517	1	−	−	NOUN
easat-10856	518	1	22	22	NUM
easat-10856	518	2	!	!	PUNCT
easat-10856	519	1	10!×12	10!×12	NUM
easat-10856	519	2	!	!	PUNCT
easat-10856	520	1	50521	50521	NUM
easat-10856	520	2	+	+	CCONJ
easat-10856	520	3	22	22	NUM
easat-10856	520	4	!	!	PUNCT
easat-10856	520	5	8!×14	8!×14	NUM
easat-10856	520	6	!	!	PUNCT
easat-10856	521	1	1385	1385	NUM
easat-10856	521	2	−	−	NOUN
easat-10856	521	3	22	22	NUM
easat-10856	521	4	!	!	PUNCT
easat-10856	522	1	6!×16	6!×16	NUM
easat-10856	522	2	!	!	PUNCT
easat-10856	523	1	61	61	NUM
easat-10856	523	2	+	+	NUM
easat-10856	523	3	22	22	NUM
easat-10856	523	4	!	!	PUNCT
easat-10856	523	5	4!×18	4!×18	VERB
easat-10856	523	6	!	!	PUNCT
easat-10856	524	1	5	5	NUM
easat-10856	524	2	−	−	NOUN
easat-10856	524	3	22	22	NUM
easat-10856	524	4	!	!	PUNCT
easat-10856	524	5	2!×20	2!×20	NUM
easat-10856	524	6	!	!	PUNCT
easat-10856	525	1	1	1	NUM
easat-10856	525	2	+	+	SYM
easat-10856	525	3	1	1	NUM
easat-10856	525	4	⇒	⇒	NOUN
easat-10856	525	5	𝐸11	𝐸11	PROPN
easat-10856	525	6	=	=	SYM
easat-10856	525	7	69348874393137901	69348874393137901	NUM
easat-10856	525	8	calculation	calculation	NOUN
easat-10856	525	9	,	,	PUNCT
easat-10856	525	10	according	accord	VERB
easat-10856	525	11	to	to	ADP
easat-10856	525	12	the	the	DET
easat-10856	525	13	binomial	binomial	ADJ
easat-10856	525	14	formula	formula	NOUN
easat-10856	525	15	for	for	ADP
easat-10856	525	16	the	the	DET
easat-10856	525	17	euler	euler	NOUN
easat-10856	525	18	number	number	NOUN
easat-10856	525	19	,	,	PUNCT
easat-10856	525	20	of	of	ADP
easat-10856	525	21	𝐸12	𝐸12	PROPN
easat-10856	525	22	𝐸12	𝐸12	PROPN
easat-10856	525	23	=	=	SYM
easat-10856	525	24	(	(	PUNCT
easat-10856	525	25	24	24	NUM
easat-10856	525	26	2	2	NUM
easat-10856	525	27	)	)	PUNCT
easat-10856	525	28	69348874393137901	69348874393137901	NUM
easat-10856	525	29	−	−	PROPN
easat-10856	525	30	(	(	PUNCT
easat-10856	525	31	24	24	NUM
easat-10856	525	32	4	4	NUM
easat-10856	525	33	)	)	PUNCT
easat-10856	525	34	370371188237525	370371188237525	NUM
easat-10856	526	1	+	+	CCONJ
easat-10856	526	2	(	(	PUNCT
easat-10856	526	3	24	24	NUM
easat-10856	526	4	6	6	NUM
easat-10856	526	5	)	)	PUNCT
easat-10856	526	6	2404879675441	2404879675441	NUM
easat-10856	526	7	−	−	PROPN
easat-10856	526	8	(	(	PUNCT
easat-10856	526	9	24	24	NUM
easat-10856	526	10	8	8	NUM
easat-10856	526	11	)	)	PUNCT
easat-10856	526	12	19391512145	19391512145	NUM
easat-10856	527	1	+	+	CCONJ
easat-10856	527	2	(	(	PUNCT
easat-10856	527	3	24	24	NUM
easat-10856	527	4	10	10	NUM
easat-10856	527	5	)	)	PUNCT
easat-10856	527	6	199360981	199360981	NUM
easat-10856	527	7	−	−	PROPN
easat-10856	527	8	(	(	PUNCT
easat-10856	527	9	24	24	NUM
easat-10856	527	10	12	12	NUM
easat-10856	527	11	)	)	PUNCT
easat-10856	527	12	2702765	2702765	NUM
easat-10856	528	1	+	+	CCONJ
easat-10856	528	2	(	(	PUNCT
easat-10856	528	3	24	24	NUM
easat-10856	528	4	14	14	NUM
easat-10856	528	5	)	)	PUNCT
easat-10856	528	6	50521	50521	NUM
easat-10856	528	7	−	−	PROPN
easat-10856	528	8	(	(	PUNCT
easat-10856	528	9	24	24	NUM
easat-10856	528	10	16	16	NUM
easat-10856	528	11	)	)	PUNCT
easat-10856	528	12	1385	1385	NUM
easat-10856	529	1	+	+	CCONJ
easat-10856	529	2	(	(	PUNCT
easat-10856	529	3	24	24	NUM
easat-10856	529	4	18	18	NUM
easat-10856	529	5	)	)	PUNCT
easat-10856	529	6	61	61	NUM
easat-10856	529	7	−	−	PROPN
easat-10856	529	8	(	(	PUNCT
easat-10856	529	9	24	24	NUM
easat-10856	529	10	20	20	NUM
easat-10856	529	11	)	)	PUNCT
easat-10856	529	12	5	5	NUM
easat-10856	530	1	+	+	CCONJ
easat-10856	530	2	(	(	PUNCT
easat-10856	530	3	24	24	NUM
easat-10856	530	4	22	22	NUM
easat-10856	530	5	)	)	PUNCT
easat-10856	530	6	1	1	NUM
easat-10856	530	7	−	−	PROPN
easat-10856	530	8	(	(	PUNCT
easat-10856	530	9	−1)12	−1)12	PROPN
easat-10856	530	10	𝐸12	𝐸12	PROPN
easat-10856	530	11	=	=	SYM
easat-10856	530	12	24	24	NUM
easat-10856	530	13	!	!	PUNCT
easat-10856	531	1	22!×2	22!×2	NUM
easat-10856	531	2	!	!	PUNCT
easat-10856	532	1	69348874393137901	69348874393137901	NUM
easat-10856	532	2	−	−	NOUN
easat-10856	533	1	24	24	NUM
easat-10856	533	2	!	!	PUNCT
easat-10856	533	3	20!×4	20!×4	NUM
easat-10856	533	4	!	!	PUNCT
easat-10856	534	1	37037118823752	37037118823752	NUM
easat-10856	534	2	+	+	CCONJ
easat-10856	534	3	24	24	NUM
easat-10856	534	4	!	!	PUNCT
easat-10856	535	1	18!×6	18!×6	ADJ
easat-10856	535	2	!	!	PUNCT
easat-10856	536	1	2404879675441	2404879675441	NUM
easat-10856	536	2	−	−	NOUN
easat-10856	536	3	24	24	NUM
easat-10856	536	4	!	!	PUNCT
easat-10856	536	5	16!×8	16!×8	NUM
easat-10856	536	6	!	!	PUNCT
easat-10856	537	1	19391512145	19391512145	NUM
easat-10856	538	1	+	+	CCONJ
easat-10856	539	1	24	24	NUM
easat-10856	539	2	!	!	PUNCT
easat-10856	539	3	14!×10	14!×10	NUM
easat-10856	539	4	!	!	NOUN
easat-10856	539	5	199360981	199360981	NUM
easat-10856	539	6	−	−	NUM
easat-10856	539	7	24	24	NUM
easat-10856	539	8	!	!	PUNCT
easat-10856	540	1	12!×12	12!×12	NUM
easat-10856	540	2	!	!	NOUN
easat-10856	540	3	2702765	2702765	NUM
easat-10856	541	1	+	+	CCONJ
easat-10856	542	1	24	24	NUM
easat-10856	542	2	!	!	X
easat-10856	542	3	10!×14	10!×14	NUM
easat-10856	542	4	!	!	PUNCT
easat-10856	543	1	50521	50521	NUM
easat-10856	543	2	−	−	NOUN
easat-10856	543	3	24	24	NUM
easat-10856	543	4	!	!	PUNCT
easat-10856	543	5	8!×16	8!×16	NUM
easat-10856	543	6	!	!	PUNCT
easat-10856	544	1	1385	1385	NUM
easat-10856	544	2	+	+	CCONJ
easat-10856	544	3	24	24	NUM
easat-10856	544	4	!	!	PUNCT
easat-10856	545	1	6!×18	6!×18	NUM
easat-10856	545	2	!	!	PUNCT
easat-10856	546	1	61	61	NUM
easat-10856	546	2	−	−	NUM
easat-10856	546	3	24	24	NUM
easat-10856	546	4	!	!	PUNCT
easat-10856	546	5	4!×20	4!×20	NUM
easat-10856	546	6	!	!	PUNCT
easat-10856	546	7	5	5	NUM
easat-10856	546	8	+	+	SYM
easat-10856	546	9	24	24	NUM
easat-10856	546	10	!	!	PUNCT
easat-10856	546	11	2!×22	2!×22	NUM
easat-10856	546	12	!	!	NOUN
easat-10856	546	13	1	1	NUM
easat-10856	546	14	−	−	NOUN
easat-10856	546	15	1	1	NUM
easat-10856	546	16	⇒	⇒	NOUN
easat-10856	546	17	𝐸12	𝐸12	PROPN
easat-10856	546	18	=	=	SYM
easat-10856	546	19	15514534163557086905	15514534163557086905	NUM
easat-10856	546	20	calculation	calculation	NOUN
easat-10856	546	21	,	,	PUNCT
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easat-10856	546	24	the	the	DET
easat-10856	546	25	binomial	binomial	ADJ
easat-10856	546	26	formula	formula	NOUN
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easat-10856	546	28	the	the	DET
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easat-10856	546	30	number	number	NOUN
easat-10856	546	31	,	,	PUNCT
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easat-10856	546	34	𝐸13	𝐸13	PROPN
easat-10856	546	35	=	=	PUNCT
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easat-10856	546	37	26	26	NUM
easat-10856	546	38	2	2	NUM
easat-10856	546	39	)	)	PUNCT
easat-10856	546	40	15514534163557086905	15514534163557086905	NUM
easat-10856	547	1	−	−	PROPN
easat-10856	547	2	(	(	PUNCT
easat-10856	547	3	26	26	NUM
easat-10856	547	4	4	4	NUM
easat-10856	547	5	)	)	PUNCT
easat-10856	547	6	69348874393137901	69348874393137901	NUM
easat-10856	548	1	+	+	CCONJ
easat-10856	548	2	(	(	PUNCT
easat-10856	548	3	26	26	NUM
easat-10856	548	4	6	6	NUM
easat-10856	548	5	)	)	PUNCT
easat-10856	548	6	370371188237525	370371188237525	NUM
easat-10856	548	7	−	−	PROPN
easat-10856	548	8	(	(	PUNCT
easat-10856	548	9	26	26	NUM
easat-10856	548	10	8	8	NUM
easat-10856	548	11	)	)	PUNCT
easat-10856	548	12	2404879675441	2404879675441	NUM
easat-10856	548	13	+	+	CCONJ
easat-10856	548	14	(	(	PUNCT
easat-10856	548	15	26	26	NUM
easat-10856	548	16	10	10	NUM
easat-10856	548	17	)	)	PUNCT
easat-10856	548	18	19391512145	19391512145	NUM
easat-10856	548	19	−	−	PROPN
easat-10856	548	20	(	(	PUNCT
easat-10856	548	21	26	26	NUM
easat-10856	548	22	12	12	NUM
easat-10856	548	23	)	)	PUNCT
easat-10856	548	24	199360981	199360981	NUM
easat-10856	548	25	+	+	CCONJ
easat-10856	548	26	(	(	PUNCT
easat-10856	548	27	26	26	NUM
easat-10856	548	28	14	14	NUM
easat-10856	548	29	)	)	PUNCT
easat-10856	548	30	2702765	2702765	NUM
easat-10856	548	31	−	−	PROPN
easat-10856	548	32	(	(	PUNCT
easat-10856	548	33	26	26	NUM
easat-10856	548	34	16	16	NUM
easat-10856	548	35	)	)	PUNCT
easat-10856	548	36	50521	50521	NUM
easat-10856	548	37	+	+	CCONJ
easat-10856	548	38	(	(	PUNCT
easat-10856	548	39	26	26	NUM
easat-10856	548	40	18	18	NUM
easat-10856	548	41	)	)	PUNCT
easat-10856	548	42	1385	1385	NUM
easat-10856	548	43	−	−	PROPN
easat-10856	548	44	(	(	PUNCT
easat-10856	548	45	26	26	NUM
easat-10856	548	46	20	20	NUM
easat-10856	548	47	)	)	PUNCT
easat-10856	548	48	61	61	NUM
easat-10856	548	49	+	+	CCONJ
easat-10856	548	50	(	(	PUNCT
easat-10856	548	51	26	26	NUM
easat-10856	548	52	22	22	NUM
easat-10856	548	53	)	)	PUNCT
easat-10856	548	54	5	5	NUM
easat-10856	548	55	−	−	PROPN
easat-10856	548	56	(	(	PUNCT
easat-10856	548	57	26	26	NUM
easat-10856	548	58	24	24	NUM
easat-10856	548	59	)	)	PUNCT
easat-10856	548	60	1	1	NUM
easat-10856	548	61	−	−	PROPN
easat-10856	548	62	(	(	PUNCT
easat-10856	548	63	−1)13	−1)13	VERB
easat-10856	548	64	𝐸13	𝐸13	NOUN
easat-10856	548	65	=	=	PUNCT
easat-10856	549	1	26	26	NUM
easat-10856	549	2	!	!	PUNCT
easat-10856	549	3	24!×2	24!×2	NUM
easat-10856	549	4	!	!	PUNCT
easat-10856	550	1	15514534163557086905	15514534163557086905	NUM
easat-10856	550	2	−	−	NUM
easat-10856	550	3	26	26	NUM
easat-10856	550	4	!	!	PUNCT
easat-10856	551	1	22!×4	22!×4	X
easat-10856	551	2	!	!	PUNCT
easat-10856	552	1	69348874393137901	69348874393137901	NUM
easat-10856	552	2	+	+	CCONJ
easat-10856	552	3	26	26	NUM
easat-10856	552	4	!	!	PUNCT
easat-10856	553	1	20!×6	20!×6	NUM
easat-10856	553	2	!	!	PUNCT
easat-10856	554	1	370371188237525	370371188237525	NUM
easat-10856	555	1	−	−	NOUN
easat-10856	555	2	26	26	NUM
easat-10856	555	3	!	!	PUNCT
easat-10856	556	1	18!×8	18!×8	NUM
easat-10856	556	2	!	!	PUNCT
easat-10856	557	1	2404879675441	2404879675441	NUM
easat-10856	557	2	+	+	CCONJ
easat-10856	557	3	26	26	NUM
easat-10856	557	4	!	!	PUNCT
easat-10856	558	1	16!×10	16!×10	NUM
easat-10856	558	2	!	!	NOUN
easat-10856	558	3	19391512145	19391512145	NUM
easat-10856	558	4	−	−	NOUN
easat-10856	559	1	26	26	NUM
easat-10856	559	2	!	!	PUNCT
easat-10856	560	1	14!×12	14!×12	NUM
easat-10856	560	2	!	!	NOUN
easat-10856	560	3	199360981	199360981	NUM
easat-10856	561	1	+	+	CCONJ
easat-10856	561	2	26	26	NUM
easat-10856	561	3	!	!	PUNCT
easat-10856	562	1	12!×14	12!×14	NUM
easat-10856	562	2	!	!	NOUN
easat-10856	562	3	2702765	2702765	NUM
easat-10856	563	1	−	−	NOUN
easat-10856	564	1	26	26	NUM
easat-10856	564	2	!	!	PUNCT
easat-10856	565	1	10!×16	10!×16	NUM
easat-10856	565	2	!	!	NOUN
easat-10856	565	3	50521	50521	NUM
easat-10856	566	1	+	+	CCONJ
easat-10856	566	2	26	26	NUM
easat-10856	566	3	!	!	PUNCT
easat-10856	566	4	8!×18	8!×18	VERB
easat-10856	566	5	!	!	PUNCT
easat-10856	567	1	1385	1385	NUM
easat-10856	567	2	−	−	NOUN
easat-10856	567	3	26	26	NUM
easat-10856	567	4	!	!	PUNCT
easat-10856	567	5	6!×20	6!×20	NOUN
easat-10856	567	6	!	!	PUNCT
easat-10856	568	1	61	61	NUM
easat-10856	568	2	+	+	SYM
easat-10856	568	3	26	26	NUM
easat-10856	568	4	!	!	PUNCT
easat-10856	568	5	4!×22	4!×22	NUM
easat-10856	568	6	!	!	PUNCT
easat-10856	569	1	5	5	NUM
easat-10856	569	2	−	−	NOUN
easat-10856	569	3	26	26	NUM
easat-10856	569	4	!	!	PUNCT
easat-10856	570	1	2!×24	2!×24	NUM
easat-10856	570	2	!	!	NOUN
easat-10856	571	1	1	1	NUM
easat-10856	571	2	+	+	SYM
easat-10856	571	3	1	1	NUM
easat-10856	571	4	⇒	⇒	NOUN
easat-10856	571	5	𝐸13	𝐸13	PROPN
easat-10856	571	6	=	=	SYM
easat-10856	571	7	4087072509293123892361	4087072509293123892361	NUM
easat-10856	571	8	calculation	calculation	NOUN
easat-10856	571	9	,	,	PUNCT
easat-10856	571	10	according	accord	VERB
easat-10856	571	11	to	to	ADP
easat-10856	571	12	the	the	DET
easat-10856	571	13	binomial	binomial	ADJ
easat-10856	571	14	formula	formula	NOUN
easat-10856	571	15	for	for	ADP
easat-10856	571	16	the	the	DET
easat-10856	571	17	euler	euler	NOUN
easat-10856	571	18	number	number	NOUN
easat-10856	571	19	,	,	PUNCT
easat-10856	571	20	of	of	ADP
easat-10856	571	21	𝐸14	𝐸14	PROPN
easat-10856	571	22	283	283	NUM
easat-10856	571	23	edelweiss	edelweiss	PROPN
easat-10856	571	24	applied	apply	VERB
easat-10856	571	25	science	science	NOUN
easat-10856	571	26	and	and	CCONJ
easat-10856	571	27	technology	technology	NOUN
easat-10856	571	28	issn	issn	PROPN
easat-10856	571	29	:	:	PUNCT
easat-10856	571	30	2576	2576	NUM
easat-10856	571	31	-	-	SYM
easat-10856	571	32	8484	8484	NUM
easat-10856	571	33	vol	vol	NOUN
easat-10856	571	34	.	.	PROPN
easat-10856	571	35	9	9	NUM
easat-10856	571	36	,	,	PUNCT
easat-10856	571	37	no	no	INTJ
easat-10856	571	38	.	.	NOUN
easat-10856	571	39	11	11	NUM
easat-10856	571	40	:	:	PUNCT
easat-10856	571	41	274	274	NUM
easat-10856	571	42	-	-	SYM
easat-10856	571	43	288	288	NUM
easat-10856	571	44	,	,	PUNCT
easat-10856	571	45	2025	2025	NUM
easat-10856	571	46	doi	doi	NOUN
easat-10856	571	47	:	:	PUNCT
easat-10856	571	48	10.55214/2576	10.55214/2576	NUM
easat-10856	571	49	-	-	PUNCT
easat-10856	571	50	8484.v9i11.10856	8484.v9i11.10856	NUM
easat-10856	571	51	©	©	PROPN
easat-10856	571	52	2025	2025	NUM
easat-10856	571	53	by	by	ADP
easat-10856	571	54	the	the	DET
easat-10856	571	55	authors	author	NOUN
easat-10856	571	56	;	;	PUNCT
easat-10856	571	57	licensee	licensee	PROPN
easat-10856	571	58	learning	learn	VERB
easat-10856	571	59	gate	gate	NOUN
easat-10856	571	60	𝐸14	𝐸14	PROPN
easat-10856	571	61	=	=	SYM
easat-10856	571	62	(	(	PUNCT
easat-10856	571	63	28	28	NUM
easat-10856	571	64	2	2	NUM
easat-10856	571	65	)	)	PUNCT
easat-10856	571	66	408707250929312892361	408707250929312892361	NUM
easat-10856	571	67	−	−	PROPN
easat-10856	571	68	(	(	PUNCT
easat-10856	571	69	28	28	NUM
easat-10856	571	70	4	4	NUM
easat-10856	571	71	)	)	PUNCT
easat-10856	571	72	15514534163557086905	15514534163557086905	NUM
easat-10856	572	1	+	+	CCONJ
easat-10856	572	2	(	(	PUNCT
easat-10856	572	3	28	28	NUM
easat-10856	572	4	6	6	NUM
easat-10856	572	5	)	)	PUNCT
easat-10856	572	6	69348874393137901	69348874393137901	NUM
easat-10856	572	7	−	−	PROPN
easat-10856	572	8	(	(	PUNCT
easat-10856	572	9	28	28	NUM
easat-10856	572	10	8	8	NUM
easat-10856	572	11	)	)	PUNCT
easat-10856	572	12	370371188237525	370371188237525	NUM
easat-10856	573	1	+	+	CCONJ
easat-10856	573	2	(	(	PUNCT
easat-10856	573	3	28	28	NUM
easat-10856	573	4	10	10	NUM
easat-10856	573	5	)	)	PUNCT
easat-10856	573	6	2404879675441	2404879675441	NUM
easat-10856	573	7	−	−	PROPN
easat-10856	574	1	(	(	PUNCT
easat-10856	574	2	28	28	NUM
easat-10856	574	3	12	12	NUM
easat-10856	574	4	)	)	PUNCT
easat-10856	574	5	19391512145	19391512145	NUM
easat-10856	575	1	+	+	CCONJ
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easat-10856	575	3	28	28	NUM
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easat-10856	575	5	)	)	PUNCT
easat-10856	575	6	199360981	199360981	NUM
easat-10856	575	7	−	−	PROPN
easat-10856	575	8	(	(	PUNCT
easat-10856	575	9	28	28	NUM
easat-10856	575	10	16	16	NUM
easat-10856	575	11	)	)	PUNCT
easat-10856	575	12	2702765	2702765	NUM
easat-10856	576	1	+	+	CCONJ
easat-10856	576	2	(	(	PUNCT
easat-10856	576	3	28	28	NUM
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easat-10856	576	5	)	)	PUNCT
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easat-10856	576	7	−	−	PROPN
easat-10856	576	8	(	(	PUNCT
easat-10856	576	9	28	28	NUM
easat-10856	576	10	20	20	NUM
easat-10856	576	11	)	)	PUNCT
easat-10856	576	12	1385	1385	NUM
easat-10856	577	1	+	+	CCONJ
easat-10856	577	2	(	(	PUNCT
easat-10856	577	3	28	28	NUM
easat-10856	577	4	22	22	NUM
easat-10856	577	5	)	)	PUNCT
easat-10856	577	6	61	61	NUM
easat-10856	577	7	−	−	PROPN
easat-10856	577	8	(	(	PUNCT
easat-10856	577	9	28	28	NUM
easat-10856	577	10	24	24	NUM
easat-10856	577	11	)	)	PUNCT
easat-10856	577	12	5	5	NUM
easat-10856	578	1	+	+	CCONJ
easat-10856	578	2	(	(	PUNCT
easat-10856	578	3	28	28	NUM
easat-10856	578	4	26	26	NUM
easat-10856	578	5	)	)	PUNCT
easat-10856	578	6	1	1	NUM
easat-10856	578	7	−	−	PROPN
easat-10856	578	8	(	(	PUNCT
easat-10856	578	9	−1)14	−1)14	PROPN
easat-10856	578	10	𝐸14	𝐸14	PROPN
easat-10856	578	11	=	=	SYM
easat-10856	578	12	28	28	NUM
easat-10856	578	13	!	!	PUNCT
easat-10856	579	1	26!×2	26!×2	X
easat-10856	579	2	!	!	PUNCT
easat-10856	580	1	4087072509293123892361	4087072509293123892361	NUM
easat-10856	581	1	−	−	NOUN
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easat-10856	581	3	!	!	PUNCT
easat-10856	581	4	24!×4	24!×4	NUM
easat-10856	581	5	!	!	PUNCT
easat-10856	582	1	15514534163557086905	15514534163557086905	NUM
easat-10856	583	1	+	+	CCONJ
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easat-10856	583	3	!	!	PUNCT
easat-10856	584	1	22!×6	22!×6	X
easat-10856	584	2	!	!	PUNCT
easat-10856	585	1	69348874393137901	69348874393137901	NUM
easat-10856	585	2	−	−	NOUN
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easat-10856	586	2	!	!	PUNCT
easat-10856	587	1	20!×8	20!×8	NUM
easat-10856	587	2	!	!	PUNCT
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easat-10856	589	1	+	+	CCONJ
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easat-10856	590	2	!	!	PUNCT
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easat-10856	592	1	−	−	NOUN
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easat-10856	592	3	!	!	PUNCT
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easat-10856	593	2	!	!	PUNCT
easat-10856	593	3	19391512145	19391512145	NUM
easat-10856	594	1	+	+	CCONJ
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easat-10856	595	2	!	!	PUNCT
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easat-10856	595	4	!	!	NOUN
easat-10856	595	5	199360981	199360981	NUM
easat-10856	595	6	−	−	PROPN
easat-10856	595	7	28	28	NUM
easat-10856	595	8	!	!	PUNCT
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easat-10856	596	2	!	!	PUNCT
easat-10856	596	3	2702765	2702765	NUM
easat-10856	597	1	+	+	CCONJ
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easat-10856	597	3	!	!	PUNCT
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easat-10856	599	1	50521	50521	NUM
easat-10856	600	1	−	−	NOUN
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easat-10856	600	3	!	!	PUNCT
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easat-10856	600	5	!	!	PUNCT
easat-10856	601	1	1385	1385	NUM
easat-10856	601	2	+	+	CCONJ
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easat-10856	601	4	!	!	PUNCT
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easat-10856	602	2	!	!	PROPN
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easat-10856	603	2	−	−	NUM
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easat-10856	603	4	!	!	PUNCT
easat-10856	604	1	4!×24	4!×24	NOUN
easat-10856	604	2	!	!	PUNCT
easat-10856	605	1	5	5	NUM
easat-10856	605	2	+	+	SYM
easat-10856	605	3	28	28	NUM
easat-10856	605	4	!	!	PUNCT
easat-10856	606	1	2!×24	2!×24	NUM
easat-10856	606	2	!	!	NOUN
easat-10856	606	3	1	1	NUM
easat-10856	606	4	−	−	NUM
easat-10856	606	5	1	1	NUM
easat-10856	606	6	⇒	⇒	NOUN
easat-10856	606	7	𝐸14	𝐸14	PROPN
easat-10856	606	8	=	=	SYM
easat-10856	606	9	1252259641403629865468285	1252259641403629865468285	NUM
easat-10856	606	10	calculation	calculation	NOUN
easat-10856	606	11	,	,	PUNCT
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easat-10856	606	13	to	to	ADP
easat-10856	606	14	the	the	DET
easat-10856	606	15	binomial	binomial	ADJ
easat-10856	606	16	formula	formula	NOUN
easat-10856	606	17	for	for	ADP
easat-10856	606	18	the	the	DET
easat-10856	606	19	euler	euler	NOUN
easat-10856	606	20	number	number	NOUN
easat-10856	606	21	,	,	PUNCT
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easat-10856	606	24	𝐸15	𝐸15	PROPN
easat-10856	606	25	=	=	SYM
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easat-10856	606	28	2	2	NUM
easat-10856	606	29	)	)	PUNCT
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easat-10856	606	31	−	−	PROPN
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easat-10856	606	33	30	30	NUM
easat-10856	606	34	4	4	NUM
easat-10856	606	35	)	)	PUNCT
easat-10856	606	36	4087072509293123892361	4087072509293123892361	NUM
easat-10856	607	1	+	+	CCONJ
easat-10856	607	2	(	(	PUNCT
easat-10856	607	3	30	30	NUM
easat-10856	607	4	6	6	NUM
easat-10856	607	5	)	)	PUNCT
easat-10856	607	6	15514534163557086905	15514534163557086905	NUM
easat-10856	607	7	−	−	PROPN
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easat-10856	607	11	)	)	PUNCT
easat-10856	607	12	69348874393137901	69348874393137901	NUM
easat-10856	608	1	+	+	CCONJ
easat-10856	608	2	(	(	PUNCT
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easat-10856	608	4	10	10	NUM
easat-10856	608	5	)	)	PUNCT
easat-10856	608	6	370371188237525	370371188237525	NUM
easat-10856	608	7	−	−	PROPN
easat-10856	608	8	(	(	PUNCT
easat-10856	608	9	30	30	NUM
easat-10856	608	10	12	12	NUM
easat-10856	608	11	)	)	PUNCT
easat-10856	608	12	2404879675441	2404879675441	NUM
easat-10856	608	13	+	+	CCONJ
easat-10856	608	14	(	(	PUNCT
easat-10856	608	15	30	30	NUM
easat-10856	608	16	14	14	NUM
easat-10856	608	17	)	)	PUNCT
easat-10856	608	18	19391512145	19391512145	NUM
easat-10856	608	19	−	−	PROPN
easat-10856	608	20	(	(	PUNCT
easat-10856	608	21	30	30	NUM
easat-10856	608	22	16	16	NUM
easat-10856	608	23	)	)	PUNCT
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easat-10856	609	1	+	+	CCONJ
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easat-10856	609	3	30	30	NUM
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easat-10856	609	5	)	)	PUNCT
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easat-10856	609	7	−	−	PROPN
easat-10856	609	8	(	(	PUNCT
easat-10856	609	9	30	30	NUM
easat-10856	609	10	20	20	NUM
easat-10856	609	11	)	)	PUNCT
easat-10856	609	12	50521	50521	NUM
easat-10856	610	1	+	+	CCONJ
easat-10856	610	2	(	(	PUNCT
easat-10856	610	3	30	30	NUM
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easat-10856	610	5	)	)	PUNCT
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easat-10856	610	7	−	−	PROPN
easat-10856	610	8	(	(	PUNCT
easat-10856	610	9	30	30	NUM
easat-10856	610	10	24	24	NUM
easat-10856	610	11	)	)	PUNCT
easat-10856	610	12	61	61	NUM
easat-10856	611	1	+	+	CCONJ
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easat-10856	611	3	30	30	NUM
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easat-10856	611	5	)	)	PUNCT
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easat-10856	611	7	−	−	PROPN
easat-10856	611	8	(	(	PUNCT
easat-10856	611	9	30	30	NUM
easat-10856	611	10	28	28	NUM
easat-10856	611	11	)	)	PUNCT
easat-10856	611	12	1	1	NUM
easat-10856	611	13	−	−	NOUN
easat-10856	611	14	(	(	PUNCT
easat-10856	611	15	−1)15	−1)15	NOUN
easat-10856	611	16	𝐸15	𝐸15	PROPN
easat-10856	611	17	=	=	PUNCT
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easat-10856	611	19	!	!	PUNCT
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easat-10856	612	4	2	2	NUM
easat-10856	612	5	!	!	SYM
easat-10856	612	6	1252259641403629865468285	1252259641403629865468285	NUM
easat-10856	612	7	−	−	NOUN
easat-10856	612	8	30	30	NUM
easat-10856	612	9	!	!	PUNCT
easat-10856	612	10	26	26	NUM
easat-10856	612	11	!	!	X
easat-10856	612	12	×	×	NOUN
easat-10856	612	13	4	4	NUM
easat-10856	612	14	!	!	NUM
easat-10856	612	15	4087072509293123892361	4087072509293123892361	NUM
easat-10856	613	1	+	+	CCONJ
easat-10856	613	2	30	30	NUM
easat-10856	613	3	!	!	SYM
easat-10856	614	1	24	24	NUM
easat-10856	614	2	!	!	PUNCT
easat-10856	614	3	×	×	NOUN
easat-10856	614	4	6	6	NUM
easat-10856	614	5	!	!	PUNCT
easat-10856	615	1	15514534163557086905	15514534163557086905	NUM
easat-10856	615	2	−	−	NOUN
easat-10856	615	3	30	30	NUM
easat-10856	615	4	!	!	PUNCT
easat-10856	616	1	22	22	NUM
easat-10856	616	2	!	!	PUNCT
easat-10856	617	1	×	×	NOUN
easat-10856	617	2	8	8	NUM
easat-10856	617	3	!	!	PUNCT
easat-10856	617	4	69348874393137901	69348874393137901	NUM
easat-10856	618	1	+	+	CCONJ
easat-10856	618	2	30	30	NUM
easat-10856	618	3	!	!	SYM
easat-10856	618	4	20	20	NUM
easat-10856	618	5	!	!	PUNCT
easat-10856	618	6	×	×	NOUN
easat-10856	618	7	10	10	NUM
easat-10856	618	8	!	!	PUNCT
easat-10856	619	1	370371188237525	370371188237525	NUM
easat-10856	620	1	−	−	NOUN
easat-10856	620	2	30	30	NUM
easat-10856	620	3	!	!	SYM
easat-10856	621	1	18	18	NUM
easat-10856	621	2	!	!	PUNCT
easat-10856	621	3	×	×	NOUN
easat-10856	621	4	12	12	NUM
easat-10856	621	5	!	!	PUNCT
easat-10856	621	6	2404879675441	2404879675441	NUM
easat-10856	622	1	+	+	CCONJ
easat-10856	622	2	30	30	NUM
easat-10856	622	3	!	!	X
easat-10856	623	1	16	16	NUM
easat-10856	623	2	!	!	PUNCT
easat-10856	624	1	×	×	NOUN
easat-10856	624	2	14	14	NUM
easat-10856	624	3	!	!	PUNCT
easat-10856	624	4	19391512145	19391512145	NUM
easat-10856	625	1	−	−	NOUN
easat-10856	625	2	30	30	NUM
easat-10856	625	3	!	!	PUNCT
easat-10856	626	1	14	14	NUM
easat-10856	626	2	!	!	PUNCT
easat-10856	626	3	×	×	NOUN
easat-10856	626	4	16	16	NUM
easat-10856	626	5	!	!	PUNCT
easat-10856	626	6	199360981	199360981	NUM
easat-10856	627	1	+	+	CCONJ
easat-10856	627	2	30	30	NUM
easat-10856	627	3	!	!	PUNCT
easat-10856	628	1	12	12	NUM
easat-10856	628	2	!	!	PUNCT
easat-10856	629	1	×	×	NOUN
easat-10856	629	2	18	18	NUM
easat-10856	629	3	!	!	PUNCT
easat-10856	629	4	2702765	2702765	NUM
easat-10856	630	1	−	−	NOUN
easat-10856	630	2	30	30	NUM
easat-10856	630	3	!	!	PUNCT
easat-10856	631	1	10	10	NUM
easat-10856	631	2	!	!	PUNCT
easat-10856	631	3	×	×	NOUN
easat-10856	631	4	20	20	NUM
easat-10856	631	5	!	!	PUNCT
easat-10856	631	6	50521	50521	NUM
easat-10856	632	1	+	+	CCONJ
easat-10856	633	1	30	30	NUM
easat-10856	633	2	!	!	NOUN
easat-10856	633	3	8	8	NUM
easat-10856	633	4	!	!	X
easat-10856	633	5	×	×	NOUN
easat-10856	633	6	22	22	NUM
easat-10856	633	7	!	!	PUNCT
easat-10856	633	8	1385	1385	NUM
easat-10856	634	1	−	−	NOUN
easat-10856	634	2	30	30	NUM
easat-10856	634	3	!	!	NOUN
easat-10856	635	1	6	6	NUM
easat-10856	635	2	!	!	X
easat-10856	635	3	×	×	NOUN
easat-10856	635	4	24	24	NUM
easat-10856	635	5	!	!	PUNCT
easat-10856	635	6	61	61	NUM
easat-10856	636	1	+	+	SYM
easat-10856	636	2	30	30	NUM
easat-10856	636	3	!	!	NOUN
easat-10856	636	4	4	4	NUM
easat-10856	636	5	!	!	NUM
easat-10856	636	6	×	×	NOUN
easat-10856	636	7	26	26	NUM
easat-10856	636	8	!	!	NOUN
easat-10856	637	1	5	5	NUM
easat-10856	637	2	−	−	NOUN
easat-10856	637	3	30	30	NUM
easat-10856	637	4	!	!	NOUN
easat-10856	638	1	2	2	NUM
easat-10856	638	2	!	!	NUM
easat-10856	638	3	×	×	NOUN
easat-10856	638	4	28	28	NUM
easat-10856	638	5	!	!	PUNCT
easat-10856	638	6	1	1	NUM
easat-10856	638	7	+	+	SYM
easat-10856	638	8	1	1	NUM
easat-10856	638	9	⇒	⇒	NOUN
easat-10856	638	10	𝐸15	𝐸15	PROPN
easat-10856	638	11	=	=	SYM
easat-10856	638	12	441543893249023104553682821	441543893249023104553682821	NUM
easat-10856	638	13	3	3	X
easat-10856	638	14	.	.	PUNCT
easat-10856	638	15	results	result	NOUN
easat-10856	638	16	having	having	AUX
easat-10856	638	17	carried	carry	VERB
easat-10856	638	18	out	out	ADP
easat-10856	638	19	the	the	DET
easat-10856	638	20	appropriate	appropriate	ADJ
easat-10856	638	21	and	and	CCONJ
easat-10856	638	22	proposed	propose	VERB
easat-10856	638	23	calculations	calculation	NOUN
easat-10856	638	24	,	,	PUNCT
easat-10856	638	25	we	we	PRON
easat-10856	638	26	present	present	VERB
easat-10856	638	27	the	the	DET
easat-10856	638	28	table	table	NOUN
easat-10856	638	29	of	of	ADP
easat-10856	638	30	the	the	DET
easat-10856	638	31	first	first	ADJ
easat-10856	638	32	20	20	NUM
easat-10856	638	33	bernoulli	bernoulli	NOUN
easat-10856	638	34	and	and	CCONJ
easat-10856	638	35	euler	euler	NOUN
easat-10856	638	36	numbers	number	NOUN
easat-10856	638	37	listed	list	VERB
easat-10856	638	38	in	in	ADP
easat-10856	638	39	tables	table	NOUN
easat-10856	638	40	1	1	NUM
easat-10856	638	41	and	and	CCONJ
easat-10856	638	42	2	2	NUM
easat-10856	638	43	,	,	PUNCT
easat-10856	638	44	in	in	ADP
easat-10856	638	45	which	which	PRON
easat-10856	638	46	the	the	DET
easat-10856	638	47	applications	application	NOUN
easat-10856	638	48	of	of	ADP
easat-10856	638	49	bernoulli	bernoulli	PROPN
easat-10856	638	50	and	and	CCONJ
easat-10856	638	51	euler	euler	NOUN
easat-10856	638	52	numbers	number	NOUN
easat-10856	638	53	were	be	AUX
easat-10856	638	54	carried	carry	VERB
easat-10856	638	55	out	out	ADP
easat-10856	638	56	separately	separately	ADV
easat-10856	638	57	.	.	PUNCT
easat-10856	639	1	the	the	DET
easat-10856	639	2	first	first	ADJ
easat-10856	639	3	application	application	NOUN
easat-10856	639	4	corresponds	correspond	VERB
easat-10856	639	5	to	to	ADP
easat-10856	639	6	the	the	DET
easat-10856	639	7	bernoulli	bernoulli	NOUN
easat-10856	639	8	numbers	number	NOUN
easat-10856	639	9	,	,	PUNCT
easat-10856	639	10	in	in	ADP
easat-10856	639	11	solving	solve	VERB
easat-10856	639	12	the	the	DET
easat-10856	639	13	integral	integral	NOUN
easat-10856	639	14	of	of	ADP
easat-10856	639	15	ln⁡(𝑐𝑜𝑠𝑥	ln⁡(𝑐𝑜𝑠𝑥	PROPN
easat-10856	639	16	)	)	PUNCT
easat-10856	639	17	.	.	PUNCT
easat-10856	640	1	284	284	NUM
easat-10856	640	2	edelweiss	edelweiss	PROPN
easat-10856	640	3	applied	apply	VERB
easat-10856	640	4	science	science	NOUN
easat-10856	640	5	and	and	CCONJ
easat-10856	640	6	technology	technology	NOUN
easat-10856	640	7	issn	issn	PROPN
easat-10856	640	8	:	:	PUNCT
easat-10856	640	9	2576	2576	NUM
easat-10856	640	10	-	-	SYM
easat-10856	640	11	8484	8484	NUM
easat-10856	640	12	vol	vol	NOUN
easat-10856	640	13	.	.	PROPN
easat-10856	641	1	9	9	NUM
easat-10856	641	2	,	,	PUNCT
easat-10856	641	3	no	no	INTJ
easat-10856	641	4	.	.	NOUN
easat-10856	641	5	11	11	NUM
easat-10856	641	6	:	:	PUNCT
easat-10856	641	7	274	274	NUM
easat-10856	641	8	-	-	SYM
easat-10856	641	9	288	288	NUM
easat-10856	641	10	,	,	PUNCT
easat-10856	641	11	2025	2025	NUM
easat-10856	641	12	doi	doi	NOUN
easat-10856	641	13	:	:	PUNCT
easat-10856	641	14	10.55214/2576	10.55214/2576	NUM
easat-10856	641	15	-	-	PUNCT
easat-10856	641	16	8484.v9i11.10856	8484.v9i11.10856	NUM
easat-10856	641	17	©	©	PROPN
easat-10856	641	18	2025	2025	NUM
easat-10856	641	19	by	by	ADP
easat-10856	641	20	the	the	DET
easat-10856	641	21	authors	author	NOUN
easat-10856	641	22	;	;	PUNCT
easat-10856	641	23	licensee	licensee	PROPN
easat-10856	641	24	learning	learn	VERB
easat-10856	641	25	gate	gate	NOUN
easat-10856	641	26	table	table	NOUN
easat-10856	641	27	1	1	NUM
easat-10856	641	28	.	.	PUNCT
easat-10856	642	1	the	the	DET
easat-10856	642	2	bernoulli	bernoulli	PROPN
easat-10856	642	3	numbers	number	NOUN
easat-10856	642	4	.	.	PUNCT
easat-10856	643	1	𝒏	𝒏	AUX
easat-10856	643	2	𝑩𝒏	𝑩𝒏	PROPN
easat-10856	643	3	1	1	NUM
easat-10856	643	4	1/6	1/6	NUM
easat-10856	643	5	2	2	NUM
easat-10856	643	6	1/30	1/30	NUM
easat-10856	643	7	3	3	NUM
easat-10856	643	8	1/42	1/42	NUM
easat-10856	643	9	4	4	NUM
easat-10856	643	10	1/30	1/30	NUM
easat-10856	643	11	5	5	NUM
easat-10856	643	12	5/66	5/66	NUM
easat-10856	643	13	6	6	NUM
easat-10856	643	14	691/2730	691/2730	NUM
easat-10856	643	15	7	7	NUM
easat-10856	643	16	7/6	7/6	NUM
easat-10856	643	17	8	8	NUM
easat-10856	643	18	3617/510	3617/510	NUM
easat-10856	643	19	9	9	NUM
easat-10856	643	20	43867/798	43867/798	NUM
easat-10856	643	21	10	10	NUM
easat-10856	643	22	174611/330	174611/330	NUM
easat-10856	643	23	11	11	NUM
easat-10856	643	24	854513/138	854513/138	NUM
easat-10856	643	25	12	12	NUM
easat-10856	643	26	236364091/2730	236364091/2730	NUM
easat-10856	643	27	13	13	NUM
easat-10856	643	28	8553103/6	8553103/6	NUM
easat-10856	643	29	14	14	NUM
easat-10856	643	30	23749461029/870	23749461029/870	NUM
easat-10856	643	31	15	15	NUM
easat-10856	643	32	8615841276005/14322	8615841276005/14322	NUM
easat-10856	643	33	16	16	NUM
easat-10856	643	34	7709321041217/510	7709321041217/510	NUM
easat-10856	643	35	17	17	NUM
easat-10856	643	36	2577687858367/6	2577687858367/6	NUM
easat-10856	643	37	18	18	NUM
easat-10856	643	38	26315271553053477373/1919190	26315271553053477373/1919190	NUM
easat-10856	643	39	19	19	NUM
easat-10856	643	40	2929993913841559/6	2929993913841559/6	NUM
easat-10856	643	41	20	20	NUM
easat-10856	643	42	261082718496449122051/13530	261082718496449122051/13530	NUM
easat-10856	643	43	3.1	3.1	NUM
easat-10856	643	44	.	.	PUNCT
easat-10856	644	1	for	for	ADP
easat-10856	644	2	the	the	DET
easat-10856	644	3	bernoulli	bernoulli	PROPN
easat-10856	644	4	numbers	number	NOUN
easat-10856	644	5	∫	∫	PROPN
easat-10856	644	6	𝑥	𝑥	PRON
easat-10856	644	7	𝑠𝑒𝑛(𝑎𝑥	𝑠𝑒𝑛(𝑎𝑥	NOUN
easat-10856	644	8	)	)	PUNCT
easat-10856	644	9	𝑑𝑥	𝑑𝑥	VERB
easat-10856	644	10	=	=	SYM
easat-10856	644	11	1	1	NUM
easat-10856	644	12	𝑎2	𝑎2	NOUN
easat-10856	645	1	[	[	X
easat-10856	645	2	𝑎𝑥	𝑎𝑥	X
easat-10856	645	3	+	+	X
easat-10856	645	4	(	(	PUNCT
easat-10856	645	5	𝑎𝑥)3	𝑎𝑥)3	PROPN
easat-10856	645	6	3×3	3×3	NUM
easat-10856	645	7	!	!	PUNCT
easat-10856	646	1	+	+	CCONJ
easat-10856	646	2	7(𝑎𝑥)5	7(𝑎𝑥)5	NOUN
easat-10856	646	3	3×5×5	3×5×5	NUM
easat-10856	646	4	!	!	PUNCT
easat-10856	647	1	+	+	PUNCT
easat-10856	647	2	31(𝑎𝑥)7	31(𝑎𝑥)7	NUM
easat-10856	647	3	3×7×7	3×7×7	NOUN
easat-10856	647	4	!	!	PUNCT
easat-10856	648	1	+	+	X
easat-10856	648	2	.	.	PUNCT
easat-10856	648	3	.	.	PUNCT
easat-10856	648	4	.	.	PUNCT
easat-10856	649	1	+	+	CCONJ
easat-10856	649	2	2(22𝑛−1−1	2(22𝑛−1−1	NUM
easat-10856	649	3	)	)	PUNCT
easat-10856	649	4	(	(	PUNCT
easat-10856	649	5	2𝑛+1	2𝑛+1	NOUN
easat-10856	649	6	)	)	PUNCT
easat-10856	649	7	!	!	PUNCT
easat-10856	650	1	𝐵𝑛(𝑎𝑥	𝐵𝑛(𝑎𝑥	NOUN
easat-10856	650	2	)	)	PUNCT
easat-10856	650	3	2𝑛+1	2𝑛+1	NUM
easat-10856	651	1	+	+	PROPN
easat-10856	651	2	.	.	PUNCT
easat-10856	651	3	.	.	PUNCT
easat-10856	651	4	.	.	PUNCT
easat-10856	652	1	]	]	PUNCT
easat-10856	652	2	…	…	PUNCT
easat-10856	652	3	(	(	PUNCT
easat-10856	652	4	a	a	X
easat-10856	652	5	)	)	PUNCT
easat-10856	652	6	∫𝑥𝑡𝑔(𝑎𝑥)𝑑𝑥	∫𝑥𝑡𝑔(𝑎𝑥)𝑑𝑥	PUNCT
easat-10856	653	1	=	=	PRON
easat-10856	653	2	𝑎𝑥3	𝑎𝑥3	VERB
easat-10856	653	3	3	3	NUM
easat-10856	653	4	+	+	CCONJ
easat-10856	653	5	𝑎3𝑥5	𝑎3𝑥5	X
easat-10856	653	6	15	15	NUM
easat-10856	653	7	+	+	SYM
easat-10856	653	8	2𝑎5𝑥7	2𝑎5𝑥7	NUM
easat-10856	653	9	105	105	NUM
easat-10856	653	10	+	+	NUM
easat-10856	653	11	17𝑎7𝑥9	17𝑎7𝑥9	NUM
easat-10856	653	12	2835	2835	NUM
easat-10856	653	13	+	+	NOUN
easat-10856	653	14	.	.	PUNCT
easat-10856	653	15	.	.	PUNCT
easat-10856	653	16	.	.	PUNCT
easat-10856	654	1	+	+	CCONJ
easat-10856	654	2	22𝑛(22𝑛−1)𝐵𝑛𝑎	22𝑛(22𝑛−1)𝐵𝑛𝑎	NUM
easat-10856	654	3	2𝑛−1𝑥2𝑛+1	2𝑛−1𝑥2𝑛+1	NUM
easat-10856	654	4	(	(	PUNCT
easat-10856	654	5	2𝑛+1	2𝑛+1	NUM
easat-10856	654	6	)	)	PUNCT
easat-10856	654	7	!	!	PUNCT
easat-10856	655	1	+	+	X
easat-10856	655	2	.	.	PUNCT
easat-10856	655	3	..	..	PUNCT
easat-10856	655	4	(	(	PUNCT
easat-10856	655	5	b	b	X
easat-10856	655	6	)	)	PUNCT
easat-10856	655	7	∫	∫	PROPN
easat-10856	655	8	𝑡𝑔(𝑎𝑥	𝑡𝑔(𝑎𝑥	NOUN
easat-10856	655	9	)	)	PUNCT
easat-10856	656	1	𝑥	𝑥	NOUN
easat-10856	656	2	𝑑𝑥	𝑑𝑥	NOUN
easat-10856	656	3	=	=	SYM
easat-10856	656	4	𝑎𝑥	𝑎𝑥	NOUN
easat-10856	656	5	+	+	CCONJ
easat-10856	656	6	(	(	PUNCT
easat-10856	656	7	𝑎𝑥)3	𝑎𝑥)3	PROPN
easat-10856	656	8	9	9	NUM
easat-10856	656	9	+	+	NUM
easat-10856	656	10	2(𝑎𝑥)5	2(𝑎𝑥)5	NUM
easat-10856	656	11	75	75	NUM
easat-10856	657	1	+	+	CCONJ
easat-10856	657	2	17(𝑎𝑥)7	17(𝑎𝑥)7	NUM
easat-10856	657	3	2205	2205	NUM
easat-10856	657	4	+	+	NOUN
easat-10856	657	5	.	.	PUNCT
easat-10856	657	6	.	.	PUNCT
easat-10856	657	7	.	.	PUNCT
easat-10856	658	1	+	+	CCONJ
easat-10856	658	2	22𝑛(22𝑛−1)𝐵𝑛(𝑎𝑥	22𝑛(22𝑛−1)𝐵𝑛(𝑎𝑥	X
easat-10856	658	3	)	)	SYM
easat-10856	658	4	2𝑛−1	2𝑛−1	NUM
easat-10856	658	5	(	(	PUNCT
easat-10856	658	6	2𝑛−1)(2𝑛	2𝑛−1)(2𝑛	NUM
easat-10856	658	7	)	)	PUNCT
easat-10856	658	8	!	!	PUNCT
easat-10856	659	1	+	+	X
easat-10856	659	2	.	.	PUNCT
easat-10856	659	3	..	..	PUNCT
easat-10856	659	4	(	(	PUNCT
easat-10856	659	5	c	c	X
easat-10856	659	6	)	)	PUNCT
easat-10856	659	7	∫	∫	PROPN
easat-10856	659	8	𝑙𝑛	𝑙𝑛	PROPN
easat-10856	659	9	(	(	PUNCT
easat-10856	659	10	𝑡𝑔𝑥)𝑑𝑥	𝑡𝑔𝑥)𝑑𝑥	NOUN
easat-10856	659	11	=	=	PUNCT
easat-10856	659	12	𝑥	𝑥	NOUN
easat-10856	659	13	𝑙𝑛	𝑙𝑛	NOUN
easat-10856	660	1	𝑥	𝑥	X
easat-10856	660	2	−	−	PROPN
easat-10856	660	3	𝑥	𝑥	PROPN
easat-10856	661	1	+	+	CCONJ
easat-10856	661	2	𝑥3	𝑥3	NOUN
easat-10856	661	3	9	9	NUM
easat-10856	661	4	+	+	NUM
easat-10856	661	5	7𝑥5	7𝑥5	NUM
easat-10856	661	6	450	450	NUM
easat-10856	661	7	+	+	NOUN
easat-10856	661	8	.	.	PUNCT
easat-10856	661	9	.	.	PUNCT
easat-10856	662	1	.	.	PUNCT
easat-10856	663	1	+	+	CCONJ
easat-10856	663	2	22𝑛(22𝑛−1−1)𝐵𝑛	22𝑛(22𝑛−1−1)𝐵𝑛	NUM
easat-10856	663	3	𝑛(2𝑛+1	𝑛(2𝑛+1	NOUN
easat-10856	663	4	)	)	PUNCT
easat-10856	663	5	!	!	PUNCT
easat-10856	664	1	𝑥2𝑛+1	𝑥2𝑛+1	PROPN
easat-10856	664	2	+	+	PROPN
easat-10856	664	3	.	.	PUNCT
easat-10856	664	4	.	.	PUNCT
easat-10856	664	5	.(d	.(d	X
easat-10856	664	6	)	)	PUNCT
easat-10856	664	7	∫	∫	PROPN
easat-10856	665	1	ln(𝑐𝑜𝑠𝑥	ln(𝑐𝑜𝑠𝑥	PROPN
easat-10856	665	2	)	)	PUNCT
easat-10856	665	3	𝑑𝑥	𝑑𝑥	VERB
easat-10856	665	4	=	=	SYM
easat-10856	666	1	−	−	PROPN
easat-10856	666	2	22𝑛−1×(22𝑛−1)×𝐵𝑛×𝑥	22𝑛−1×(22𝑛−1)×𝐵𝑛×𝑥	NUM
easat-10856	666	3	2𝑛+1	2𝑛+1	PROPN
easat-10856	666	4	𝑛(2𝑛+1	𝑛(2𝑛+1	NOUN
easat-10856	666	5	)	)	PUNCT
easat-10856	666	6	!	!	PUNCT
easat-10856	666	7	...	...	PUNCT
easat-10856	667	1	(	(	PUNCT
easat-10856	667	2	e	e	NOUN
easat-10856	667	3	)	)	PUNCT
easat-10856	667	4	3.1.1	3.1.1	NUM
easat-10856	667	5	.	.	PUNCT
easat-10856	668	1	application	application	NOUN
easat-10856	668	2	of	of	ADP
easat-10856	668	3	the	the	DET
easat-10856	668	4	bernoulli	bernoulli	NOUN
easat-10856	668	5	numbers	number	NOUN
easat-10856	668	6	(	(	PUNCT
easat-10856	668	7	𝐵𝑛	𝐵𝑛	PROPN
easat-10856	668	8	)	)	PUNCT
easat-10856	668	9	.	.	PUNCT
easat-10856	669	1	for	for	ADP
easat-10856	669	2	the	the	DET
easat-10856	669	3	expression	expression	NOUN
easat-10856	669	4	∫	∫	PROPN
easat-10856	669	5	ln(𝑐𝑜𝑠𝑥	ln(𝑐𝑜𝑠𝑥	PROPN
easat-10856	669	6	)	)	PUNCT
easat-10856	669	7	𝑑𝑥	𝑑𝑥	VERB
easat-10856	669	8	(	(	PUNCT
easat-10856	669	9	e	e	NOUN
easat-10856	669	10	)	)	PUNCT
easat-10856	669	11	;	;	PUNCT
easat-10856	669	12	we	we	PRON
easat-10856	669	13	have	have	VERB
easat-10856	669	14	:	:	PUNCT
easat-10856	669	15	•	•	ADV
easat-10856	669	16	for	for	ADP
easat-10856	669	17	:	:	PUNCT
easat-10856	669	18	𝐵1	𝐵1	NOUN
easat-10856	669	19	=	=	SYM
easat-10856	669	20	1/6	1/6	NUM
easat-10856	669	21	∫ln(𝑐𝑜𝑠𝑥	∫ln(𝑐𝑜𝑠𝑥	NOUN
easat-10856	669	22	)	)	PUNCT
easat-10856	669	23	𝑑𝑥	𝑑𝑥	VERB
easat-10856	669	24	=	=	SYM
easat-10856	669	25	−	−	PROPN
easat-10856	669	26	𝑥3	𝑥3	NOUN
easat-10856	669	27	6	6	NUM
easat-10856	669	28	•	•	NOUN
easat-10856	669	29	for	for	ADP
easat-10856	669	30	:	:	PUNCT
easat-10856	669	31	𝐵1	𝐵1	NOUN
easat-10856	669	32	=	=	SYM
easat-10856	670	1	1/6	1/6	NUM
easat-10856	670	2	y	y	NOUN
easat-10856	670	3	⁡𝐵2	⁡𝐵2	NOUN
easat-10856	670	4	=	=	NUM
easat-10856	670	5	1/30	1/30	NUM
easat-10856	670	6	∫ln(𝑐𝑜𝑠𝑥	∫ln(𝑐𝑜𝑠𝑥	NOUN
easat-10856	670	7	)	)	PUNCT
easat-10856	670	8	𝑑𝑥	𝑑𝑥	VERB
easat-10856	670	9	=	=	SYM
easat-10856	670	10	−	−	PROPN
easat-10856	670	11	𝑥3	𝑥3	NOUN
easat-10856	670	12	6	6	NUM
easat-10856	670	13	−	−	NOUN
easat-10856	670	14	𝑥5	𝑥5	ADV
easat-10856	670	15	60	60	NUM
easat-10856	670	16	•	•	NOUN
easat-10856	670	17	for	for	ADP
easat-10856	670	18	:	:	PUNCT
easat-10856	670	19	𝐵1	𝐵1	NOUN
easat-10856	670	20	=	=	PUNCT
easat-10856	670	21	1/6,⁡𝐵2	1/6,⁡𝐵2	NUM
easat-10856	670	22	=	=	SYM
easat-10856	670	23	1/30	1/30	NUM
easat-10856	670	24	y	y	NUM
easat-10856	670	25	𝐵3	𝐵3	NOUN
easat-10856	671	1	=	=	PUNCT
easat-10856	672	1	1/42	1/42	NUM
easat-10856	672	2	∫ln(𝑐𝑜𝑠𝑥	∫ln(𝑐𝑜𝑠𝑥	NUM
easat-10856	672	3	)	)	PUNCT
easat-10856	672	4	𝑑𝑥	𝑑𝑥	VERB
easat-10856	672	5	=	=	SYM
easat-10856	672	6	−	−	PROPN
easat-10856	672	7	𝑥3	𝑥3	NOUN
easat-10856	672	8	6	6	NUM
easat-10856	672	9	−	−	NOUN
easat-10856	672	10	𝑥5	𝑥5	PROPN
easat-10856	672	11	60	60	NUM
easat-10856	672	12	−	−	NUM
easat-10856	672	13	𝑥7	𝑥7	VERB
easat-10856	672	14	210	210	NUM
easat-10856	672	15	•	•	NOUN
easat-10856	672	16	for	for	ADP
easat-10856	672	17	:	:	PUNCT
easat-10856	672	18	𝐵1	𝐵1	NOUN
easat-10856	672	19	=	=	PUNCT
easat-10856	672	20	1/6,⁡𝐵2	1/6,⁡𝐵2	PROPN
easat-10856	672	21	=	=	SYM
easat-10856	672	22	1/30	1/30	NUM
easat-10856	672	23	,	,	PUNCT
easat-10856	672	24	𝐵3	𝐵3	NOUN
easat-10856	673	1	=	=	PUNCT
easat-10856	674	1	1/42	1/42	NUM
easat-10856	674	2	y	y	PROPN
easat-10856	674	3	𝐵4	𝐵4	NOUN
easat-10856	674	4	=	=	SYM
easat-10856	674	5	1/30	1/30	NUM
easat-10856	674	6	∫	∫	NUM
easat-10856	674	7	ln(𝑐𝑜𝑠𝑥	ln(𝑐𝑜𝑠𝑥	PROPN
easat-10856	674	8	)	)	PUNCT
easat-10856	674	9	𝑑𝑥	𝑑𝑥	VERB
easat-10856	674	10	=	=	SYM
easat-10856	674	11	−	−	PROPN
easat-10856	674	12	𝑥3	𝑥3	NOUN
easat-10856	674	13	6	6	NUM
easat-10856	674	14	−	−	NOUN
easat-10856	674	15	𝑥5	𝑥5	PROPN
easat-10856	674	16	60	60	NUM
easat-10856	674	17	−	−	NUM
easat-10856	674	18	𝑥7	𝑥7	VERB
easat-10856	674	19	210	210	NUM
easat-10856	674	20	−	−	PROPN
easat-10856	674	21	17𝑥9	17𝑥9	NUM
easat-10856	674	22	22680	22680	NUM
easat-10856	674	23	•	•	NOUN
easat-10856	674	24	for	for	ADP
easat-10856	674	25	:	:	PUNCT
easat-10856	674	26	𝐵1	𝐵1	NOUN
easat-10856	674	27	=	=	PUNCT
easat-10856	674	28	1/6,⁡𝐵2	1/6,⁡𝐵2	PROPN
easat-10856	674	29	=	=	SYM
easat-10856	674	30	1/30	1/30	NUM
easat-10856	674	31	,	,	PUNCT
easat-10856	674	32	𝐵3	𝐵3	NOUN
easat-10856	675	1	=	=	SYM
easat-10856	676	1	1/42	1/42	NUM
easat-10856	676	2	,	,	PUNCT
easat-10856	676	3	𝐵4	𝐵4	NOUN
easat-10856	676	4	=	=	SYM
easat-10856	676	5	1/30	1/30	NUM
easat-10856	676	6	y	y	NOUN
easat-10856	676	7	𝐵5	𝐵5	NOUN
easat-10856	676	8	=	=	NOUN
easat-10856	676	9	5/66	5/66	NUM
easat-10856	676	10	.	.	PUNCT
easat-10856	677	1	285	285	NUM
easat-10856	677	2	edelweiss	edelweiss	PROPN
easat-10856	677	3	applied	apply	VERB
easat-10856	677	4	science	science	NOUN
easat-10856	677	5	and	and	CCONJ
easat-10856	677	6	technology	technology	NOUN
easat-10856	677	7	issn	issn	PROPN
easat-10856	677	8	:	:	PUNCT
easat-10856	677	9	2576	2576	NUM
easat-10856	677	10	-	-	SYM
easat-10856	677	11	8484	8484	NUM
easat-10856	677	12	vol	vol	NOUN
easat-10856	677	13	.	.	PROPN
easat-10856	678	1	9	9	NUM
easat-10856	678	2	,	,	PUNCT
easat-10856	678	3	no	no	INTJ
easat-10856	678	4	.	.	NOUN
easat-10856	678	5	11	11	NUM
easat-10856	678	6	:	:	PUNCT
easat-10856	678	7	274	274	NUM
easat-10856	678	8	-	-	SYM
easat-10856	678	9	288	288	NUM
easat-10856	678	10	,	,	PUNCT
easat-10856	678	11	2025	2025	NUM
easat-10856	678	12	doi	doi	NOUN
easat-10856	678	13	:	:	PUNCT
easat-10856	678	14	10.55214/2576	10.55214/2576	NUM
easat-10856	678	15	-	-	PUNCT
easat-10856	678	16	8484.v9i11.10856	8484.v9i11.10856	NUM
easat-10856	678	17	©	©	PROPN
easat-10856	678	18	2025	2025	NUM
easat-10856	678	19	by	by	ADP
easat-10856	678	20	the	the	DET
easat-10856	678	21	authors	author	NOUN
easat-10856	678	22	;	;	PUNCT
easat-10856	678	23	licensee	licensee	PROPN
easat-10856	678	24	learning	learn	VERB
easat-10856	678	25	gate	gate	PROPN
easat-10856	678	26	∫ln(𝑐𝑜𝑠𝑥	∫ln(𝑐𝑜𝑠𝑥	PROPN
easat-10856	678	27	)	)	PUNCT
easat-10856	678	28	𝑑𝑥	𝑑𝑥	VERB
easat-10856	678	29	=	=	SYM
easat-10856	679	1	−	−	PROPN
easat-10856	679	2	𝑥3	𝑥3	NOUN
easat-10856	679	3	6	6	NUM
easat-10856	679	4	−	−	NOUN
easat-10856	679	5	𝑥5	𝑥5	PROPN
easat-10856	679	6	60	60	NUM
easat-10856	679	7	−	−	NUM
easat-10856	679	8	𝑥7	𝑥7	VERB
easat-10856	679	9	210	210	NUM
easat-10856	679	10	−	−	PROPN
easat-10856	679	11	17𝑥9	17𝑥9	NUM
easat-10856	679	12	22680	22680	NUM
easat-10856	679	13	−	−	NOUN
easat-10856	679	14	31𝑥11	31𝑥11	NUM
easat-10856	679	15	311850	311850	NUM
easat-10856	679	16	•	•	NOUN
easat-10856	679	17	for	for	ADP
easat-10856	679	18	:	:	PUNCT
easat-10856	679	19	𝐵1	𝐵1	NOUN
easat-10856	679	20	=	=	PUNCT
easat-10856	679	21	1/6,⁡𝐵2	1/6,⁡𝐵2	PROPN
easat-10856	679	22	=	=	SYM
easat-10856	679	23	1/30	1/30	NUM
easat-10856	679	24	,	,	PUNCT
easat-10856	679	25	𝐵3	𝐵3	NOUN
easat-10856	679	26	=	=	SYM
easat-10856	679	27	1/42	1/42	NUM
easat-10856	679	28	,	,	PUNCT
easat-10856	679	29	𝐵4	𝐵4	NOUN
easat-10856	679	30	=	=	SYM
easat-10856	679	31	1/30	1/30	NUM
easat-10856	679	32	,	,	PUNCT
easat-10856	679	33	𝐵5	𝐵5	NOUN
easat-10856	679	34	=	=	NOUN
easat-10856	679	35	5/66	5/66	NUM
easat-10856	679	36	y	y	NUM
easat-10856	679	37	𝐵6	𝐵6	NOUN
easat-10856	679	38	=	=	PUNCT
easat-10856	679	39	691/2730	691/2730	NUM
easat-10856	679	40	.	.	PUNCT
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easat-10856	680	3	)	)	PUNCT
easat-10856	680	4	𝑑𝑥	𝑑𝑥	VERB
easat-10856	680	5	=	=	SYM
easat-10856	680	6	−	−	PROPN
easat-10856	680	7	𝑥3	𝑥3	NOUN
easat-10856	680	8	6	6	NUM
easat-10856	680	9	−	−	NOUN
easat-10856	680	10	𝑥5	𝑥5	PROPN
easat-10856	680	11	60	60	NUM
easat-10856	680	12	−	−	NUM
easat-10856	680	13	𝑥7	𝑥7	VERB
easat-10856	680	14	210	210	NUM
easat-10856	680	15	−	−	PROPN
easat-10856	680	16	17𝑥9	17𝑥9	NUM
easat-10856	680	17	22680	22680	NUM
easat-10856	680	18	−	−	NOUN
easat-10856	680	19	31𝑥11	31𝑥11	NUM
easat-10856	680	20	311850	311850	NUM
easat-10856	681	1	−	−	NOUN
easat-10856	682	1	691𝑥13	691𝑥13	NUM
easat-10856	682	2	4455	4455	NUM
easat-10856	682	3	•	•	NOUN
easat-10856	682	4	for	for	ADP
easat-10856	682	5	:	:	PUNCT
easat-10856	682	6	𝐵1	𝐵1	NOUN
easat-10856	682	7	=	=	PUNCT
easat-10856	682	8	1/6,⁡𝐵2	1/6,⁡𝐵2	PROPN
easat-10856	682	9	=	=	SYM
easat-10856	682	10	1/30	1/30	NUM
easat-10856	682	11	,	,	PUNCT
easat-10856	682	12	𝐵3	𝐵3	NOUN
easat-10856	682	13	=	=	SYM
easat-10856	682	14	1/42	1/42	NUM
easat-10856	682	15	,	,	PUNCT
easat-10856	682	16	𝐵4	𝐵4	NOUN
easat-10856	682	17	=	=	SYM
easat-10856	682	18	1/30	1/30	NUM
easat-10856	682	19	,	,	PUNCT
easat-10856	682	20	𝐵5	𝐵5	NOUN
easat-10856	682	21	=	=	SYM
easat-10856	682	22	5/66	5/66	NUM
easat-10856	682	23	,	,	PUNCT
easat-10856	682	24	𝐵6	𝐵6	NOUN
easat-10856	682	25	=	=	PUNCT
easat-10856	683	1	691/2730	691/2730	NUM
easat-10856	684	1	y	y	SYM
easat-10856	684	2	𝐵7	𝐵7	NOUN
easat-10856	684	3	=	=	SYM
easat-10856	684	4	7/6	7/6	NUM
easat-10856	684	5	.	.	PUNCT
easat-10856	684	6	∫	∫	PROPN
easat-10856	684	7	ln(𝑐𝑜𝑠𝑥	ln(𝑐𝑜𝑠𝑥	PROPN
easat-10856	684	8	)	)	PUNCT
easat-10856	684	9	𝑑𝑥	𝑑𝑥	VERB
easat-10856	684	10	=	=	SYM
easat-10856	684	11	−	−	PROPN
easat-10856	684	12	𝑥3	𝑥3	NOUN
easat-10856	684	13	6	6	NUM
easat-10856	684	14	−	−	NOUN
easat-10856	684	15	𝑥5	𝑥5	PROPN
easat-10856	684	16	60	60	NUM
easat-10856	684	17	−	−	NUM
easat-10856	684	18	𝑥7	𝑥7	VERB
easat-10856	684	19	210	210	NUM
easat-10856	684	20	−	−	PROPN
easat-10856	684	21	17𝑥9	17𝑥9	NUM
easat-10856	684	22	22680	22680	NUM
easat-10856	684	23	−	−	NOUN
easat-10856	684	24	31𝑥11	31𝑥11	NUM
easat-10856	684	25	311850	311850	NUM
easat-10856	685	1	−	−	NOUN
easat-10856	686	1	691𝑥13	691𝑥13	NUM
easat-10856	686	2	4455	4455	NUM
easat-10856	686	3	−	−	NUM
easat-10856	686	4	10922𝑥15	10922𝑥15	NUM
easat-10856	686	5	638512875	638512875	NUM
easat-10856	686	6	•	•	NOUN
easat-10856	686	7	for	for	ADP
easat-10856	686	8	:	:	PUNCT
easat-10856	686	9	𝐵1	𝐵1	NOUN
easat-10856	686	10	=	=	PUNCT
easat-10856	686	11	1/6,⁡𝐵2	1/6,⁡𝐵2	PROPN
easat-10856	686	12	=	=	SYM
easat-10856	686	13	1/30	1/30	NUM
easat-10856	686	14	,	,	PUNCT
easat-10856	686	15	𝐵3	𝐵3	NOUN
easat-10856	686	16	=	=	SYM
easat-10856	686	17	1/42	1/42	NUM
easat-10856	686	18	,	,	PUNCT
easat-10856	686	19	𝐵4	𝐵4	NOUN
easat-10856	686	20	=	=	SYM
easat-10856	686	21	1/30	1/30	NUM
easat-10856	686	22	,	,	PUNCT
easat-10856	686	23	𝐵5	𝐵5	NOUN
easat-10856	686	24	=	=	SYM
easat-10856	686	25	5/66	5/66	NUM
easat-10856	686	26	,	,	PUNCT
easat-10856	686	27	𝐵6	𝐵6	NOUN
easat-10856	686	28	=	=	SYM
easat-10856	686	29	691/2730	691/2730	NUM
easat-10856	686	30	,	,	PUNCT
easat-10856	686	31	𝐵7	𝐵7	NOUN
easat-10856	686	32	=	=	SYM
easat-10856	686	33	7/6	7/6	NUM
easat-10856	686	34	y	y	PROPN
easat-10856	686	35	𝐵8	𝐵8	NOUN
easat-10856	686	36	=	=	SYM
easat-10856	686	37	3617/510	3617/510	NUM
easat-10856	686	38	.	.	PUNCT
easat-10856	686	39	∫	∫	PROPN
easat-10856	686	40	ln(𝑐𝑜𝑠𝑥	ln(𝑐𝑜𝑠𝑥	PROPN
easat-10856	686	41	)	)	PUNCT
easat-10856	686	42	𝑑𝑥	𝑑𝑥	VERB
easat-10856	686	43	=	=	SYM
easat-10856	686	44	−	−	PROPN
easat-10856	686	45	𝑥3	𝑥3	NOUN
easat-10856	686	46	6	6	NUM
easat-10856	686	47	−	−	NOUN
easat-10856	687	1	𝑥5	𝑥5	PROPN
easat-10856	687	2	60	60	NUM
easat-10856	687	3	−	−	NUM
easat-10856	687	4	𝑥7	𝑥7	VERB
easat-10856	687	5	210	210	NUM
easat-10856	687	6	−	−	PROPN
easat-10856	687	7	17𝑥9	17𝑥9	NUM
easat-10856	687	8	22680	22680	NUM
easat-10856	687	9	−	−	NOUN
easat-10856	687	10	31𝑥11	31𝑥11	NUM
easat-10856	687	11	311850	311850	NUM
easat-10856	688	1	−	−	NOUN
easat-10856	689	1	691𝑥13	691𝑥13	NUM
easat-10856	689	2	4455	4455	NUM
easat-10856	689	3	−	−	NUM
easat-10856	689	4	10922𝑥15	10922𝑥15	NUM
easat-10856	689	5	638512875	638512875	NUM
easat-10856	689	6	−	−	PROPN
easat-10856	689	7	929569𝑥17	929569𝑥17	NUM
easat-10856	689	8	173675502000	173675502000	NUM
easat-10856	689	9	+	+	ADJ
easat-10856	689	10	⋯	⋯	PROPN
easat-10856	689	11	;	;	PUNCT
easat-10856	689	12	and	and	CCONJ
easat-10856	689	13	so	so	ADV
easat-10856	689	14	on	on	ADV
easat-10856	689	15	,	,	PUNCT
easat-10856	689	16	the	the	DET
easat-10856	689	17	bernoulli	bernoulli	NOUN
easat-10856	689	18	numbers	number	NOUN
easat-10856	689	19	could	could	AUX
easat-10856	689	20	continue	continue	VERB
easat-10856	689	21	to	to	PART
easat-10856	689	22	be	be	AUX
easat-10856	689	23	applied	apply	VERB
easat-10856	689	24	to	to	ADP
easat-10856	689	25	other	other	ADJ
easat-10856	689	26	integrals	integral	NOUN
easat-10856	689	27	and	and	CCONJ
easat-10856	689	28	mathematical	mathematical	ADJ
easat-10856	689	29	expressions	expression	NOUN
easat-10856	689	30	in	in	ADP
easat-10856	689	31	which	which	PRON
easat-10856	689	32	the	the	DET
easat-10856	689	33	bernoulli	bernoulli	NOUN
easat-10856	689	34	numbers	number	NOUN
easat-10856	689	35	are	be	AUX
easat-10856	689	36	necessary	necessary	ADJ
easat-10856	689	37	.	.	PUNCT
easat-10856	690	1	the	the	DET
easat-10856	690	2	second	second	ADJ
easat-10856	690	3	application	application	NOUN
easat-10856	690	4	corresponds	correspond	VERB
easat-10856	690	5	to	to	ADP
easat-10856	690	6	the	the	DET
easat-10856	690	7	euler	euler	NOUN
easat-10856	690	8	numbers	number	NOUN
easat-10856	690	9	,	,	PUNCT
easat-10856	690	10	in	in	ADP
easat-10856	690	11	solving	solve	VERB
easat-10856	690	12	the	the	DET
easat-10856	690	13	integral	integral	ADJ
easat-10856	690	14	of⁡[sec⁡(𝑎𝑥	of⁡[sec⁡(𝑎𝑥	NOUN
easat-10856	690	15	)	)	PUNCT
easat-10856	690	16	]	]	PUNCT
easat-10856	691	1	𝑥⁄	𝑥⁄	NUM
easat-10856	691	2	.	.	PUNCT
easat-10856	691	3	table	table	NOUN
easat-10856	691	4	2	2	NUM
easat-10856	691	5	.	.	PUNCT
easat-10856	692	1	the	the	DET
easat-10856	692	2	euler	euler	NOUN
easat-10856	692	3	numbers	number	NOUN
easat-10856	692	4	.	.	PUNCT
easat-10856	693	1	n	n	CCONJ
easat-10856	693	2	en	en	ADV
easat-10856	693	3	1	1	NUM
easat-10856	693	4	1	1	NUM
easat-10856	693	5	2	2	NUM
easat-10856	693	6	5	5	NUM
easat-10856	693	7	3	3	NUM
easat-10856	693	8	61	61	NUM
easat-10856	693	9	4	4	NUM
easat-10856	693	10	1385	1385	NUM
easat-10856	693	11	5	5	NUM
easat-10856	693	12	50521	50521	NUM
easat-10856	693	13	6	6	NUM
easat-10856	693	14	2702765	2702765	NUM
easat-10856	693	15	7	7	NUM
easat-10856	693	16	199360891	199360891	NUM
easat-10856	693	17	8	8	NUM
easat-10856	693	18	19391512145	19391512145	NUM
easat-10856	693	19	9	9	NUM
easat-10856	693	20	2404879675441	2404879675441	NUM
easat-10856	693	21	10	10	NUM
easat-10856	693	22	370371188237525	370371188237525	NUM
easat-10856	693	23	11	11	NUM
easat-10856	693	24	69348874393137901	69348874393137901	NUM
easat-10856	693	25	12	12	NUM
easat-10856	693	26	15514534163557086905	15514534163557086905	NUM
easat-10856	693	27	13	13	NUM
easat-10856	693	28	4087072509293123892361	4087072509293123892361	NUM
easat-10856	693	29	14	14	NUM
easat-10856	693	30	1252259641403629865468285	1252259641403629865468285	NUM
easat-10856	693	31	15	15	NUM
easat-10856	693	32	441543893249023104553682821	441543893249023104553682821	NUM
easat-10856	693	33	16	16	NUM
easat-10856	693	34	177519391579539289436664789665	177519391579539289436664789665	NUM
easat-10856	693	35	17	17	NUM
easat-10856	693	36	80723299235887898062168247453281	80723299235887898062168247453281	NUM
easat-10856	693	37	18	18	NUM
easat-10856	693	38	41222060339517702122347079671259045	41222060339517702122347079671259045	NUM
easat-10856	693	39	19	19	NUM
easat-10856	693	40	23489580527043108252017828576198947741	23489580527043108252017828576198947741	NUM
easat-10856	693	41	20	20	NUM
easat-10856	693	42	14851150718114980017877156781405826684425	14851150718114980017877156781405826684425	NUM
easat-10856	693	43	3.2	3.2	NUM
easat-10856	693	44	.	.	PUNCT
easat-10856	694	1	for	for	ADP
easat-10856	694	2	the	the	DET
easat-10856	694	3	euler	euler	PROPN
easat-10856	694	4	numbers	number	NOUN
easat-10856	694	5	∫	∫	PROPN
easat-10856	694	6	𝑥	𝑥	SYM
easat-10856	694	7	𝑐𝑜𝑠(𝑎𝑥	𝑐𝑜𝑠(𝑎𝑥	NOUN
easat-10856	694	8	)	)	PUNCT
easat-10856	694	9	𝑑𝑥	𝑑𝑥	VERB
easat-10856	694	10	=	=	SYM
easat-10856	694	11	1	1	NUM
easat-10856	694	12	𝑎2	𝑎2	NOUN
easat-10856	694	13	[	[	PUNCT
easat-10856	694	14	(	(	PUNCT
easat-10856	694	15	𝑎𝑥)2	𝑎𝑥)2	PROPN
easat-10856	694	16	2	2	NUM
easat-10856	694	17	+	+	CCONJ
easat-10856	694	18	(	(	PUNCT
easat-10856	694	19	𝑎𝑥)4	𝑎𝑥)4	NOUN
easat-10856	694	20	4×2	4×2	NOUN
easat-10856	694	21	!	!	PUNCT
easat-10856	695	1	+	+	CCONJ
easat-10856	695	2	5(𝑎𝑥)6	5(𝑎𝑥)6	NUM
easat-10856	695	3	6×4	6×4	NOUN
easat-10856	695	4	!	!	PUNCT
easat-10856	696	1	+	+	CCONJ
easat-10856	696	2	61(𝑎𝑥)8	61(𝑎𝑥)8	NUM
easat-10856	696	3	8×6	8×6	NUM
easat-10856	696	4	!	!	PUNCT
easat-10856	697	1	+	+	X
easat-10856	697	2	.	.	PUNCT
easat-10856	697	3	.	.	PUNCT
easat-10856	697	4	.	.	PUNCT
easat-10856	698	1	+	+	CCONJ
easat-10856	698	2	𝐸𝑛(𝑎𝑥	𝐸𝑛(𝑎𝑥	NOUN
easat-10856	698	3	)	)	PUNCT
easat-10856	698	4	2𝑛+2	2𝑛+2	NOUN
easat-10856	698	5	(	(	PUNCT
easat-10856	698	6	2𝑛+2)(2𝑛	2𝑛+2)(2𝑛	NOUN
easat-10856	698	7	)	)	PUNCT
easat-10856	698	8	!	!	PUNCT
easat-10856	699	1	+	+	X
easat-10856	699	2	.	.	PUNCT
easat-10856	699	3	.	.	PUNCT
easat-10856	699	4	.	.	PUNCT
easat-10856	700	1	]	]	X
easat-10856	700	2	...	...	PUNCT
easat-10856	700	3	(	(	PUNCT
easat-10856	700	4	f	f	X
easat-10856	700	5	)	)	PUNCT
easat-10856	700	6	∫𝑥	∫𝑥	PROPN
easat-10856	700	7	𝑠𝑒𝑐	𝑠𝑒𝑐	ADJ
easat-10856	700	8	(	(	PUNCT
easat-10856	700	9	𝑎𝑥)𝑑𝑥	𝑎𝑥)𝑑𝑥	PUNCT
easat-10856	700	10	=	=	SYM
easat-10856	700	11	1	1	NUM
easat-10856	700	12	𝑎2	𝑎2	NOUN
easat-10856	700	13	[	[	PUNCT
easat-10856	700	14	(	(	PUNCT
easat-10856	700	15	𝑎𝑥)2	𝑎𝑥)2	PROPN
easat-10856	700	16	2	2	NUM
easat-10856	700	17	+	+	CCONJ
easat-10856	700	18	(	(	PUNCT
easat-10856	700	19	𝑎𝑥)4	𝑎𝑥)4	NOUN
easat-10856	700	20	8	8	NUM
easat-10856	700	21	+	+	CCONJ
easat-10856	700	22	5(𝑎𝑥)6	5(𝑎𝑥)6	NUM
easat-10856	700	23	144	144	NUM
easat-10856	701	1	+	+	CCONJ
easat-10856	701	2	61(𝑎𝑥)8	61(𝑎𝑥)8	NUM
easat-10856	701	3	5760	5760	NUM
easat-10856	701	4	+	+	NOUN
easat-10856	701	5	.	.	PUNCT
easat-10856	701	6	.	.	PUNCT
easat-10856	701	7	.	.	PUNCT
easat-10856	702	1	+	+	CCONJ
easat-10856	702	2	𝐸𝑛(𝑎𝑥	𝐸𝑛(𝑎𝑥	NOUN
easat-10856	702	3	)	)	PUNCT
easat-10856	702	4	2𝑛+2	2𝑛+2	NOUN
easat-10856	702	5	(	(	PUNCT
easat-10856	702	6	2𝑛+2)(2𝑛	2𝑛+2)(2𝑛	NOUN
easat-10856	702	7	)	)	PUNCT
easat-10856	702	8	!	!	PUNCT
easat-10856	703	1	+	+	X
easat-10856	703	2	.	.	PUNCT
easat-10856	703	3	.	.	PUNCT
easat-10856	703	4	.	.	PUNCT
easat-10856	704	1	]	]	X
easat-10856	704	2	...	...	PUNCT
easat-10856	704	3	(	(	PUNCT
easat-10856	704	4	g	g	NOUN
easat-10856	704	5	)	)	PUNCT
easat-10856	704	6	∫	∫	PROPN
easat-10856	705	1	𝑥	𝑥	PROPN
easat-10856	705	2	𝑐𝑜𝑠ℎ(𝑎𝑥	𝑐𝑜𝑠ℎ(𝑎𝑥	PROPN
easat-10856	705	3	)	)	PUNCT
easat-10856	705	4	𝑑𝑥	𝑑𝑥	VERB
easat-10856	705	5	=	=	SYM
easat-10856	705	6	1	1	NUM
easat-10856	705	7	𝑎2	𝑎2	NOUN
easat-10856	705	8	[	[	PUNCT
easat-10856	705	9	(	(	PUNCT
easat-10856	705	10	𝑎𝑥)2	𝑎𝑥)2	PROPN
easat-10856	705	11	2	2	NUM
easat-10856	705	12	−	−	PROPN
easat-10856	705	13	(	(	PUNCT
easat-10856	705	14	𝑎𝑥)4	𝑎𝑥)4	NOUN
easat-10856	705	15	8	8	NUM
easat-10856	705	16	+	+	CCONJ
easat-10856	705	17	5(𝑎𝑥)6	5(𝑎𝑥)6	NUM
easat-10856	706	1	144	144	NUM
easat-10856	706	2	−	−	NOUN
easat-10856	706	3	61(𝑎𝑥)8	61(𝑎𝑥)8	NUM
easat-10856	706	4	5760	5760	NUM
easat-10856	706	5	+	+	NOUN
easat-10856	706	6	.	.	PUNCT
easat-10856	706	7	.	.	PUNCT
easat-10856	706	8	.	.	PUNCT
easat-10856	707	1	+	+	CCONJ
easat-10856	707	2	(	(	PUNCT
easat-10856	707	3	−1)𝑛𝐸𝑛(𝑎𝑥	−1)𝑛𝐸𝑛(𝑎𝑥	NOUN
easat-10856	707	4	)	)	PUNCT
easat-10856	707	5	2𝑛+2	2𝑛+2	NOUN
easat-10856	707	6	(	(	PUNCT
easat-10856	707	7	2𝑛+2)(2𝑛	2𝑛+2)(2𝑛	NOUN
easat-10856	707	8	)	)	PUNCT
easat-10856	707	9	!	!	PUNCT
easat-10856	708	1	+	+	X
easat-10856	708	2	.	.	PUNCT
easat-10856	708	3	.	.	PUNCT
easat-10856	708	4	.	.	PUNCT
easat-10856	709	1	]	]	X
easat-10856	709	2	...	...	PUNCT
easat-10856	709	3	(	(	PUNCT
easat-10856	709	4	h	h	NOUN
easat-10856	709	5	)	)	PUNCT
easat-10856	709	6	∫	∫	PROPN
easat-10856	709	7	𝑠𝑒𝑐(𝑎𝑥	𝑠𝑒𝑐(𝑎𝑥	NOUN
easat-10856	709	8	)	)	PUNCT
easat-10856	710	1	𝑥	𝑥	PROPN
easat-10856	710	2	𝑑𝑥	𝑑𝑥	NOUN
easat-10856	710	3	=	=	PUNCT
easat-10856	710	4	𝑙𝑛	𝑙𝑛	NOUN
easat-10856	710	5	𝑥	𝑥	NOUN
easat-10856	710	6	+	+	NUM
easat-10856	710	7	𝐸𝑛(𝑎𝑥	𝐸𝑛(𝑎𝑥	X
easat-10856	710	8	)	)	PUNCT
easat-10856	710	9	2𝑛	2𝑛	PROPN
easat-10856	710	10	2𝑛(2𝑛	2𝑛(2𝑛	NUM
easat-10856	710	11	)	)	PUNCT
easat-10856	710	12	!	!	PUNCT
easat-10856	710	13	...	...	PUNCT
easat-10856	711	1	(	(	PUNCT
easat-10856	711	2	i	i	NOUN
easat-10856	711	3	)	)	PUNCT
easat-10856	711	4	3.2.1	3.2.1	X
easat-10856	711	5	.	.	PUNCT
easat-10856	712	1	application	application	NOUN
easat-10856	712	2	of	of	ADP
easat-10856	712	3	the	the	DET
easat-10856	712	4	euler	euler	NOUN
easat-10856	712	5	numbers	number	NOUN
easat-10856	712	6	(	(	PUNCT
easat-10856	712	7	𝐸𝑛	𝐸𝑛	NOUN
easat-10856	712	8	)	)	PUNCT
easat-10856	712	9	.	.	PUNCT
easat-10856	713	1	for	for	ADP
easat-10856	713	2	example	example	NOUN
easat-10856	713	3	,	,	PUNCT
easat-10856	713	4	for	for	ADP
easat-10856	713	5	the	the	DET
easat-10856	713	6	expression	expression	NOUN
easat-10856	713	7	∫	∫	PROPN
easat-10856	713	8	𝑠𝑒𝑐(𝑎𝑥	𝑠𝑒𝑐(𝑎𝑥	NOUN
easat-10856	713	9	)	)	PUNCT
easat-10856	713	10	𝑥	𝑥	PROPN
easat-10856	713	11	𝑑𝑥	𝑑𝑥	NOUN
easat-10856	713	12	(	(	PUNCT
easat-10856	713	13	i	i	NOUN
easat-10856	713	14	)	)	PUNCT
easat-10856	713	15	;	;	PUNCT
easat-10856	713	16	we	we	PRON
easat-10856	713	17	have	have	VERB
easat-10856	713	18	:	:	PUNCT
easat-10856	713	19	286	286	NUM
easat-10856	713	20	edelweiss	edelweiss	PROPN
easat-10856	713	21	applied	apply	VERB
easat-10856	713	22	science	science	NOUN
easat-10856	713	23	and	and	CCONJ
easat-10856	713	24	technology	technology	NOUN
easat-10856	713	25	issn	issn	PROPN
easat-10856	713	26	:	:	PUNCT
easat-10856	713	27	2576	2576	NUM
easat-10856	713	28	-	-	SYM
easat-10856	713	29	8484	8484	NUM
easat-10856	713	30	vol	vol	NOUN
easat-10856	713	31	.	.	PROPN
easat-10856	714	1	9	9	NUM
easat-10856	714	2	,	,	PUNCT
easat-10856	714	3	no	no	INTJ
easat-10856	714	4	.	.	NOUN
easat-10856	714	5	11	11	NUM
easat-10856	714	6	:	:	PUNCT
easat-10856	714	7	274	274	NUM
easat-10856	714	8	-	-	SYM
easat-10856	714	9	288	288	NUM
easat-10856	714	10	,	,	PUNCT
easat-10856	714	11	2025	2025	NUM
easat-10856	714	12	doi	doi	NOUN
easat-10856	714	13	:	:	PUNCT
easat-10856	714	14	10.55214/2576	10.55214/2576	NUM
easat-10856	714	15	-	-	PUNCT
easat-10856	714	16	8484.v9i11.10856	8484.v9i11.10856	NUM
easat-10856	714	17	©	©	PROPN
easat-10856	714	18	2025	2025	NUM
easat-10856	714	19	by	by	ADP
easat-10856	714	20	the	the	DET
easat-10856	714	21	authors	author	NOUN
easat-10856	714	22	;	;	PUNCT
easat-10856	714	23	licensee	licensee	PROPN
easat-10856	714	24	learning	learning	NOUN
easat-10856	714	25	gate	gate	NOUN
easat-10856	714	26	for	for	ADP
easat-10856	714	27	𝐸1	𝐸1	NOUN
easat-10856	714	28	=	=	SYM
easat-10856	714	29	1	1	NUM
easat-10856	714	30	∫	∫	PROPN
easat-10856	714	31	𝑠𝑒𝑐(𝑎𝑥	𝑠𝑒𝑐(𝑎𝑥	NOUN
easat-10856	714	32	)	)	PUNCT
easat-10856	715	1	𝑥	𝑥	PROPN
easat-10856	715	2	𝑑𝑥	𝑑𝑥	NOUN
easat-10856	715	3	=	=	PUNCT
easat-10856	715	4	𝑙𝑛	𝑙𝑛	NOUN
easat-10856	715	5	𝑥	𝑥	NOUN
easat-10856	716	1	+	+	CCONJ
easat-10856	716	2	(	(	PUNCT
easat-10856	716	3	𝑎𝑥)2	𝑎𝑥)2	PROPN
easat-10856	716	4	4	4	NUM
easat-10856	716	5	for	for	ADP
easat-10856	716	6	𝐸1	𝐸1	NOUN
easat-10856	716	7	=	=	SYM
easat-10856	716	8	1	1	NUM
easat-10856	716	9	y	y	PROPN
easat-10856	716	10	𝐸2	𝐸2	PROPN
easat-10856	716	11	=	=	SYM
easat-10856	716	12	5	5	NUM
easat-10856	716	13	∫	∫	PROPN
easat-10856	716	14	𝑠𝑒𝑐(𝑎𝑥	𝑠𝑒𝑐(𝑎𝑥	NOUN
easat-10856	716	15	)	)	PUNCT
easat-10856	716	16	𝑥	𝑥	PROPN
easat-10856	716	17	𝑑𝑥	𝑑𝑥	NOUN
easat-10856	716	18	=	=	PUNCT
easat-10856	716	19	𝑙𝑛	𝑙𝑛	NOUN
easat-10856	716	20	𝑥	𝑥	NOUN
easat-10856	717	1	+	+	CCONJ
easat-10856	717	2	(	(	PUNCT
easat-10856	717	3	𝑎𝑥)2	𝑎𝑥)2	PROPN
easat-10856	717	4	4	4	NUM
easat-10856	717	5	+	+	NUM
easat-10856	717	6	5(𝑎𝑥)4	5(𝑎𝑥)4	NUM
easat-10856	717	7	96	96	NUM
easat-10856	717	8	for	for	ADP
easat-10856	717	9	𝐸1	𝐸1	NOUN
easat-10856	717	10	=	=	SYM
easat-10856	717	11	1	1	NUM
easat-10856	717	12	,	,	PUNCT
easat-10856	717	13	𝐸2	𝐸2	NOUN
easat-10856	717	14	=	=	SYM
easat-10856	717	15	5	5	NUM
easat-10856	717	16	y	y	PROPN
easat-10856	717	17	𝐸3	𝐸3	NOUN
easat-10856	717	18	=	=	NOUN
easat-10856	717	19	61	61	NUM
easat-10856	717	20	∫	∫	NUM
easat-10856	717	21	𝑠𝑒𝑐(𝑎𝑥	𝑠𝑒𝑐(𝑎𝑥	NOUN
easat-10856	717	22	)	)	PUNCT
easat-10856	717	23	𝑥	𝑥	PROPN
easat-10856	717	24	𝑑𝑥	𝑑𝑥	NOUN
easat-10856	717	25	=	=	PUNCT
easat-10856	717	26	𝑙𝑛	𝑙𝑛	NOUN
easat-10856	717	27	𝑥	𝑥	NOUN
easat-10856	718	1	+	+	CCONJ
easat-10856	718	2	(	(	PUNCT
easat-10856	718	3	𝑎𝑥)2	𝑎𝑥)2	PROPN
easat-10856	718	4	4	4	NUM
easat-10856	718	5	+	+	NUM
easat-10856	718	6	5(𝑎𝑥)4	5(𝑎𝑥)4	NOUN
easat-10856	718	7	96	96	NUM
easat-10856	719	1	+	+	NUM
easat-10856	719	2	61(𝑎𝑥)6	61(𝑎𝑥)6	NOUN
easat-10856	719	3	4320	4320	NUM
easat-10856	719	4	for	for	ADP
easat-10856	719	5	𝐸1	𝐸1	NOUN
easat-10856	719	6	=	=	SYM
easat-10856	719	7	1	1	NUM
easat-10856	719	8	,	,	PUNCT
easat-10856	719	9	𝐸2	𝐸2	ADJ
easat-10856	719	10	=	=	SYM
easat-10856	719	11	5	5	NUM
easat-10856	719	12	,	,	PUNCT
easat-10856	719	13	𝐸3	𝐸3	NOUN
easat-10856	719	14	=	=	NOUN
easat-10856	719	15	61	61	NUM
easat-10856	719	16	y	y	PROPN
easat-10856	719	17	𝐸4	𝐸4	NOUN
easat-10856	719	18	=	=	NOUN
easat-10856	719	19	1385	1385	NUM
easat-10856	719	20	∫	∫	NOUN
easat-10856	719	21	𝑠𝑒𝑐(𝑎𝑥	𝑠𝑒𝑐(𝑎𝑥	NOUN
easat-10856	719	22	)	)	PUNCT
easat-10856	720	1	𝑥	𝑥	PROPN
easat-10856	720	2	𝑑𝑥	𝑑𝑥	NOUN
easat-10856	720	3	=	=	PUNCT
easat-10856	720	4	𝑙𝑛	𝑙𝑛	NOUN
easat-10856	720	5	𝑥	𝑥	NOUN
easat-10856	721	1	+	+	CCONJ
easat-10856	721	2	(	(	PUNCT
easat-10856	721	3	𝑎𝑥)2	𝑎𝑥)2	PROPN
easat-10856	721	4	4	4	NUM
easat-10856	721	5	+	+	NUM
easat-10856	721	6	5(𝑎𝑥)4	5(𝑎𝑥)4	NOUN
easat-10856	721	7	96	96	NUM
easat-10856	722	1	+	+	NUM
easat-10856	722	2	61(𝑎𝑥)6	61(𝑎𝑥)6	NOUN
easat-10856	722	3	4320	4320	NUM
easat-10856	722	4	+	+	SYM
easat-10856	722	5	277(𝑎𝑥)8	277(𝑎𝑥)8	NUM
easat-10856	722	6	64512	64512	NUM
easat-10856	722	7	for	for	ADP
easat-10856	722	8	𝐸1	𝐸1	NOUN
easat-10856	722	9	=	=	SYM
easat-10856	722	10	1	1	NUM
easat-10856	722	11	,	,	PUNCT
easat-10856	722	12	𝐸2	𝐸2	ADJ
easat-10856	722	13	=	=	SYM
easat-10856	722	14	5	5	NUM
easat-10856	722	15	,	,	PUNCT
easat-10856	722	16	𝐸3	𝐸3	NOUN
easat-10856	722	17	=	=	SYM
easat-10856	722	18	61	61	NUM
easat-10856	722	19	,	,	PUNCT
easat-10856	722	20	𝐸4	𝐸4	NOUN
easat-10856	722	21	=	=	NOUN
easat-10856	722	22	1385	1385	NUM
easat-10856	722	23	y	y	NOUN
easat-10856	722	24	𝐸5	𝐸5	NOUN
easat-10856	722	25	=	=	SYM
easat-10856	722	26	50521	50521	NUM
easat-10856	722	27	∫	∫	PROPN
easat-10856	722	28	𝑠𝑒𝑐(𝑎𝑥	𝑠𝑒𝑐(𝑎𝑥	NOUN
easat-10856	722	29	)	)	PUNCT
easat-10856	723	1	𝑥	𝑥	PROPN
easat-10856	723	2	𝑑𝑥	𝑑𝑥	NOUN
easat-10856	723	3	=	=	PUNCT
easat-10856	723	4	𝑙𝑛	𝑙𝑛	NOUN
easat-10856	723	5	𝑥	𝑥	NOUN
easat-10856	724	1	+	+	CCONJ
easat-10856	724	2	(	(	PUNCT
easat-10856	724	3	𝑎𝑥)2	𝑎𝑥)2	PROPN
easat-10856	724	4	4	4	NUM
easat-10856	724	5	+	+	NUM
easat-10856	724	6	5(𝑎𝑥)4	5(𝑎𝑥)4	NOUN
easat-10856	724	7	96	96	NUM
easat-10856	725	1	+	+	NUM
easat-10856	725	2	61(𝑎𝑥)6	61(𝑎𝑥)6	NOUN
easat-10856	725	3	4320	4320	NUM
easat-10856	725	4	+	+	SYM
easat-10856	725	5	277(𝑎𝑥)8	277(𝑎𝑥)8	NUM
easat-10856	725	6	64512	64512	NUM
easat-10856	725	7	+	+	CCONJ
easat-10856	725	8	50521(𝑎𝑥)10	50521(𝑎𝑥)10	NUM
easat-10856	725	9	36288000	36288000	NUM
easat-10856	725	10	for	for	ADP
easat-10856	725	11	𝐸1	𝐸1	NOUN
easat-10856	725	12	=	=	SYM
easat-10856	725	13	1	1	NUM
easat-10856	725	14	,	,	PUNCT
easat-10856	725	15	𝐸2	𝐸2	ADJ
easat-10856	725	16	=	=	SYM
easat-10856	725	17	5	5	NUM
easat-10856	725	18	,	,	PUNCT
easat-10856	725	19	𝐸3	𝐸3	NOUN
easat-10856	725	20	=	=	SYM
easat-10856	725	21	61	61	NUM
easat-10856	725	22	,	,	PUNCT
easat-10856	725	23	𝐸4	𝐸4	NOUN
easat-10856	725	24	=	=	SYM
easat-10856	725	25	1385	1385	NUM
easat-10856	725	26	,	,	PUNCT
easat-10856	725	27	𝐸5	𝐸5	NOUN
easat-10856	725	28	=	=	SYM
easat-10856	725	29	50521	50521	NUM
easat-10856	725	30	y	y	PROPN
easat-10856	725	31	𝐸6	𝐸6	PROPN
easat-10856	725	32	=	=	SYM
easat-10856	725	33	2702765	2702765	NUM
easat-10856	725	34	∫	∫	PROPN
easat-10856	725	35	𝑠𝑒𝑐(𝑎𝑥	𝑠𝑒𝑐(𝑎𝑥	NOUN
easat-10856	725	36	)	)	PUNCT
easat-10856	726	1	𝑥	𝑥	PROPN
easat-10856	726	2	𝑑𝑥	𝑑𝑥	NOUN
easat-10856	726	3	=	=	PUNCT
easat-10856	726	4	𝑙𝑛	𝑙𝑛	NOUN
easat-10856	726	5	𝑥	𝑥	NOUN
easat-10856	727	1	+	+	CCONJ
easat-10856	727	2	(	(	PUNCT
easat-10856	727	3	𝑎𝑥)2	𝑎𝑥)2	PROPN
easat-10856	727	4	4	4	NUM
easat-10856	727	5	+	+	NUM
easat-10856	727	6	5(𝑎𝑥)4	5(𝑎𝑥)4	NOUN
easat-10856	727	7	96	96	NUM
easat-10856	728	1	+	+	NUM
easat-10856	728	2	61(𝑎𝑥)6	61(𝑎𝑥)6	NOUN
easat-10856	728	3	4320	4320	NUM
easat-10856	728	4	+	+	SYM
easat-10856	728	5	277(𝑎𝑥)8	277(𝑎𝑥)8	NUM
easat-10856	728	6	64512	64512	NUM
easat-10856	728	7	+	+	CCONJ
easat-10856	728	8	50521(𝑎𝑥)10	50521(𝑎𝑥)10	NUM
easat-10856	728	9	36288000	36288000	NUM
easat-10856	728	10	+	+	CCONJ
easat-10856	728	11	540553(𝑎𝑥)12	540553(𝑎𝑥)12	NUM
easat-10856	728	12	1149603840	1149603840	NUM
easat-10856	728	13	for	for	ADP
easat-10856	728	14	𝐸1	𝐸1	NOUN
easat-10856	728	15	=	=	SYM
easat-10856	728	16	1	1	NUM
easat-10856	728	17	,	,	PUNCT
easat-10856	728	18	𝐸2	𝐸2	ADJ
easat-10856	728	19	=	=	SYM
easat-10856	728	20	5	5	NUM
easat-10856	728	21	,	,	PUNCT
easat-10856	728	22	𝐸3	𝐸3	NOUN
easat-10856	728	23	=	=	SYM
easat-10856	728	24	61	61	NUM
easat-10856	728	25	,	,	PUNCT
easat-10856	728	26	𝐸4	𝐸4	NOUN
easat-10856	728	27	=	=	SYM
easat-10856	728	28	1385	1385	NUM
easat-10856	728	29	,	,	PUNCT
easat-10856	728	30	𝐸5	𝐸5	NOUN
easat-10856	728	31	=	=	SYM
easat-10856	728	32	50521	50521	NUM
easat-10856	728	33	,	,	PUNCT
easat-10856	728	34	𝐸6	𝐸6	NOUN
easat-10856	728	35	=	=	SYM
easat-10856	728	36	2702765	2702765	NUM
easat-10856	728	37	y	y	PROPN
easat-10856	728	38	𝐸7	𝐸7	NOUN
easat-10856	728	39	=	=	SYM
easat-10856	728	40	199360891	199360891	NUM
easat-10856	728	41	∫	∫	NOUN
easat-10856	728	42	𝑠𝑒𝑐(𝑎𝑥	𝑠𝑒𝑐(𝑎𝑥	NOUN
easat-10856	728	43	)	)	PUNCT
easat-10856	729	1	𝑥	𝑥	PROPN
easat-10856	729	2	𝑑𝑥	𝑑𝑥	NOUN
easat-10856	729	3	=	=	PUNCT
easat-10856	729	4	𝑙𝑛	𝑙𝑛	NOUN
easat-10856	729	5	𝑥	𝑥	NOUN
easat-10856	730	1	+	+	CCONJ
easat-10856	730	2	(	(	PUNCT
easat-10856	730	3	𝑎𝑥)2	𝑎𝑥)2	PROPN
easat-10856	730	4	4	4	NUM
easat-10856	730	5	+	+	NUM
easat-10856	730	6	5(𝑎𝑥)4	5(𝑎𝑥)4	NOUN
easat-10856	730	7	96	96	NUM
easat-10856	731	1	+	+	NUM
easat-10856	731	2	61(𝑎𝑥)6	61(𝑎𝑥)6	NOUN
easat-10856	731	3	4320	4320	NUM
easat-10856	731	4	+	+	SYM
easat-10856	731	5	277(𝑎𝑥)8	277(𝑎𝑥)8	NUM
easat-10856	731	6	64512	64512	NUM
easat-10856	731	7	+	+	CCONJ
easat-10856	731	8	50521(𝑎𝑥)10	50521(𝑎𝑥)10	NUM
easat-10856	731	9	36288000	36288000	NUM
easat-10856	731	10	+	+	CCONJ
easat-10856	731	11	540553(𝑎𝑥)12	540553(𝑎𝑥)12	NUM
easat-10856	731	12	1149603840	1149603840	NUM
easat-10856	731	13	+	+	CCONJ
easat-10856	731	14	199360891𝑥14	199360891𝑥14	NUM
easat-10856	731	15	1220496076800	1220496076800	NUM
easat-10856	731	16	for	for	ADP
easat-10856	731	17	𝐸1	𝐸1	NOUN
easat-10856	731	18	=	=	SYM
easat-10856	731	19	1	1	NUM
easat-10856	731	20	,	,	PUNCT
easat-10856	731	21	𝐸2	𝐸2	ADJ
easat-10856	731	22	=	=	SYM
easat-10856	731	23	5	5	NUM
easat-10856	731	24	,	,	PUNCT
easat-10856	731	25	𝐸3	𝐸3	NOUN
easat-10856	731	26	=	=	SYM
easat-10856	731	27	61	61	NUM
easat-10856	731	28	,	,	PUNCT
easat-10856	731	29	𝐸4	𝐸4	NOUN
easat-10856	731	30	=	=	SYM
easat-10856	731	31	1385	1385	NUM
easat-10856	731	32	,	,	PUNCT
easat-10856	731	33	𝐸5	𝐸5	NOUN
easat-10856	731	34	=	=	SYM
easat-10856	731	35	50521	50521	NUM
easat-10856	731	36	,	,	PUNCT
easat-10856	731	37	𝐸6	𝐸6	PROPN
easat-10856	731	38	=	=	SYM
easat-10856	731	39	2702765	2702765	NUM
easat-10856	731	40	,	,	PUNCT
easat-10856	731	41	𝐸7	𝐸7	NOUN
easat-10856	731	42	=	=	SYM
easat-10856	731	43	199360891	199360891	NUM
easat-10856	731	44	y	y	NOUN
easat-10856	731	45	𝐸8	𝐸8	NOUN
easat-10856	731	46	=	=	SYM
easat-10856	731	47	19391512145	19391512145	NUM
easat-10856	731	48	⁡⁡∫	⁡⁡∫	ADP
easat-10856	731	49	𝑠𝑒𝑐(𝑎𝑥	𝑠𝑒𝑐(𝑎𝑥	NOUN
easat-10856	731	50	)	)	PUNCT
easat-10856	731	51	𝑥	𝑥	PROPN
easat-10856	731	52	𝑑𝑥	𝑑𝑥	NOUN
easat-10856	731	53	=	=	PUNCT
easat-10856	731	54	𝑙𝑛	𝑙𝑛	NOUN
easat-10856	731	55	𝑥	𝑥	NOUN
easat-10856	732	1	+	+	CCONJ
easat-10856	732	2	(	(	PUNCT
easat-10856	732	3	𝑎𝑥)2	𝑎𝑥)2	PROPN
easat-10856	732	4	4	4	NUM
easat-10856	732	5	+	+	NUM
easat-10856	732	6	5(𝑎𝑥)4	5(𝑎𝑥)4	NOUN
easat-10856	732	7	96	96	NUM
easat-10856	733	1	+	+	NUM
easat-10856	733	2	61(𝑎𝑥)6	61(𝑎𝑥)6	NOUN
easat-10856	733	3	4320	4320	NUM
easat-10856	733	4	+	+	SYM
easat-10856	733	5	277(𝑎𝑥)8	277(𝑎𝑥)8	NUM
easat-10856	733	6	64512	64512	NUM
easat-10856	733	7	+	+	CCONJ
easat-10856	733	8	50521(𝑎𝑥)10	50521(𝑎𝑥)10	NUM
easat-10856	733	9	36288000	36288000	NUM
easat-10856	733	10	+	+	CCONJ
easat-10856	733	11	540553(𝑎𝑥)12	540553(𝑎𝑥)12	NUM
easat-10856	733	12	1149603840	1149603840	NUM
easat-10856	733	13	+	+	CCONJ
easat-10856	733	14	199360891𝑥14	199360891𝑥14	NUM
easat-10856	733	15	1220496076800	1220496076800	NUM
easat-10856	733	16	+	+	CCONJ
easat-10856	733	17	3878302429(𝑎𝑥)16	3878302429(𝑎𝑥)16	NUM
easat-10856	733	18	66952927641600	66952927641600	NUM
easat-10856	734	1	+	+	VERB
easat-10856	734	2	⋯	⋯	VERB
easat-10856	734	3	for	for	ADP
easat-10856	734	4	𝐸1	𝐸1	NOUN
easat-10856	734	5	=	=	SYM
easat-10856	734	6	1	1	NUM
easat-10856	734	7	,	,	PUNCT
easat-10856	734	8	𝐸2	𝐸2	ADJ
easat-10856	734	9	=	=	SYM
easat-10856	734	10	5	5	NUM
easat-10856	734	11	,	,	PUNCT
easat-10856	734	12	𝐸3	𝐸3	NOUN
easat-10856	734	13	=	=	SYM
easat-10856	734	14	61	61	NUM
easat-10856	734	15	,	,	PUNCT
easat-10856	734	16	𝐸4	𝐸4	NOUN
easat-10856	734	17	=	=	SYM
easat-10856	734	18	1385	1385	NUM
easat-10856	734	19	,	,	PUNCT
easat-10856	734	20	𝐸5	𝐸5	NOUN
easat-10856	734	21	=	=	SYM
easat-10856	734	22	50521	50521	NUM
easat-10856	734	23	,	,	PUNCT
easat-10856	734	24	𝐸6	𝐸6	PROPN
easat-10856	734	25	=	=	SYM
easat-10856	734	26	2702765	2702765	NUM
easat-10856	734	27	,	,	PUNCT
easat-10856	734	28	𝐸7	𝐸7	NOUN
easat-10856	734	29	=	=	SYM
easat-10856	734	30	199360891	199360891	NUM
easat-10856	734	31	,	,	PUNCT
easat-10856	734	32	𝐸8	𝐸8	NOUN
easat-10856	734	33	=	=	SYM
easat-10856	734	34	19391512145	19391512145	NUM
easat-10856	734	35	y	y	PROPN
easat-10856	734	36	𝐸9	𝐸9	NOUN
easat-10856	734	37	=	=	SYM
easat-10856	734	38	2404879675441	2404879675441	NUM
easat-10856	734	39	⁡⁡∫	⁡⁡∫	ADP
easat-10856	734	40	𝑠𝑒𝑐(𝑎𝑥	𝑠𝑒𝑐(𝑎𝑥	NOUN
easat-10856	734	41	)	)	PUNCT
easat-10856	734	42	𝑥	𝑥	PROPN
easat-10856	734	43	𝑑𝑥	𝑑𝑥	NOUN
easat-10856	734	44	=	=	PUNCT
easat-10856	734	45	𝑙𝑛	𝑙𝑛	NOUN
easat-10856	734	46	𝑥	𝑥	NOUN
easat-10856	735	1	+	+	CCONJ
easat-10856	736	1	(	(	PUNCT
easat-10856	736	2	𝑎𝑥)2	𝑎𝑥)2	PROPN
easat-10856	736	3	4	4	NUM
easat-10856	736	4	+	+	NUM
easat-10856	736	5	5(𝑎𝑥)4	5(𝑎𝑥)4	NOUN
easat-10856	736	6	96	96	NUM
easat-10856	737	1	+	+	NUM
easat-10856	737	2	61(𝑎𝑥)6	61(𝑎𝑥)6	NOUN
easat-10856	737	3	4320	4320	NUM
easat-10856	737	4	+	+	SYM
easat-10856	737	5	277(𝑎𝑥)8	277(𝑎𝑥)8	NUM
easat-10856	737	6	64512	64512	NUM
easat-10856	737	7	+	+	CCONJ
easat-10856	737	8	50521(𝑎𝑥)10	50521(𝑎𝑥)10	NUM
easat-10856	737	9	36288000	36288000	NUM
easat-10856	737	10	+	+	CCONJ
easat-10856	737	11	540553(𝑎𝑥)12	540553(𝑎𝑥)12	NUM
easat-10856	737	12	1149603840	1149603840	NUM
easat-10856	737	13	+	+	CCONJ
easat-10856	737	14	199360891𝑥14	199360891𝑥14	NUM
easat-10856	737	15	1220496076800	1220496076800	NUM
easat-10856	737	16	+	+	CCONJ
easat-10856	737	17	3878302429(𝑎𝑥)16	3878302429(𝑎𝑥)16	NUM
easat-10856	737	18	66952927641600	66952927641600	NUM
easat-10856	737	19	+	+	CCONJ
easat-10856	737	20	2404879675441(𝑎𝑥)18	2404879675441(𝑎𝑥)18	NUM
easat-10856	737	21	115242726703104000	115242726703104000	NUM
easat-10856	738	1	+	+	ADJ
easat-10856	738	2	…	…	PUNCT
easat-10856	738	3	for	for	ADP
easat-10856	738	4	𝐸1	𝐸1	NOUN
easat-10856	738	5	=	=	SYM
easat-10856	738	6	1	1	NUM
easat-10856	738	7	,	,	PUNCT
easat-10856	738	8	𝐸2	𝐸2	ADJ
easat-10856	738	9	=	=	SYM
easat-10856	738	10	5	5	NUM
easat-10856	738	11	,	,	PUNCT
easat-10856	738	12	𝐸3	𝐸3	NOUN
easat-10856	738	13	=	=	SYM
easat-10856	738	14	61	61	NUM
easat-10856	738	15	,	,	PUNCT
easat-10856	738	16	𝐸4	𝐸4	NOUN
easat-10856	738	17	=	=	SYM
easat-10856	738	18	1385	1385	NUM
easat-10856	738	19	,	,	PUNCT
easat-10856	738	20	𝐸5	𝐸5	NOUN
easat-10856	738	21	=	=	SYM
easat-10856	738	22	50521	50521	NUM
easat-10856	738	23	,	,	PUNCT
easat-10856	738	24	𝐸6	𝐸6	PROPN
easat-10856	738	25	=	=	SYM
easat-10856	738	26	2702765	2702765	NUM
easat-10856	738	27	,	,	PUNCT
easat-10856	738	28	𝐸7	𝐸7	NOUN
easat-10856	738	29	=	=	SYM
easat-10856	738	30	199360891	199360891	NUM
easat-10856	738	31	,	,	PUNCT
easat-10856	738	32	𝐸8	𝐸8	NOUN
easat-10856	738	33	=	=	SYM
easat-10856	738	34	19391512145	19391512145	NUM
easat-10856	738	35	,	,	PUNCT
easat-10856	738	36	𝐸9	𝐸9	NOUN
easat-10856	738	37	=	=	SYM
easat-10856	738	38	2404879675441	2404879675441	NUM
easat-10856	738	39	y	y	PROPN
easat-10856	738	40	𝐸10	𝐸10	PROPN
easat-10856	738	41	=	=	PUNCT
easat-10856	738	42	370371188237525	370371188237525	NUM
easat-10856	738	43	∫	∫	NOUN
easat-10856	738	44	𝑠𝑒𝑐(𝑎𝑥	𝑠𝑒𝑐(𝑎𝑥	NOUN
easat-10856	738	45	)	)	PUNCT
easat-10856	739	1	𝑥	𝑥	PROPN
easat-10856	739	2	𝑑𝑥	𝑑𝑥	NOUN
easat-10856	739	3	=	=	PUNCT
easat-10856	739	4	𝑙𝑛	𝑙𝑛	NOUN
easat-10856	739	5	𝑥	𝑥	NOUN
easat-10856	740	1	+	+	CCONJ
easat-10856	740	2	(	(	PUNCT
easat-10856	740	3	𝑎𝑥)2	𝑎𝑥)2	PROPN
easat-10856	740	4	4	4	NUM
easat-10856	740	5	+	+	NUM
easat-10856	740	6	5(𝑎𝑥)4	5(𝑎𝑥)4	NOUN
easat-10856	740	7	96	96	NUM
easat-10856	741	1	+	+	NUM
easat-10856	741	2	61(𝑎𝑥)6	61(𝑎𝑥)6	NOUN
easat-10856	741	3	4320	4320	NUM
easat-10856	741	4	+	+	SYM
easat-10856	741	5	277(𝑎𝑥)8	277(𝑎𝑥)8	NUM
easat-10856	741	6	64512	64512	NUM
easat-10856	741	7	+	+	CCONJ
easat-10856	741	8	50521(𝑎𝑥)10	50521(𝑎𝑥)10	NUM
easat-10856	741	9	36288000	36288000	NUM
easat-10856	741	10	+	+	CCONJ
easat-10856	741	11	540553(𝑎𝑥)12	540553(𝑎𝑥)12	NUM
easat-10856	741	12	1149603840	1149603840	NUM
easat-10856	741	13	+	+	CCONJ
easat-10856	741	14	199360891𝑥14	199360891𝑥14	NUM
easat-10856	741	15	1220496076800	1220496076800	NUM
easat-10856	741	16	+	+	CCONJ
easat-10856	741	17	3878302429(𝑎𝑥)16	3878302429(𝑎𝑥)16	NUM
easat-10856	741	18	66952927641600	66952927641600	NUM
easat-10856	741	19	+	+	CCONJ
easat-10856	741	20	2404879675441(𝑎𝑥)18	2404879675441(𝑎𝑥)18	NUM
easat-10856	741	21	115242726703104000	115242726703104000	NUM
easat-10856	741	22	+	+	CCONJ
easat-10856	741	23	14814847529501(𝑎𝑥)20	14814847529501(𝑎𝑥)20	NUM
easat-10856	741	24	1946321606541312000	1946321606541312000	NUM
easat-10856	742	1	+	+	VERB
easat-10856	742	2	⋯	⋯	VERB
easat-10856	742	3	for	for	ADP
easat-10856	742	4	𝐸1	𝐸1	NOUN
easat-10856	742	5	=	=	SYM
easat-10856	742	6	1	1	NUM
easat-10856	742	7	,	,	PUNCT
easat-10856	742	8	𝐸2	𝐸2	ADJ
easat-10856	742	9	=	=	SYM
easat-10856	742	10	5	5	NUM
easat-10856	742	11	,	,	PUNCT
easat-10856	742	12	𝐸3	𝐸3	NOUN
easat-10856	742	13	=	=	SYM
easat-10856	742	14	61	61	NUM
easat-10856	742	15	,	,	PUNCT
easat-10856	742	16	𝐸4	𝐸4	NOUN
easat-10856	742	17	=	=	SYM
easat-10856	742	18	1385	1385	NUM
easat-10856	742	19	,	,	PUNCT
easat-10856	742	20	𝐸5	𝐸5	NOUN
easat-10856	742	21	=	=	SYM
easat-10856	742	22	50521	50521	NUM
easat-10856	742	23	,	,	PUNCT
easat-10856	742	24	𝐸6	𝐸6	PROPN
easat-10856	742	25	=	=	SYM
easat-10856	742	26	2702765	2702765	NUM
easat-10856	742	27	,	,	PUNCT
easat-10856	742	28	𝐸7	𝐸7	NOUN
easat-10856	742	29	=	=	SYM
easat-10856	742	30	199360891	199360891	NUM
easat-10856	742	31	,	,	PUNCT
easat-10856	742	32	𝐸8	𝐸8	NOUN
easat-10856	742	33	=	=	SYM
easat-10856	742	34	19391512145	19391512145	NUM
easat-10856	742	35	,	,	PUNCT
easat-10856	742	36	𝐸9	𝐸9	NOUN
easat-10856	742	37	=	=	SYM
easat-10856	742	38	2404879675441	2404879675441	NUM
easat-10856	742	39	,	,	PUNCT
easat-10856	742	40	𝐸10	𝐸10	NOUN
easat-10856	742	41	=	=	PUNCT
easat-10856	742	42	370371188237525	370371188237525	NUM
easat-10856	742	43	y	y	PROPN
easat-10856	742	44	𝐸11	𝐸11	PROPN
easat-10856	742	45	=	=	PUNCT
easat-10856	742	46	69348874393137901	69348874393137901	NUM
easat-10856	742	47	∫	∫	NOUN
easat-10856	742	48	𝑠𝑒𝑐(𝑎𝑥	𝑠𝑒𝑐(𝑎𝑥	NOUN
easat-10856	742	49	)	)	PUNCT
easat-10856	742	50	𝑥	𝑥	PROPN
easat-10856	742	51	𝑑𝑥	𝑑𝑥	NOUN
easat-10856	742	52	=	=	PUNCT
easat-10856	742	53	𝑙𝑛	𝑙𝑛	NOUN
easat-10856	742	54	𝑥	𝑥	NOUN
easat-10856	743	1	+	+	CCONJ
easat-10856	743	2	(	(	PUNCT
easat-10856	743	3	𝑎𝑥)2	𝑎𝑥)2	PROPN
easat-10856	743	4	4	4	NUM
easat-10856	743	5	+	+	NUM
easat-10856	743	6	5(𝑎𝑥)4	5(𝑎𝑥)4	NOUN
easat-10856	743	7	96	96	NUM
easat-10856	744	1	+	+	NUM
easat-10856	744	2	61(𝑎𝑥)6	61(𝑎𝑥)6	NOUN
easat-10856	744	3	4320	4320	NUM
easat-10856	744	4	+	+	SYM
easat-10856	744	5	277(𝑎𝑥)8	277(𝑎𝑥)8	NUM
easat-10856	744	6	64512	64512	NUM
easat-10856	744	7	+	+	CCONJ
easat-10856	744	8	50521(𝑎𝑥)10	50521(𝑎𝑥)10	NUM
easat-10856	744	9	36288000	36288000	NUM
easat-10856	744	10	+	+	CCONJ
easat-10856	744	11	540553(𝑎𝑥)12	540553(𝑎𝑥)12	NUM
easat-10856	744	12	1149603840	1149603840	NUM
easat-10856	744	13	+	+	CCONJ
easat-10856	744	14	199360891𝑥14	199360891𝑥14	NUM
easat-10856	744	15	1220496076800	1220496076800	NUM
easat-10856	744	16	+	+	CCONJ
easat-10856	744	17	3878302429(𝑎𝑥)16	3878302429(𝑎𝑥)16	NUM
easat-10856	744	18	66952927641600	66952927641600	NUM
easat-10856	744	19	+	+	CCONJ
easat-10856	744	20	2404879675441(𝑎𝑥)18	2404879675441(𝑎𝑥)18	NUM
easat-10856	744	21	115242726703104000	115242726703104000	NUM
easat-10856	744	22	+	+	CCONJ
easat-10856	744	23	14814847529501(𝑎𝑥)20	14814847529501(𝑎𝑥)20	NUM
easat-10856	744	24	1946321606541312000	1946321606541312000	NUM
easat-10856	744	25	+	+	CCONJ
easat-10856	744	26	69348874393137901(𝑎𝑥)22	69348874393137901(𝑎𝑥)22	NUM
easat-10856	744	27	24728016011107368960000	24728016011107368960000	NUM
easat-10856	745	1	+	+	VERB
easat-10856	745	2	⋯	⋯	VERB
easat-10856	745	3	for	for	ADP
easat-10856	745	4	𝐸1	𝐸1	NOUN
easat-10856	745	5	=	=	SYM
easat-10856	745	6	1	1	NUM
easat-10856	745	7	,	,	PUNCT
easat-10856	745	8	𝐸2	𝐸2	ADJ
easat-10856	745	9	=	=	SYM
easat-10856	745	10	5	5	NUM
easat-10856	745	11	,	,	PUNCT
easat-10856	745	12	𝐸3	𝐸3	NOUN
easat-10856	745	13	=	=	SYM
easat-10856	745	14	61	61	NUM
easat-10856	745	15	,	,	PUNCT
easat-10856	745	16	𝐸4	𝐸4	NOUN
easat-10856	745	17	=	=	SYM
easat-10856	745	18	1385	1385	NUM
easat-10856	745	19	,	,	PUNCT
easat-10856	745	20	𝐸5	𝐸5	NOUN
easat-10856	745	21	=	=	SYM
easat-10856	745	22	50521	50521	NUM
easat-10856	745	23	,	,	PUNCT
easat-10856	745	24	𝐸6	𝐸6	PROPN
easat-10856	745	25	=	=	SYM
easat-10856	745	26	2702765	2702765	NUM
easat-10856	745	27	,	,	PUNCT
easat-10856	745	28	𝐸7	𝐸7	NOUN
easat-10856	745	29	=	=	SYM
easat-10856	745	30	199360891	199360891	NUM
easat-10856	745	31	,	,	PUNCT
easat-10856	745	32	𝐸8	𝐸8	NOUN
easat-10856	745	33	=	=	SYM
easat-10856	745	34	19391512145	19391512145	NUM
easat-10856	745	35	,	,	PUNCT
easat-10856	745	36	𝐸9	𝐸9	NOUN
easat-10856	745	37	=	=	SYM
easat-10856	745	38	2404879675441	2404879675441	NUM
easat-10856	745	39	,	,	PUNCT
easat-10856	745	40	𝐸10	𝐸10	PROPN
easat-10856	745	41	=	=	SYM
easat-10856	745	42	370371188237525	370371188237525	NUM
easat-10856	745	43	,	,	PUNCT
easat-10856	745	44	𝐸11	𝐸11	NOUN
easat-10856	745	45	=	=	PUNCT
easat-10856	745	46	69348874393137901	69348874393137901	NUM
easat-10856	746	1	y	y	PROPN
easat-10856	746	2	𝐸12	𝐸12	PROPN
easat-10856	746	3	=	=	SYM
easat-10856	746	4	15514534163557086905	15514534163557086905	NUM
easat-10856	746	5	∫	∫	PROPN
easat-10856	746	6	𝑠𝑒𝑐(𝑎𝑥	𝑠𝑒𝑐(𝑎𝑥	NOUN
easat-10856	746	7	)	)	PUNCT
easat-10856	746	8	𝑥	𝑥	PROPN
easat-10856	746	9	𝑑𝑥	𝑑𝑥	NOUN
easat-10856	746	10	=	=	PUNCT
easat-10856	746	11	𝑙𝑛	𝑙𝑛	NOUN
easat-10856	746	12	𝑥	𝑥	NOUN
easat-10856	747	1	+	+	CCONJ
easat-10856	747	2	(	(	PUNCT
easat-10856	747	3	𝑎𝑥)2	𝑎𝑥)2	PROPN
easat-10856	747	4	4	4	NUM
easat-10856	747	5	+	+	NUM
easat-10856	747	6	5(𝑎𝑥)4	5(𝑎𝑥)4	NOUN
easat-10856	747	7	96	96	NUM
easat-10856	748	1	+	+	NUM
easat-10856	748	2	61(𝑎𝑥)6	61(𝑎𝑥)6	NOUN
easat-10856	748	3	4320	4320	NUM
easat-10856	748	4	+	+	SYM
easat-10856	748	5	277(𝑎𝑥)8	277(𝑎𝑥)8	NUM
easat-10856	748	6	64512	64512	NUM
easat-10856	748	7	+	+	CCONJ
easat-10856	748	8	50521(𝑎𝑥)10	50521(𝑎𝑥)10	NUM
easat-10856	748	9	36288000	36288000	NUM
easat-10856	748	10	+	+	CCONJ
easat-10856	748	11	540553(𝑎𝑥)12	540553(𝑎𝑥)12	NUM
easat-10856	748	12	1149603840	1149603840	NUM
easat-10856	748	13	+	+	CCONJ
easat-10856	748	14	199360891𝑥14	199360891𝑥14	NUM
easat-10856	748	15	1220496076800	1220496076800	NUM
easat-10856	748	16	+	+	CCONJ
easat-10856	748	17	3878302429(𝑎𝑥)16	3878302429(𝑎𝑥)16	NUM
easat-10856	748	18	66952927641600	66952927641600	NUM
easat-10856	748	19	+	+	CCONJ
easat-10856	748	20	2404879675441(𝑎𝑥)18	2404879675441(𝑎𝑥)18	NUM
easat-10856	748	21	115242726703104000	115242726703104000	NUM
easat-10856	748	22	+	+	CCONJ
easat-10856	748	23	14814847529501(𝑎𝑥)20	14814847529501(𝑎𝑥)20	NUM
easat-10856	748	24	1946321606541312000	1946321606541312000	NUM
easat-10856	748	25	+	+	CCONJ
easat-10856	748	26	69348874393137901(𝑎𝑥)22	69348874393137901(𝑎𝑥)22	NUM
easat-10856	748	27	24728016011107368960000	24728016011107368960000	NUM
easat-10856	748	28	+	+	CCONJ
easat-10856	749	1	3102906832711417381(𝑎𝑥)24	3102906832711417381(𝑎𝑥)24	NUM
easat-10856	749	2	2978152328319549308928000	2978152328319549308928000	NUM
easat-10856	749	3	+	+	SYM
easat-10856	749	4	⋯	⋯	PROPN
easat-10856	749	5	;	;	PUNCT
easat-10856	749	6	and	and	CCONJ
easat-10856	749	7	so	so	ADV
easat-10856	749	8	on	on	ADV
easat-10856	749	9	,	,	PUNCT
easat-10856	749	10	the	the	DET
easat-10856	749	11	euler	euler	NOUN
easat-10856	749	12	numbers	number	NOUN
easat-10856	749	13	could	could	AUX
easat-10856	749	14	continue	continue	VERB
easat-10856	749	15	to	to	PART
easat-10856	749	16	be	be	AUX
easat-10856	749	17	applied	apply	VERB
easat-10856	749	18	.	.	PUNCT
easat-10856	750	1	287	287	NUM
easat-10856	750	2	edelweiss	edelweiss	PROPN
easat-10856	750	3	applied	apply	VERB
easat-10856	750	4	science	science	NOUN
easat-10856	750	5	and	and	CCONJ
easat-10856	750	6	technology	technology	NOUN
easat-10856	750	7	issn	issn	PROPN
easat-10856	750	8	:	:	PUNCT
easat-10856	750	9	2576	2576	NUM
easat-10856	750	10	-	-	SYM
easat-10856	750	11	8484	8484	NUM
easat-10856	750	12	vol	vol	NOUN
easat-10856	750	13	.	.	PROPN
easat-10856	751	1	9	9	NUM
easat-10856	751	2	,	,	PUNCT
easat-10856	751	3	no	no	INTJ
easat-10856	751	4	.	.	NOUN
easat-10856	751	5	11	11	NUM
easat-10856	751	6	:	:	PUNCT
easat-10856	751	7	274	274	NUM
easat-10856	751	8	-	-	SYM
easat-10856	751	9	288	288	NUM
easat-10856	751	10	,	,	PUNCT
easat-10856	751	11	2025	2025	NUM
easat-10856	751	12	doi	doi	NOUN
easat-10856	751	13	:	:	PUNCT
easat-10856	751	14	10.55214/2576	10.55214/2576	NUM
easat-10856	751	15	-	-	PUNCT
easat-10856	751	16	8484.v9i11.10856	8484.v9i11.10856	NUM
easat-10856	751	17	©	©	PROPN
easat-10856	751	18	2025	2025	NUM
easat-10856	751	19	by	by	ADP
easat-10856	751	20	the	the	DET
easat-10856	751	21	authors	author	NOUN
easat-10856	751	22	;	;	PUNCT
easat-10856	751	23	licensee	licensee	PROPN
easat-10856	751	24	learning	learning	NOUN
easat-10856	751	25	gate	gate	NOUN
easat-10856	751	26	4	4	NUM
easat-10856	751	27	.	.	PUNCT
easat-10856	751	28	discussion	discussion	NOUN
easat-10856	751	29	bernoulli	bernoulli	NOUN
easat-10856	751	30	numbers	number	NOUN
easat-10856	751	31	decrease	decrease	VERB
easat-10856	751	32	until	until	ADP
easat-10856	751	33	the	the	DET
easat-10856	751	34	third	third	ADJ
easat-10856	751	35	position	position	NOUN
easat-10856	751	36	and	and	CCONJ
easat-10856	751	37	then	then	ADV
easat-10856	751	38	increase	increase	VERB
easat-10856	751	39	indefinitely	indefinitely	ADV
easat-10856	751	40	,	,	PUNCT
easat-10856	751	41	coinciding	coincide	VERB
easat-10856	751	42	with	with	ADP
easat-10856	751	43	what	what	PRON
easat-10856	751	44	fernández	fernández	PROPN
easat-10856	752	1	[	[	X
easat-10856	752	2	5	5	NUM
easat-10856	752	3	]	]	PUNCT
easat-10856	752	4	and	and	CCONJ
easat-10856	752	5	vera	vera	NOUN
easat-10856	753	1	[	[	X
easat-10856	753	2	6	6	NUM
easat-10856	753	3	]	]	PUNCT
easat-10856	753	4	;	;	PUNCT
easat-10856	753	5	report	report	NOUN
easat-10856	753	6	;	;	PUNCT
easat-10856	753	7	they	they	PRON
easat-10856	753	8	are	be	AUX
easat-10856	753	9	the	the	DET
easat-10856	753	10	smallest	small	ADJ
easat-10856	753	11	possible	possible	ADJ
easat-10856	753	12	ratio	ratio	NOUN
easat-10856	753	13	between	between	ADP
easat-10856	753	14	two	two	NUM
easat-10856	753	15	relatively	relatively	ADV
easat-10856	753	16	prime	prime	ADJ
easat-10856	753	17	numbers	number	NOUN
easat-10856	753	18	,	,	PUNCT
easat-10856	753	19	coinciding	coincide	VERB
easat-10856	753	20	with	with	ADP
easat-10856	753	21	what	what	PRON
easat-10856	753	22	benton	benton	PROPN
easat-10856	753	23	mentions	mention	VERB
easat-10856	753	24	,	,	PUNCT
easat-10856	753	25	[	[	X
easat-10856	753	26	1	1	NUM
easat-10856	753	27	]	]	PUNCT
easat-10856	753	28	and	and	CCONJ
easat-10856	753	29	that	that	SCONJ
easat-10856	753	30	bernoulli	bernoulli	NOUN
easat-10856	753	31	numbers	number	NOUN
easat-10856	753	32	have	have	VERB
easat-10856	753	33	numerous	numerous	ADJ
easat-10856	753	34	applications	application	NOUN
easat-10856	753	35	in	in	ADP
easat-10856	753	36	the	the	DET
easat-10856	753	37	field	field	NOUN
easat-10856	753	38	of	of	ADP
easat-10856	753	39	applied	applied	ADJ
easat-10856	753	40	mathematics	mathematic	NOUN
easat-10856	753	41	,	,	PUNCT
easat-10856	753	42	mathematical	mathematical	ADJ
easat-10856	753	43	analysis	analysis	NOUN
easat-10856	753	44	,	,	PUNCT
easat-10856	753	45	and	and	CCONJ
easat-10856	753	46	engineering	engineering	NOUN
easat-10856	753	47	,	,	PUNCT
easat-10856	753	48	such	such	ADJ
easat-10856	753	49	as	as	ADP
easat-10856	753	50	derivatives	derivative	NOUN
easat-10856	753	51	and	and	CCONJ
easat-10856	753	52	integrals	integral	NOUN
easat-10856	753	53	,	,	PUNCT
easat-10856	753	54	as	as	SCONJ
easat-10856	753	55	mentioned	mention	VERB
easat-10856	753	56	by	by	ADP
easat-10856	753	57	ruíz	ruíz	NOUN
easat-10856	753	58	[	[	X
easat-10856	753	59	10	10	NUM
easat-10856	753	60	]	]	PUNCT
easat-10856	753	61	.	.	PUNCT
easat-10856	754	1	when	when	SCONJ
easat-10856	754	2	calculating	calculate	VERB
easat-10856	754	3	bernoulli	bernoulli	NOUN
easat-10856	754	4	numbers	number	NOUN
easat-10856	754	5	,	,	PUNCT
easat-10856	754	6	these	these	PRON
easat-10856	754	7	can	can	AUX
easat-10856	754	8	be	be	AUX
easat-10856	754	9	applied	apply	VERB
easat-10856	754	10	in	in	ADP
easat-10856	754	11	a	a	DET
easat-10856	754	12	wide	wide	ADJ
easat-10856	754	13	range	range	NOUN
easat-10856	754	14	of	of	ADP
easat-10856	754	15	mathematical	mathematical	ADJ
easat-10856	754	16	applications	application	NOUN
easat-10856	754	17	,	,	PUNCT
easat-10856	754	18	initially	initially	ADV
easat-10856	754	19	to	to	ADP
easat-10856	754	20	the	the	DET
easat-10856	754	21	concepts	concept	NOUN
easat-10856	754	22	of	of	ADP
easat-10856	754	23	definite	definite	ADJ
easat-10856	754	24	and	and	CCONJ
easat-10856	754	25	indefinite	indefinite	ADJ
easat-10856	754	26	integrals	integral	NOUN
easat-10856	754	27	of	of	ADP
easat-10856	754	28	trigonometric	trigonometric	ADJ
easat-10856	754	29	,	,	PUNCT
easat-10856	754	30	inverse	inverse	NOUN
easat-10856	754	31	,	,	PUNCT
easat-10856	754	32	and	and	CCONJ
easat-10856	754	33	logarithmic	logarithmic	ADJ
easat-10856	754	34	functions	function	NOUN
easat-10856	754	35	,	,	PUNCT
easat-10856	754	36	and	and	CCONJ
easat-10856	754	37	consequently	consequently	ADV
easat-10856	754	38	in	in	ADP
easat-10856	754	39	the	the	DET
easat-10856	754	40	mathematical	mathematical	ADJ
easat-10856	754	41	modeling	modeling	NOUN
easat-10856	754	42	of	of	ADP
easat-10856	754	43	a	a	DET
easat-10856	754	44	wide	wide	ADJ
easat-10856	754	45	range	range	NOUN
easat-10856	754	46	of	of	ADP
easat-10856	754	47	real	real	ADJ
easat-10856	754	48	cases	case	NOUN
easat-10856	754	49	involving	involve	VERB
easat-10856	754	50	transcendental	transcendental	ADJ
easat-10856	754	51	function	function	NOUN
easat-10856	754	52	relationships	relationship	NOUN
easat-10856	754	53	;	;	PUNCT
easat-10856	754	54	coinciding	coincide	VERB
easat-10856	754	55	with	with	ADP
easat-10856	754	56	what	what	PRON
easat-10856	754	57	was	be	AUX
easat-10856	754	58	mentioned	mention	VERB
easat-10856	754	59	by	by	ADP
easat-10856	754	60	bronshtein	bronshtein	NOUN
easat-10856	754	61	and	and	CCONJ
easat-10856	754	62	semendiaev	semendiaev	VERB
easat-10856	755	1	[	[	X
easat-10856	755	2	7	7	NUM
easat-10856	755	3	]	]	PUNCT
easat-10856	755	4	.	.	PUNCT
easat-10856	756	1	the	the	DET
easat-10856	756	2	estimated	estimate	VERB
easat-10856	756	3	euler	euler	NOUN
easat-10856	756	4	numbers	number	NOUN
easat-10856	756	5	can	can	AUX
easat-10856	756	6	be	be	AUX
easat-10856	756	7	used	use	VERB
easat-10856	756	8	in	in	ADP
easat-10856	756	9	the	the	DET
easat-10856	756	10	integral	integral	ADJ
easat-10856	756	11	calculation	calculation	NOUN
easat-10856	756	12	of	of	ADP
easat-10856	756	13	functions	function	NOUN
easat-10856	756	14	and	and	CCONJ
easat-10856	756	15	expressions	expression	NOUN
easat-10856	756	16	more	more	ADV
easat-10856	756	17	complicated	complicated	ADJ
easat-10856	756	18	than	than	ADP
easat-10856	756	19	those	those	PRON
easat-10856	756	20	involving	involve	VERB
easat-10856	756	21	bernoulli	bernoulli	NOUN
easat-10856	756	22	numbers	number	NOUN
easat-10856	756	23	.	.	PUNCT
easat-10856	757	1	therefore	therefore	ADV
easat-10856	757	2	,	,	PUNCT
easat-10856	757	3	their	their	PRON
easat-10856	757	4	application	application	NOUN
easat-10856	757	5	and	and	CCONJ
easat-10856	757	6	solution	solution	NOUN
easat-10856	757	7	to	to	ADP
easat-10856	757	8	different	different	ADJ
easat-10856	757	9	cases	case	NOUN
easat-10856	757	10	are	be	AUX
easat-10856	757	11	more	more	ADV
easat-10856	757	12	rigorous	rigorous	ADJ
easat-10856	757	13	,	,	PUNCT
easat-10856	757	14	enabling	enable	VERB
easat-10856	757	15	the	the	DET
easat-10856	757	16	solving	solving	NOUN
easat-10856	757	17	of	of	ADP
easat-10856	757	18	problems	problem	NOUN
easat-10856	757	19	of	of	ADP
easat-10856	757	20	greater	great	ADJ
easat-10856	757	21	difficulty	difficulty	NOUN
easat-10856	757	22	and	and	CCONJ
easat-10856	757	23	providing	provide	VERB
easat-10856	757	24	results	result	NOUN
easat-10856	757	25	that	that	PRON
easat-10856	757	26	are	be	AUX
easat-10856	757	27	closer	close	ADJ
easat-10856	757	28	to	to	ADP
easat-10856	757	29	reality	reality	NOUN
easat-10856	757	30	;	;	PUNCT
easat-10856	757	31	coinciding	coincide	VERB
easat-10856	757	32	with	with	ADP
easat-10856	757	33	what	what	PRON
easat-10856	757	34	was	be	AUX
easat-10856	757	35	mentioned	mention	VERB
easat-10856	757	36	by	by	ADP
easat-10856	757	37	murray	murray	NOUN
easat-10856	758	1	[	[	X
easat-10856	758	2	22	22	NUM
easat-10856	758	3	]	]	PUNCT
easat-10856	758	4	.	.	PUNCT
easat-10856	759	1	euler	euler	PROPN
easat-10856	759	2	numbers	number	NOUN
easat-10856	759	3	are	be	AUX
easat-10856	759	4	all	all	ADV
easat-10856	759	5	positive	positive	ADJ
easat-10856	759	6	,	,	PUNCT
easat-10856	759	7	agreeing	agree	VERB
easat-10856	759	8	with	with	ADP
easat-10856	759	9	what	what	PRON
easat-10856	759	10	varadarajan	varadarajan	NOUN
easat-10856	759	11	[	[	X
easat-10856	759	12	20	20	NUM
easat-10856	759	13	]	]	PUNCT
easat-10856	759	14	and	and	CCONJ
easat-10856	759	15	simmons	simmon	NOUN
easat-10856	759	16	[	[	X
easat-10856	759	17	23	23	NUM
easat-10856	759	18	]	]	PUNCT
easat-10856	759	19	mention	mention	NOUN
easat-10856	759	20	,	,	PUNCT
easat-10856	759	21	at	at	ADP
easat-10856	759	22	least	least	ADJ
easat-10856	759	23	from	from	ADP
easat-10856	759	24	position	position	NOUN
easat-10856	759	25	one	one	NUM
easat-10856	759	26	to	to	PART
easat-10856	759	27	position	position	VERB
easat-10856	759	28	twenty	twenty	NUM
easat-10856	759	29	.	.	PUNCT
easat-10856	760	1	like	like	ADP
easat-10856	760	2	bernoulli	bernoulli	NOUN
easat-10856	760	3	numbers	number	NOUN
easat-10856	760	4	,	,	PUNCT
easat-10856	760	5	euler	euler	NOUN
easat-10856	760	6	numbers	number	NOUN
easat-10856	760	7	also	also	ADV
easat-10856	760	8	participate	participate	VERB
easat-10856	760	9	in	in	ADP
easat-10856	760	10	a	a	DET
easat-10856	760	11	large	large	ADJ
easat-10856	760	12	number	number	NOUN
easat-10856	760	13	of	of	ADP
easat-10856	760	14	mathematical	mathematical	ADJ
easat-10856	760	15	relationships	relationship	NOUN
easat-10856	760	16	and	and	CCONJ
easat-10856	760	17	physical	physical	ADJ
easat-10856	760	18	phenomena	phenomenon	NOUN
easat-10856	760	19	applied	apply	VERB
easat-10856	760	20	to	to	ADP
easat-10856	760	21	technological	technological	ADJ
easat-10856	760	22	,	,	PUNCT
easat-10856	760	23	scientific	scientific	ADJ
easat-10856	760	24	,	,	PUNCT
easat-10856	760	25	and	and	CCONJ
easat-10856	760	26	engineering	engineering	NOUN
easat-10856	760	27	processes	process	NOUN
easat-10856	760	28	,	,	PUNCT
easat-10856	760	29	such	such	ADJ
easat-10856	760	30	as	as	ADP
easat-10856	760	31	those	those	PRON
easat-10856	760	32	mentioned	mention	VERB
easat-10856	760	33	by	by	ADP
easat-10856	760	34	abramowitz	abramowitz	NOUN
easat-10856	760	35	and	and	CCONJ
easat-10856	760	36	stegun	stegun	PRON
easat-10856	760	37	[	[	X
easat-10856	760	38	4	4	NUM
easat-10856	760	39	]	]	PUNCT
easat-10856	760	40	.	.	PUNCT
easat-10856	761	1	it	it	PRON
easat-10856	761	2	is	be	AUX
easat-10856	761	3	concluded	conclude	VERB
easat-10856	761	4	that	that	SCONJ
easat-10856	761	5	all	all	DET
easat-10856	761	6	the	the	DET
easat-10856	761	7	euler	euler	NOUN
easat-10856	761	8	numbers	number	NOUN
easat-10856	761	9	calculated	calculate	VERB
easat-10856	761	10	are	be	AUX
easat-10856	761	11	integers	integer	NOUN
easat-10856	761	12	and	and	CCONJ
easat-10856	761	13	positive	positive	ADJ
easat-10856	761	14	,	,	PUNCT
easat-10856	761	15	that	that	SCONJ
easat-10856	761	16	the	the	DET
easat-10856	761	17	sum	sum	NOUN
easat-10856	761	18	of	of	ADP
easat-10856	761	19	two	two	NUM
easat-10856	761	20	consecutive	consecutive	ADJ
easat-10856	761	21	euler	euler	NOUN
easat-10856	761	22	numbers	number	NOUN
easat-10856	761	23	is	be	AUX
easat-10856	761	24	divisible	divisible	ADJ
easat-10856	761	25	by	by	ADP
easat-10856	761	26	3	3	NUM
easat-10856	761	27	(	(	PUNCT
easat-10856	761	28	three	three	NUM
easat-10856	761	29	)	)	PUNCT
easat-10856	761	30	,	,	PUNCT
easat-10856	761	31	that	that	DET
easat-10856	761	32	euler	euler	NOUN
easat-10856	761	33	numbers	number	NOUN
easat-10856	761	34	alternately	alternately	ADV
easat-10856	761	35	end	end	VERB
easat-10856	761	36	in	in	ADP
easat-10856	761	37	1	1	NUM
easat-10856	761	38	or	or	CCONJ
easat-10856	761	39	5	5	NUM
easat-10856	761	40	,	,	PUNCT
easat-10856	761	41	that	that	SCONJ
easat-10856	761	42	bernoulli	bernoulli	NOUN
easat-10856	761	43	numbers	number	NOUN
easat-10856	761	44	are	be	AUX
easat-10856	761	45	all	all	ADV
easat-10856	761	46	positive	positive	ADJ
easat-10856	761	47	,	,	PUNCT
easat-10856	761	48	that	that	SCONJ
easat-10856	761	49	bernoulli	bernoulli	NOUN
easat-10856	761	50	numbers	number	NOUN
easat-10856	761	51	,	,	PUNCT
easat-10856	761	52	from	from	ADP
easat-10856	761	53	the	the	DET
easat-10856	761	54	fourth	fourth	ADJ
easat-10856	761	55	position	position	NOUN
easat-10856	761	56	onward	onward	ADV
easat-10856	761	57	,	,	PUNCT
easat-10856	761	58	grow	grow	VERB
easat-10856	761	59	indefinitely	indefinitely	ADV
easat-10856	761	60	,	,	PUNCT
easat-10856	761	61	that	that	SCONJ
easat-10856	761	62	bernoulli	bernoulli	NOUN
easat-10856	761	63	numbers	number	NOUN
easat-10856	761	64	are	be	AUX
easat-10856	761	65	the	the	DET
easat-10856	761	66	smallest	small	ADJ
easat-10856	761	67	ratio	ratio	NOUN
easat-10856	761	68	between	between	ADP
easat-10856	761	69	two	two	NUM
easat-10856	761	70	relatively	relatively	ADV
easat-10856	761	71	prime	prime	ADJ
easat-10856	761	72	numbers	number	NOUN
easat-10856	761	73	,	,	PUNCT
easat-10856	761	74	and	and	CCONJ
easat-10856	761	75	there	there	PRON
easat-10856	761	76	are	be	VERB
easat-10856	761	77	other	other	ADJ
easat-10856	761	78	more	more	ADV
easat-10856	761	79	important	important	ADJ
easat-10856	761	80	direct	direct	ADJ
easat-10856	761	81	applications	application	NOUN
easat-10856	761	82	to	to	ADP
easat-10856	761	83	the	the	DET
easat-10856	761	84	mathematics	mathematic	NOUN
easat-10856	761	85	of	of	ADP
easat-10856	761	86	bernoulli	bernoulli	PROPN
easat-10856	761	87	and	and	CCONJ
easat-10856	761	88	euler	euler	NOUN
easat-10856	761	89	numbers	number	NOUN
easat-10856	761	90	that	that	PRON
easat-10856	761	91	appear	appear	VERB
easat-10856	761	92	in	in	ADP
easat-10856	761	93	a	a	DET
easat-10856	761	94	wide	wide	ADJ
easat-10856	761	95	variety	variety	NOUN
easat-10856	761	96	of	of	ADP
easat-10856	761	97	processes	process	NOUN
easat-10856	761	98	and	and	CCONJ
easat-10856	761	99	that	that	PRON
easat-10856	761	100	are	be	AUX
easat-10856	761	101	truly	truly	ADV
easat-10856	761	102	the	the	DET
easat-10856	761	103	essence	essence	NOUN
easat-10856	761	104	of	of	ADP
easat-10856	761	105	engineering	engineering	NOUN
easat-10856	761	106	,	,	PUNCT
easat-10856	761	107	applied	apply	VERB
easat-10856	761	108	mathematics	mathematic	NOUN
easat-10856	761	109	,	,	PUNCT
easat-10856	761	110	experimental	experimental	ADJ
easat-10856	761	111	models	model	NOUN
easat-10856	761	112	,	,	PUNCT
easat-10856	761	113	and	and	CCONJ
easat-10856	761	114	their	their	PRON
easat-10856	761	115	various	various	ADJ
easat-10856	761	116	behaviors	behavior	NOUN
easat-10856	761	117	.	.	PUNCT
easat-10856	762	1	likewise	likewise	ADV
easat-10856	762	2	,	,	PUNCT
easat-10856	762	3	it	it	PRON
easat-10856	762	4	is	be	AUX
easat-10856	762	5	recommended	recommend	VERB
easat-10856	762	6	,	,	PUNCT
easat-10856	762	7	where	where	SCONJ
easat-10856	762	8	possible	possible	ADJ
easat-10856	762	9	,	,	PUNCT
easat-10856	762	10	to	to	PART
easat-10856	762	11	design	design	VERB
easat-10856	762	12	software	software	NOUN
easat-10856	762	13	and/or	and/or	CCONJ
easat-10856	762	14	special	special	ADJ
easat-10856	762	15	computer	computer	NOUN
easat-10856	762	16	programs	program	NOUN
easat-10856	762	17	to	to	PART
easat-10856	762	18	obtain	obtain	VERB
easat-10856	762	19	bernoulli	bernoulli	NOUN
easat-10856	762	20	and	and	CCONJ
easat-10856	762	21	euler	euler	VERB
easat-10856	762	22	numbers	number	NOUN
easat-10856	762	23	from	from	ADP
easat-10856	762	24	twenty	twenty	NUM
easat-10856	762	25	onward	onward	NOUN
easat-10856	762	26	,	,	PUNCT
easat-10856	762	27	in	in	ADP
easat-10856	762	28	the	the	DET
easat-10856	762	29	manner	manner	NOUN
easat-10856	762	30	indicated	indicate	VERB
easat-10856	762	31	by	by	ADP
easat-10856	762	32	the	the	DET
easat-10856	762	33	authors	author	NOUN
easat-10856	762	34	.	.	PUNCT
easat-10856	763	1	transparency	transparency	NOUN
easat-10856	763	2	:	:	PUNCT
easat-10856	763	3	the	the	DET
easat-10856	763	4	authors	author	NOUN
easat-10856	763	5	confirm	confirm	VERB
easat-10856	763	6	that	that	SCONJ
easat-10856	763	7	the	the	DET
easat-10856	763	8	manuscript	manuscript	NOUN
easat-10856	763	9	is	be	AUX
easat-10856	763	10	an	an	DET
easat-10856	763	11	honest	honest	ADJ
easat-10856	763	12	,	,	PUNCT
easat-10856	763	13	accurate	accurate	ADJ
easat-10856	763	14	,	,	PUNCT
easat-10856	763	15	and	and	CCONJ
easat-10856	763	16	transparent	transparent	ADJ
easat-10856	763	17	account	account	NOUN
easat-10856	763	18	of	of	ADP
easat-10856	763	19	the	the	DET
easat-10856	763	20	study	study	NOUN
easat-10856	763	21	;	;	PUNCT
easat-10856	763	22	that	that	SCONJ
easat-10856	763	23	no	no	DET
easat-10856	763	24	vital	vital	ADJ
easat-10856	763	25	features	feature	NOUN
easat-10856	763	26	of	of	ADP
easat-10856	763	27	the	the	DET
easat-10856	763	28	study	study	NOUN
easat-10856	763	29	have	have	AUX
easat-10856	763	30	been	be	AUX
easat-10856	763	31	omitted	omit	VERB
easat-10856	763	32	;	;	PUNCT
easat-10856	763	33	and	and	CCONJ
easat-10856	763	34	that	that	SCONJ
easat-10856	763	35	any	any	DET
easat-10856	763	36	discrepancies	discrepancy	NOUN
easat-10856	763	37	from	from	ADP
easat-10856	763	38	the	the	DET
easat-10856	763	39	study	study	NOUN
easat-10856	763	40	as	as	SCONJ
easat-10856	763	41	planned	plan	VERB
easat-10856	763	42	have	have	AUX
easat-10856	763	43	been	be	AUX
easat-10856	763	44	explained	explain	VERB
easat-10856	763	45	.	.	PUNCT
easat-10856	764	1	this	this	DET
easat-10856	764	2	study	study	NOUN
easat-10856	764	3	followed	follow	VERB
easat-10856	764	4	all	all	DET
easat-10856	764	5	ethical	ethical	ADJ
easat-10856	764	6	practices	practice	NOUN
easat-10856	764	7	during	during	ADP
easat-10856	764	8	writing	writing	NOUN
easat-10856	764	9	.	.	PUNCT
easat-10856	765	1	copyright	copyright	NOUN
easat-10856	765	2	:	:	PUNCT
easat-10856	765	3	©	©	PROPN
easat-10856	765	4	2025	2025	NUM
easat-10856	765	5	by	by	ADP
easat-10856	765	6	the	the	DET
easat-10856	765	7	authors	author	NOUN
easat-10856	765	8	.	.	PUNCT
easat-10856	766	1	this	this	DET
easat-10856	766	2	article	article	NOUN
easat-10856	766	3	is	be	AUX
easat-10856	766	4	an	an	DET
easat-10856	766	5	open	open	ADJ
easat-10856	766	6	-	-	PUNCT
easat-10856	766	7	access	access	NOUN
easat-10856	766	8	article	article	NOUN
easat-10856	766	9	distributed	distribute	VERB
easat-10856	766	10	under	under	ADP
easat-10856	766	11	the	the	DET
easat-10856	766	12	terms	term	NOUN
easat-10856	766	13	and	and	CCONJ
easat-10856	766	14	conditions	condition	NOUN
easat-10856	766	15	of	of	ADP
easat-10856	766	16	the	the	DET
easat-10856	766	17	creative	creative	ADJ
easat-10856	766	18	commons	common	NOUN
easat-10856	766	19	attribution	attribution	NOUN
easat-10856	766	20	(	(	PUNCT
easat-10856	766	21	cc	cc	NOUN
easat-10856	766	22	by	by	ADP
easat-10856	766	23	)	)	PUNCT
easat-10856	766	24	license	license	NOUN
easat-10856	766	25	(	(	PUNCT
easat-10856	766	26	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
easat-10856	766	27	)	)	PUNCT
easat-10856	766	28	.	.	PUNCT
easat-10856	767	1	references	reference	NOUN
easat-10856	767	2	[	[	X
easat-10856	767	3	1	1	NUM
easat-10856	767	4	]	]	PUNCT
easat-10856	767	5	w.	w.	PROPN
easat-10856	767	6	benton	benton	PROPN
easat-10856	767	7	,	,	PUNCT
easat-10856	767	8	encyclopedia	encyclopedia	PROPN
easat-10856	767	9	britannica	britannica	PROPN
easat-10856	767	10	.	.	PUNCT
easat-10856	768	1	usa	usa	PROPN
easat-10856	768	2	:	:	PUNCT
easat-10856	768	3	tomo	tomo	PROPN
easat-10856	768	4	-	-	PUNCT
easat-10856	768	5	iii	iii	PROPN
easat-10856	768	6	.	.	PROPN
easat-10856	768	7	inc	inc	PROPN
easat-10856	768	8	.	.	PROPN
easat-10856	768	9	printed	print	VERB
easat-10856	768	10	,	,	PUNCT
easat-10856	768	11	1964	1964	NUM
easat-10856	768	12	.	.	PUNCT
easat-10856	769	1	[	[	X
easat-10856	769	2	2	2	NUM
easat-10856	769	3	]	]	PUNCT
easat-10856	769	4	c.	c.	PROPN
easat-10856	769	5	b.	b.	PROPN
easat-10856	769	6	boyer	boyer	PROPN
easat-10856	769	7	,	,	PUNCT
easat-10856	769	8	history	history	NOUN
easat-10856	769	9	of	of	ADP
easat-10856	769	10	mathematics	mathematic	NOUN
easat-10856	769	11	(	(	PUNCT
easat-10856	769	12	m.	m.	NOUN
easat-10856	769	13	martínez	martínez	PROPN
easat-10856	769	14	pérez	pérez	NOUN
easat-10856	769	15	,	,	PUNCT
easat-10856	769	16	trans	trans	PROPN
easat-10856	769	17	.	.	PUNCT
easat-10856	769	18	)	)	PUNCT
easat-10856	769	19	.	.	PUNCT
easat-10856	770	1	madrid	madrid	PROPN
easat-10856	770	2	,	,	PUNCT
easat-10856	770	3	spain	spain	PROPN
easat-10856	770	4	:	:	PUNCT
easat-10856	770	5	alianza	alianza	PROPN
easat-10856	770	6	editorial	editorial	NOUN
easat-10856	770	7	,	,	PUNCT
easat-10856	770	8	1987	1987	NUM
easat-10856	770	9	.	.	PUNCT
easat-10856	771	1	[	[	X
easat-10856	771	2	3	3	X
easat-10856	771	3	]	]	X
easat-10856	771	4	r.	r.	X
easat-10856	771	5	courant	courant	PROPN
easat-10856	771	6	and	and	CCONJ
easat-10856	771	7	f.	f.	PROPN
easat-10856	771	8	john	john	PROPN
easat-10856	771	9	,	,	PUNCT
easat-10856	771	10	introduction	introduction	NOUN
easat-10856	771	11	to	to	ADP
easat-10856	771	12	calculus	calculus	NOUN
easat-10856	771	13	and	and	CCONJ
easat-10856	771	14	mathematical	mathematical	ADJ
easat-10856	771	15	analysis	analysis	NOUN
easat-10856	771	16	:	:	PUNCT
easat-10856	771	17	volume	volume	NOUN
easat-10856	771	18	1	1	NUM
easat-10856	771	19	(	(	PUNCT
easat-10856	771	20	chapter	chapter	NOUN
easat-10856	771	21	8	8	NUM
easat-10856	771	22	,	,	PUNCT
easat-10856	771	23	trigonometric	trigonometric	ADJ
easat-10856	771	24	series	series	NOUN
easat-10856	771	25	)	)	PUNCT
easat-10856	771	26	.	.	PUNCT
easat-10856	772	1	méxico	méxico	PROPN
easat-10856	772	2	,	,	PUNCT
easat-10856	772	3	d.f	d.f	PROPN
easat-10856	772	4	:	:	PUNCT
easat-10856	772	5	editorial	editorial	NOUN
easat-10856	772	6	limusa	limusa	NOUN
easat-10856	772	7	,	,	PUNCT
easat-10856	772	8	2015	2015	NUM
easat-10856	772	9	.	.	PUNCT
easat-10856	773	1	[	[	X
easat-10856	773	2	4	4	X
easat-10856	773	3	]	]	PUNCT
easat-10856	773	4	m.	m.	NOUN
easat-10856	773	5	abramowitz	abramowitz	PROPN
easat-10856	773	6	and	and	CCONJ
easat-10856	773	7	i.	i.	PROPN
easat-10856	773	8	a.	a.	PROPN
easat-10856	773	9	stegun	stegun	PROPN
easat-10856	773	10	,	,	PUNCT
easat-10856	773	11	handbook	handbook	NOUN
easat-10856	773	12	of	of	ADP
easat-10856	773	13	mathematical	mathematical	ADJ
easat-10856	773	14	functions	function	NOUN
easat-10856	773	15	with	with	ADP
easat-10856	773	16	formulas	formula	NOUN
easat-10856	773	17	,	,	PUNCT
easat-10856	773	18	graphs	graph	NOUN
easat-10856	773	19	,	,	PUNCT
easat-10856	773	20	and	and	CCONJ
easat-10856	773	21	mathematical	mathematical	ADJ
easat-10856	773	22	tables	table	NOUN
easat-10856	773	23	.	.	PUNCT
easat-10856	774	1	new	new	PROPN
easat-10856	774	2	york	york	PROPN
easat-10856	774	3	:	:	PUNCT
easat-10856	774	4	dover	dover	PROPN
easat-10856	774	5	publications	publications	PROPN
easat-10856	774	6	,	,	PUNCT
easat-10856	774	7	inc	inc	PROPN
easat-10856	774	8	,	,	PUNCT
easat-10856	774	9	1965	1965	NUM
easat-10856	774	10	.	.	PUNCT
easat-10856	775	1	[	[	X
easat-10856	775	2	5	5	X
easat-10856	775	3	]	]	PUNCT
easat-10856	775	4	b.	b.	PROPN
easat-10856	775	5	d.	d.	PROPN
easat-10856	775	6	j.	j.	PROPN
easat-10856	775	7	fernández	fernández	PROPN
easat-10856	775	8	,	,	PUNCT
easat-10856	775	9	"	"	PUNCT
easat-10856	775	10	bernoulli	bernoulli	NOUN
easat-10856	775	11	numbers	number	NOUN
easat-10856	775	12	:	:	PUNCT
easat-10856	775	13	a	a	DET
easat-10856	775	14	study	study	NOUN
easat-10856	775	15	on	on	ADP
easat-10856	775	16	their	their	PRON
easat-10856	775	17	importance	importance	NOUN
easat-10856	775	18	,	,	PUNCT
easat-10856	775	19	consequences	consequence	NOUN
easat-10856	775	20	,	,	PUNCT
easat-10856	775	21	and	and	CCONJ
easat-10856	775	22	some	some	DET
easat-10856	775	23	applications	application	NOUN
easat-10856	775	24	in	in	ADP
easat-10856	775	25	number	number	NOUN
easat-10856	775	26	theory	theory	NOUN
easat-10856	775	27	,	,	PUNCT
easat-10856	775	28	"	"	PUNCT
easat-10856	775	29	thesis	thesis	NOUN
easat-10856	775	30	to	to	PART
easat-10856	775	31	obtain	obtain	VERB
easat-10856	775	32	the	the	DET
easat-10856	775	33	degree	degree	NOUN
easat-10856	775	34	of	of	ADP
easat-10856	775	35	bachelor	bachelor	NOUN
easat-10856	775	36	of	of	ADP
easat-10856	775	37	science	science	NOUN
easat-10856	775	38	in	in	ADP
easat-10856	775	39	physics	physics	NOUN
easat-10856	775	40	and	and	CCONJ
easat-10856	775	41	mathematics	mathematic	NOUN
easat-10856	775	42	with	with	ADP
easat-10856	775	43	a	a	DET
easat-10856	775	44	specialization	specialization	NOUN
easat-10856	775	45	in	in	ADP
easat-10856	775	46	mathematics	mathematic	NOUN
easat-10856	775	47	.	.	PUNCT
easat-10856	776	1	national	national	PROPN
easat-10856	776	2	polytechnic	polytechnic	PROPN
easat-10856	776	3	institute	institute	PROPN
easat-10856	776	4	,	,	PUNCT
easat-10856	776	5	higher	high	ADJ
easat-10856	776	6	school	school	NOUN
easat-10856	776	7	of	of	ADP
easat-10856	776	8	physics	physics	NOUN
easat-10856	776	9	and	and	CCONJ
easat-10856	776	10	mathematics	mathematic	NOUN
easat-10856	776	11	]	]	PUNCT
easat-10856	776	12	.	.	PUNCT
easat-10856	777	1	mexico	mexico	PROPN
easat-10856	777	2	city	city	PROPN
easat-10856	777	3	,	,	PUNCT
easat-10856	777	4	2012	2012	NUM
easat-10856	777	5	.	.	PUNCT
easat-10856	778	1	[	[	X
easat-10856	778	2	6	6	NUM
easat-10856	778	3	]	]	PUNCT
easat-10856	778	4	f.	f.	PROPN
easat-10856	778	5	vera	vera	PROPN
easat-10856	778	6	,	,	PUNCT
easat-10856	778	7	mathematics	mathematic	NOUN
easat-10856	778	8	and	and	CCONJ
easat-10856	778	9	numbers	number	NOUN
easat-10856	778	10	.	.	PUNCT
easat-10856	779	1	buenos	buenos	PROPN
easat-10856	779	2	aires	aires	PROPN
easat-10856	779	3	,	,	PUNCT
easat-10856	779	4	argentina	argentina	PROPN
easat-10856	779	5	:	:	PUNCT
easat-10856	779	6	kapelusz	kapelusz	PROPN
easat-10856	779	7	,	,	PUNCT
easat-10856	779	8	1960	1960	NUM
easat-10856	779	9	.	.	PUNCT
easat-10856	780	1	[	[	X
easat-10856	780	2	7	7	X
easat-10856	780	3	]	]	X
easat-10856	780	4	i.	i.	PROPN
easat-10856	780	5	bronshtein	bronshtein	PROPN
easat-10856	780	6	and	and	CCONJ
easat-10856	780	7	r.	r.	PROPN
easat-10856	780	8	semendiaev	semendiaev	PROPN
easat-10856	780	9	,	,	PUNCT
easat-10856	780	10	mathematics	mathematic	NOUN
easat-10856	780	11	handbook	handbook	NOUN
easat-10856	780	12	for	for	ADP
easat-10856	780	13	engineers	engineer	NOUN
easat-10856	780	14	and	and	CCONJ
easat-10856	780	15	students	student	NOUN
easat-10856	780	16	.	.	PUNCT
easat-10856	781	1	moscú	moscú	ADJ
easat-10856	781	2	,	,	PUNCT
easat-10856	781	3	rusia	rusia	PROPN
easat-10856	781	4	:	:	PUNCT
easat-10856	781	5	mir	mir	PROPN
easat-10856	781	6	,	,	PUNCT
easat-10856	781	7	2018	2018	NUM
easat-10856	781	8	.	.	PUNCT
easat-10856	782	1	[	[	X
easat-10856	782	2	8	8	NUM
easat-10856	782	3	]	]	X
easat-10856	782	4	o.	o.	PROPN
easat-10856	782	5	marín	marín	PROPN
easat-10856	782	6	,	,	PUNCT
easat-10856	782	7	history	history	NOUN
easat-10856	782	8	of	of	ADP
easat-10856	782	9	mathematics	mathematic	NOUN
easat-10856	782	10	and	and	CCONJ
easat-10856	782	11	its	its	PRON
easat-10856	782	12	great	great	ADJ
easat-10856	782	13	exponents	exponent	NOUN
easat-10856	782	14	.	.	PUNCT
easat-10856	783	1	lima	lima	PROPN
easat-10856	783	2	,	,	PUNCT
easat-10856	783	3	perú	perú	PROPN
easat-10856	783	4	:	:	PUNCT
easat-10856	783	5	vpa	vpa	PROPN
easat-10856	783	6	-	-	PUNCT
easat-10856	783	7	utp	utp	PROPN
easat-10856	783	8	,	,	PUNCT
easat-10856	783	9	2003	2003	NUM
easat-10856	783	10	.	.	PUNCT
easat-10856	784	1	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
easat-10856	784	2	288	288	NUM
easat-10856	784	3	edelweiss	edelweiss	PROPN
easat-10856	784	4	applied	apply	VERB
easat-10856	784	5	science	science	NOUN
easat-10856	784	6	and	and	CCONJ
easat-10856	784	7	technology	technology	NOUN
easat-10856	784	8	issn	issn	PROPN
easat-10856	784	9	:	:	PUNCT
easat-10856	784	10	2576	2576	NUM
easat-10856	784	11	-	-	SYM
easat-10856	784	12	8484	8484	NUM
easat-10856	784	13	vol	vol	NOUN
easat-10856	784	14	.	.	PROPN
easat-10856	785	1	9	9	NUM
easat-10856	785	2	,	,	PUNCT
easat-10856	785	3	no	no	INTJ
easat-10856	785	4	.	.	NOUN
easat-10856	785	5	11	11	NUM
easat-10856	785	6	:	:	PUNCT
easat-10856	785	7	274	274	NUM
easat-10856	785	8	-	-	SYM
easat-10856	785	9	288	288	NUM
easat-10856	785	10	,	,	PUNCT
easat-10856	785	11	2025	2025	NUM
easat-10856	785	12	doi	doi	NOUN
easat-10856	785	13	:	:	PUNCT
easat-10856	785	14	10.55214/2576	10.55214/2576	NUM
easat-10856	785	15	-	-	PUNCT
easat-10856	785	16	8484.v9i11.10856	8484.v9i11.10856	NUM
easat-10856	785	17	©	©	PROPN
easat-10856	785	18	2025	2025	NUM
easat-10856	785	19	by	by	ADP
easat-10856	785	20	the	the	DET
easat-10856	785	21	authors	author	NOUN
easat-10856	785	22	;	;	PUNCT
easat-10856	785	23	licensee	licensee	PROPN
easat-10856	785	24	learning	learning	NOUN
easat-10856	785	25	gate	gate	NOUN
easat-10856	786	1	[	[	X
easat-10856	786	2	9	9	NUM
easat-10856	786	3	]	]	PUNCT
easat-10856	786	4	j.	j.	PROPN
easat-10856	786	5	m.	m.	PROPN
easat-10856	786	6	child	child	PROPN
easat-10856	786	7	,	,	PUNCT
easat-10856	786	8	the	the	DET
easat-10856	786	9	early	early	ADJ
easat-10856	786	10	mathematical	mathematical	ADJ
easat-10856	786	11	manuscripts	manuscript	NOUN
easat-10856	786	12	of	of	ADP
easat-10856	786	13	leibniz	leibniz	PROPN
easat-10856	786	14	.	.	PUNCT
easat-10856	787	1	chicago	chicago	PROPN
easat-10856	787	2	.	.	PUNCT
easat-10856	788	1	londres	londre	NOUN
easat-10856	788	2	:	:	PUNCT
easat-10856	788	3	the	the	DET
easat-10856	788	4	open	open	ADJ
easat-10856	788	5	court	court	NOUN
easat-10856	788	6	publishing	publishing	NOUN
easat-10856	788	7	company	company	NOUN
easat-10856	788	8	,	,	PUNCT
easat-10856	788	9	2017	2017	NUM
easat-10856	788	10	.	.	PUNCT
easat-10856	789	1	[	[	X
easat-10856	789	2	10	10	NUM
easat-10856	789	3	]	]	PUNCT
easat-10856	789	4	a.	a.	NOUN
easat-10856	789	5	ruíz	ruíz	PROPN
easat-10856	789	6	,	,	PUNCT
easat-10856	789	7	number	number	NOUN
easat-10856	789	8	theory	theory	NOUN
easat-10856	789	9	.	.	PUNCT
easat-10856	790	1	lima	lima	PROPN
easat-10856	790	2	,	,	PUNCT
easat-10856	790	3	perú	perú	PROPN
easat-10856	790	4	:	:	PUNCT
easat-10856	790	5	san	san	PROPN
easat-10856	790	6	marcos	marcos	PROPN
easat-10856	790	7	,	,	PUNCT
easat-10856	790	8	2016	2016	NUM
easat-10856	790	9	.	.	PUNCT
easat-10856	791	1	[	[	X
easat-10856	791	2	11	11	NUM
easat-10856	791	3	]	]	X
easat-10856	791	4	o.	o.	PROPN
easat-10856	791	5	martínez	martínez	PROPN
easat-10856	791	6	,	,	PUNCT
easat-10856	791	7	m.	m.	NOUN
easat-10856	791	8	cand	cand	PROPN
easat-10856	791	9	,	,	PUNCT
easat-10856	791	10	f.	f.	PROPN
easat-10856	791	11	domínguez	domínguez	PROPN
easat-10856	791	12	,	,	PUNCT
easat-10856	791	13	and	and	CCONJ
easat-10856	791	14	g.	g.	PROPN
easat-10856	791	15	m.	m.	NOUN
easat-10856	791	16	forner	forner	PROPN
easat-10856	791	17	gambau	gambau	PROPN
easat-10856	791	18	,	,	PUNCT
easat-10856	791	19	historical	historical	ADJ
easat-10856	791	20	background	background	NOUN
easat-10856	791	21	of	of	ADP
easat-10856	791	22	the	the	DET
easat-10856	791	23	construction	construction	NOUN
easat-10856	791	24	of	of	ADP
easat-10856	791	25	logarithms	logarithm	NOUN
easat-10856	791	26	.	.	PUNCT
easat-10856	792	1	in	in	ADP
easat-10856	792	2	the	the	DET
easat-10856	792	3	construction	construction	NOUN
easat-10856	792	4	of	of	ADP
easat-10856	792	5	logarithms	logarithm	NOUN
easat-10856	792	6	:	:	PUNCT
easat-10856	792	7	history	history	NOUN
easat-10856	792	8	and	and	CCONJ
easat-10856	792	9	didactic	didactic	ADJ
easat-10856	792	10	project	project	NOUN
easat-10856	792	11	.	.	PUNCT
easat-10856	793	1	méxico	méxico	PROPN
easat-10856	793	2	:	:	PUNCT
easat-10856	793	3	publicaciones	publicaciones	PROPN
easat-10856	793	4	de	de	X
easat-10856	793	5	la	la	X
easat-10856	793	6	universidad	universidad	PROPN
easat-10856	793	7	de	de	X
easat-10856	793	8	león	león	PROPN
easat-10856	793	9	,	,	PUNCT
easat-10856	793	10	2014	2014	NUM
easat-10856	793	11	.	.	PUNCT
easat-10856	794	1	[	[	X
easat-10856	794	2	12	12	NUM
easat-10856	794	3	]	]	X
easat-10856	794	4	f.	f.	PROPN
easat-10856	794	5	vega	vega	PROPN
easat-10856	794	6	-	-	PUNCT
easat-10856	794	7	calderón	calderón	PROPN
easat-10856	794	8	,	,	PUNCT
easat-10856	794	9	l.	l.	PROPN
easat-10856	794	10	gallegos	gallegos	PROPN
easat-10856	794	11	-	-	PUNCT
easat-10856	794	12	cázares	cázare	NOUN
easat-10856	794	13	,	,	PUNCT
easat-10856	794	14	and	and	CCONJ
easat-10856	794	15	f.	f.	PROPN
easat-10856	794	16	flores	flores	PROPN
easat-10856	794	17	-	-	PUNCT
easat-10856	794	18	camacho	camacho	PROPN
easat-10856	794	19	,	,	PUNCT
easat-10856	794	20	"	"	PUNCT
easat-10856	794	21	conceptual	conceptual	ADJ
easat-10856	794	22	difficulties	difficulty	NOUN
easat-10856	794	23	in	in	ADP
easat-10856	794	24	understanding	understand	VERB
easat-10856	794	25	bernoulli	bernoulli	PROPN
easat-10856	794	26	's	's	PART
easat-10856	794	27	equation	equation	NOUN
easat-10856	794	28	,	,	PUNCT
easat-10856	794	29	"	"	PUNCT
easat-10856	794	30	revista	revista	PROPN
easat-10856	794	31	eureka	eureka	PROPN
easat-10856	794	32	sobre	sobre	PROPN
easat-10856	794	33	enseñanza	enseñanza	PROPN
easat-10856	794	34	y	y	PROPN
easat-10856	794	35	divulgación	divulgación	PROPN
easat-10856	794	36	de	de	PROPN
easat-10856	794	37	las	las	PROPN
easat-10856	794	38	ciencias	ciencias	PROPN
easat-10856	794	39	,	,	PUNCT
easat-10856	794	40	vol	vol	NOUN
easat-10856	794	41	.	.	PROPN
easat-10856	795	1	14	14	NUM
easat-10856	795	2	,	,	PUNCT
easat-10856	795	3	no	no	INTJ
easat-10856	795	4	.	.	NOUN
easat-10856	795	5	2	2	NUM
easat-10856	795	6	,	,	PUNCT
easat-10856	795	7	pp	pp	ADJ
easat-10856	795	8	.	.	PUNCT
easat-10856	796	1	339	339	NUM
easat-10856	796	2	-	-	SYM
easat-10856	796	3	352	352	NUM
easat-10856	796	4	,	,	PUNCT
easat-10856	796	5	2017	2017	NUM
easat-10856	796	6	.	.	PUNCT
easat-10856	797	1	[	[	X
easat-10856	797	2	13	13	NUM
easat-10856	797	3	]	]	SYM
easat-10856	797	4	á	á	PROPN
easat-10856	797	5	.	.	PUNCT
easat-10856	797	6	j.	j.	PROPN
easat-10856	797	7	sierra	sierra	PROPN
easat-10856	797	8	cotes	cotes	PROPN
easat-10856	797	9	and	and	CCONJ
easat-10856	797	10	l.	l.	PROPN
easat-10856	797	11	a.	a.	PROPN
easat-10856	797	12	gómez	gómez	PROPN
easat-10856	797	13	yance	yance	NOUN
easat-10856	797	14	,	,	PUNCT
easat-10856	797	15	"	"	PUNCT
easat-10856	797	16	determination	determination	NOUN
easat-10856	797	17	of	of	ADP
easat-10856	797	18	the	the	DET
easat-10856	797	19	influence	influence	NOUN
easat-10856	797	20	of	of	ADP
easat-10856	797	21	diameter	diameter	NOUN
easat-10856	797	22	,	,	PUNCT
easat-10856	797	23	jet	jet	NOUN
easat-10856	797	24	velocity	velocity	NOUN
easat-10856	797	25	and	and	CCONJ
easat-10856	797	26	flow	flow	NOUN
easat-10856	797	27	rate	rate	NOUN
easat-10856	797	28	at	at	ADP
easat-10856	797	29	different	different	ADJ
easat-10856	797	30	heights	height	NOUN
easat-10856	797	31	on	on	ADP
easat-10856	797	32	the	the	DET
easat-10856	797	33	vertical	vertical	ADJ
easat-10856	797	34	discharge	discharge	NOUN
easat-10856	797	35	of	of	ADP
easat-10856	797	36	fluids	fluid	NOUN
easat-10856	797	37	through	through	ADP
easat-10856	797	38	orifices	orifice	NOUN
easat-10856	797	39	with	with	ADP
easat-10856	797	40	inlet	inlet	NOUN
easat-10856	797	41	and	and	CCONJ
easat-10856	797	42	outlet	outlet	NOUN
easat-10856	797	43	profiles	profile	NOUN
easat-10856	797	44	,	,	PUNCT
easat-10856	797	45	"	"	PUNCT
easat-10856	797	46	2020	2020	NUM
easat-10856	797	47	.	.	PUNCT
easat-10856	798	1	[	[	X
easat-10856	798	2	14	14	NUM
easat-10856	798	3	]	]	X
easat-10856	798	4	f.	f.	PROPN
easat-10856	798	5	huancapaza	huancapaza	PROPN
easat-10856	798	6	,	,	PUNCT
easat-10856	798	7	"	"	PUNCT
easat-10856	798	8	comparative	comparative	ADJ
easat-10856	798	9	analysis	analysis	NOUN
easat-10856	798	10	of	of	ADP
easat-10856	798	11	numerical	numerical	ADJ
easat-10856	798	12	methods	method	NOUN
easat-10856	798	13	to	to	PART
easat-10856	798	14	obtain	obtain	VERB
easat-10856	798	15	the	the	DET
easat-10856	798	16	dynamic	dynamic	ADJ
easat-10856	798	17	response	response	NOUN
easat-10856	798	18	of	of	ADP
easat-10856	798	19	structures	structure	NOUN
easat-10856	798	20	,	,	PUNCT
easat-10856	798	21	"	"	PUNCT
easat-10856	798	22	undergraduate	undergraduate	NOUN
easat-10856	798	23	thesis	thesis	NOUN
easat-10856	798	24	,	,	PUNCT
easat-10856	798	25	private	private	ADJ
easat-10856	798	26	university	university	NOUN
easat-10856	798	27	of	of	ADP
easat-10856	798	28	tacna	tacna	PROPN
easat-10856	798	29	.	.	PUNCT
easat-10856	799	1	tacna	tacna	PROPN
easat-10856	799	2	,	,	PUNCT
easat-10856	799	3	peru	peru	PROPN
easat-10856	799	4	,	,	PUNCT
easat-10856	799	5	2021	2021	NUM
easat-10856	799	6	.	.	PUNCT
easat-10856	800	1	[	[	X
easat-10856	800	2	15	15	NUM
easat-10856	800	3	]	]	X
easat-10856	800	4	f.	f.	NOUN
easat-10856	800	5	torres	torres	PROPN
easat-10856	800	6	,	,	PUNCT
easat-10856	800	7	"	"	PUNCT
easat-10856	800	8	generation	generation	NOUN
easat-10856	800	9	of	of	ADP
easat-10856	800	10	a	a	DET
easat-10856	800	11	mathematical	mathematical	ADJ
easat-10856	800	12	model	model	NOUN
easat-10856	800	13	for	for	ADP
easat-10856	800	14	the	the	DET
easat-10856	800	15	study	study	NOUN
easat-10856	800	16	of	of	ADP
easat-10856	800	17	reservoir	reservoir	PROPN
easat-10856	800	18	operation	operation	NOUN
easat-10856	800	19	with	with	ADP
easat-10856	800	20	a	a	DET
easat-10856	800	21	multipurpose	multipurpose	NOUN
easat-10856	800	22	approach	approach	NOUN
easat-10856	800	23	,	,	PUNCT
easat-10856	800	24	"	"	PUNCT
easat-10856	800	25	thesis	thesis	NOUN
easat-10856	800	26	for	for	ADP
easat-10856	800	27	obtaining	obtain	VERB
easat-10856	800	28	the	the	DET
easat-10856	800	29	degree	degree	NOUN
easat-10856	800	30	of	of	ADP
easat-10856	800	31	mechanical	mechanical	ADJ
easat-10856	800	32	engineer	engineer	NOUN
easat-10856	800	33	in	in	ADP
easat-10856	800	34	fluid	fluid	ADJ
easat-10856	800	35	mechanics	mechanic	NOUN
easat-10856	800	36	.	.	PUNCT
easat-10856	801	1	national	national	PROPN
easat-10856	801	2	university	university	PROPN
easat-10856	801	3	of	of	ADP
easat-10856	801	4	san	san	PROPN
easat-10856	801	5	marcos	marcos	PROPN
easat-10856	801	6	]	]	PUNCT
easat-10856	801	7	.	.	PUNCT
easat-10856	802	1	lima	lima	PROPN
easat-10856	802	2	,	,	PUNCT
easat-10856	802	3	peru	peru	PROPN
easat-10856	802	4	,	,	PUNCT
easat-10856	802	5	2017	2017	NUM
easat-10856	802	6	.	.	PUNCT
easat-10856	803	1	[	[	X
easat-10856	803	2	16	16	NUM
easat-10856	803	3	]	]	PUNCT
easat-10856	803	4	r.	r.	PROPN
easat-10856	803	5	r.	r.	PROPN
easat-10856	803	6	zamora	zamora	PROPN
easat-10856	803	7	,	,	PUNCT
easat-10856	803	8	o.	o.	PROPN
easat-10856	803	9	b.	b.	PROPN
easat-10856	803	10	manrique	manrique	PROPN
easat-10856	803	11	,	,	PUNCT
easat-10856	803	12	and	and	CCONJ
easat-10856	803	13	p.	p.	PROPN
easat-10856	803	14	l.	l.	PROPN
easat-10856	803	15	balbón	balbón	PROPN
easat-10856	803	16	,	,	PUNCT
easat-10856	803	17	"	"	PUNCT
easat-10856	803	18	energy	energy	NOUN
easat-10856	803	19	balance	balance	NOUN
easat-10856	803	20	in	in	ADP
easat-10856	803	21	simple	simple	ADJ
easat-10856	803	22	pipes	pipe	NOUN
easat-10856	803	23	applied	apply	VERB
easat-10856	803	24	to	to	ADP
easat-10856	803	25	hydraulic	hydraulic	ADJ
easat-10856	803	26	engineering	engineering	NOUN
easat-10856	803	27	,	,	PUNCT
easat-10856	803	28	"	"	PUNCT
easat-10856	803	29	universidad	universidad	PROPN
easat-10856	803	30	&	&	CCONJ
easat-10856	803	31	ciencia	ciencia	PROPN
easat-10856	803	32	,	,	PUNCT
easat-10856	803	33	vol	vol	NOUN
easat-10856	803	34	.	.	NOUN
easat-10856	804	1	9	9	NUM
easat-10856	804	2	,	,	PUNCT
easat-10856	804	3	no	no	INTJ
easat-10856	804	4	.	.	NOUN
easat-10856	804	5	2	2	NUM
easat-10856	804	6	,	,	PUNCT
easat-10856	804	7	pp	pp	ADJ
easat-10856	804	8	.	.	PUNCT
easat-10856	805	1	2227–2690	2227–2690	NUM
easat-10856	805	2	,	,	PUNCT
easat-10856	805	3	2020	2020	NUM
easat-10856	805	4	.	.	PUNCT
easat-10856	806	1	[	[	X
easat-10856	806	2	17	17	NUM
easat-10856	806	3	]	]	X
easat-10856	806	4	r.	r.	PROPN
easat-10856	806	5	o.	o.	PROPN
easat-10856	806	6	estela	estela	PROPN
easat-10856	806	7	urbina	urbina	PROPN
easat-10856	806	8	et	et	PROPN
easat-10856	806	9	al	al	PROPN
easat-10856	806	10	.	.	PROPN
easat-10856	806	11	,	,	PUNCT
easat-10856	806	12	"	"	PUNCT
easat-10856	806	13	numerical	numerical	ADJ
easat-10856	806	14	methods	method	NOUN
easat-10856	806	15	applied	apply	VERB
easat-10856	806	16	to	to	ADP
easat-10856	806	17	hydraulic	hydraulic	ADJ
easat-10856	806	18	calculation	calculation	NOUN
easat-10856	806	19	in	in	ADP
easat-10856	806	20	irrigation	irrigation	NOUN
easat-10856	806	21	canals	canal	NOUN
easat-10856	806	22	of	of	ADP
easat-10856	806	23	bagua	bagua	NOUN
easat-10856	806	24	,	,	PUNCT
easat-10856	806	25	"	"	PUNCT
easat-10856	806	26	revista	revista	PROPN
easat-10856	806	27	científica	científica	PROPN
easat-10856	806	28	dékamu	dékamu	PROPN
easat-10856	806	29	agropec	agropec	PROPN
easat-10856	806	30	,	,	PUNCT
easat-10856	806	31	vol	vol	NOUN
easat-10856	806	32	.	.	PROPN
easat-10856	807	1	3	3	NUM
easat-10856	807	2	,	,	PUNCT
easat-10856	807	3	no	no	INTJ
easat-10856	807	4	.	.	NOUN
easat-10856	807	5	1	1	NUM
easat-10856	807	6	,	,	PUNCT
easat-10856	807	7	pp	pp	ADJ
easat-10856	807	8	.	.	PUNCT
easat-10856	808	1	20	20	NUM
easat-10856	808	2	-	-	SYM
easat-10856	808	3	34	34	NUM
easat-10856	808	4	,	,	PUNCT
easat-10856	808	5	2022	2022	NUM
easat-10856	808	6	.	.	PUNCT
easat-10856	809	1	https://doi.org/10.55996/dekamuagropec.v3i1.70	https://doi.org/10.55996/dekamuagropec.v3i1.70	X
easat-10856	810	1	[	[	X
easat-10856	810	2	18	18	NUM
easat-10856	810	3	]	]	X
easat-10856	810	4	o.	o.	PROPN
easat-10856	810	5	marín	marín	PROPN
easat-10856	810	6	-	-	PUNCT
easat-10856	810	7	machuca	machuca	NOUN
easat-10856	810	8	et	et	PROPN
easat-10856	810	9	al	al	PROPN
easat-10856	810	10	.	.	PROPN
easat-10856	810	11	,	,	PUNCT
easat-10856	810	12	"	"	PUNCT
easat-10856	810	13	quantification	quantification	NOUN
easat-10856	810	14	of	of	ADP
easat-10856	810	15	the	the	DET
easat-10856	810	16	alkalinity	alkalinity	NOUN
easat-10856	810	17	of	of	ADP
easat-10856	810	18	natural	natural	ADJ
easat-10856	810	19	water	water	NOUN
easat-10856	810	20	by	by	ADP
easat-10856	810	21	applying	apply	VERB
easat-10856	810	22	bernoulli	bernoulli	NOUN
easat-10856	810	23	numbers	number	NOUN
easat-10856	810	24	and	and	CCONJ
easat-10856	810	25	simpson	simpson	PROPN
easat-10856	810	26	's	's	PART
easat-10856	810	27	approximate	approximate	ADJ
easat-10856	810	28	integral	integral	ADJ
easat-10856	810	29	,	,	PUNCT
easat-10856	810	30	"	"	PUNCT
easat-10856	810	31	biotempo	biotempo	ADJ
easat-10856	810	32	,	,	PUNCT
easat-10856	810	33	vol	vol	NOUN
easat-10856	810	34	.	.	PROPN
easat-10856	810	35	20	20	NUM
easat-10856	810	36	,	,	PUNCT
easat-10856	810	37	no	no	INTJ
easat-10856	810	38	.	.	NOUN
easat-10856	810	39	2	2	NUM
easat-10856	810	40	,	,	PUNCT
easat-10856	810	41	pp	pp	ADJ
easat-10856	810	42	.	.	PUNCT
easat-10856	811	1	183	183	NUM
easat-10856	811	2	-	-	SYM
easat-10856	811	3	196	196	NUM
easat-10856	811	4	,	,	PUNCT
easat-10856	811	5	2023	2023	NUM
easat-10856	811	6	.	.	PUNCT
easat-10856	812	1	https://doi.org/10.31381/biotempo.v20i2.5945	https://doi.org/10.31381/biotempo.v20i2.5945	NUM
easat-10856	812	2	[	[	X
easat-10856	812	3	19	19	NUM
easat-10856	812	4	]	]	PUNCT
easat-10856	812	5	j.	j.	PROPN
easat-10856	812	6	bernoulli	bernoulli	PROPN
easat-10856	812	7	,	,	PUNCT
easat-10856	812	8	the	the	DET
easat-10856	812	9	art	art	NOUN
easat-10856	812	10	of	of	ADP
easat-10856	812	11	guessing	guessing	NOUN
easat-10856	812	12	.	.	PUNCT
easat-10856	813	1	basel	basel	PROPN
easat-10856	813	2	,	,	PUNCT
easat-10856	813	3	switzerland	switzerland	PROPN
easat-10856	813	4	:	:	PUNCT
easat-10856	813	5	thurneysen	thurneysen	PROPN
easat-10856	813	6	,	,	PUNCT
easat-10856	813	7	1713	1713	NUM
easat-10856	813	8	.	.	PUNCT
easat-10856	814	1	[	[	X
easat-10856	814	2	20	20	NUM
easat-10856	814	3	]	]	PUNCT
easat-10856	814	4	v.	v.	ADP
easat-10856	814	5	varadarajan	varadarajan	ADJ
easat-10856	814	6	,	,	PUNCT
easat-10856	814	7	"	"	PUNCT
easat-10856	814	8	euler	euler	NOUN
easat-10856	814	9	and	and	CCONJ
easat-10856	814	10	his	his	PRON
easat-10856	814	11	work	work	NOUN
easat-10856	814	12	on	on	ADP
easat-10856	814	13	infinite	infinite	ADJ
easat-10856	814	14	series	series	NOUN
easat-10856	814	15	,	,	PUNCT
easat-10856	814	16	"	"	PUNCT
easat-10856	814	17	bulletin	bulletin	NOUN
easat-10856	814	18	of	of	ADP
easat-10856	814	19	the	the	DET
easat-10856	814	20	american	american	PROPN
easat-10856	814	21	mathematical	mathematical	PROPN
easat-10856	814	22	society	society	NOUN
easat-10856	814	23	,	,	PUNCT
easat-10856	814	24	vol	vol	NOUN
easat-10856	814	25	.	.	PROPN
easat-10856	814	26	44	44	NUM
easat-10856	814	27	,	,	PUNCT
easat-10856	814	28	no	no	INTJ
easat-10856	814	29	.	.	NOUN
easat-10856	814	30	4	4	NUM
easat-10856	814	31	,	,	PUNCT
easat-10856	814	32	pp	pp	ADJ
easat-10856	814	33	.	.	PUNCT
easat-10856	815	1	515	515	NUM
easat-10856	815	2	-	-	SYM
easat-10856	815	3	539	539	NUM
easat-10856	815	4	,	,	PUNCT
easat-10856	815	5	2007	2007	NUM
easat-10856	815	6	.	.	PUNCT
easat-10856	816	1	[	[	X
easat-10856	816	2	21	21	NUM
easat-10856	816	3	]	]	PUNCT
easat-10856	816	4	a.	a.	NOUN
easat-10856	816	5	tsuneo	tsuneo	PROPN
easat-10856	816	6	,	,	PUNCT
easat-10856	816	7	i.	i.	PROPN
easat-10856	816	8	tomoyoshi	tomoyoshi	PROPN
easat-10856	816	9	,	,	PUNCT
easat-10856	816	10	and	and	CCONJ
easat-10856	816	11	k.	k.	PROPN
easat-10856	816	12	masanobu	masanobu	PROPN
easat-10856	816	13	,	,	PUNCT
easat-10856	816	14	bernoulli	bernoulli	NOUN
easat-10856	816	15	numbers	number	NOUN
easat-10856	816	16	and	and	CCONJ
easat-10856	816	17	zeta	zeta	NOUN
easat-10856	816	18	functions	function	NOUN
easat-10856	816	19	(	(	PUNCT
easat-10856	816	20	springer	springer	NOUN
easat-10856	816	21	monographs	monograph	NOUN
easat-10856	816	22	in	in	ADP
easat-10856	816	23	mathematics	mathematic	NOUN
easat-10856	816	24	;	;	PUNCT
easat-10856	816	25	with	with	ADP
easat-10856	816	26	an	an	DET
easat-10856	816	27	appendix	appendix	NOUN
easat-10856	816	28	by	by	ADP
easat-10856	816	29	d.	d.	PROPN
easat-10856	816	30	zagier	zagier	PROPN
easat-10856	816	31	)	)	PUNCT
easat-10856	816	32	.	.	PUNCT
easat-10856	817	1	tokyo	tokyo	PROPN
easat-10856	817	2	,	,	PUNCT
easat-10856	817	3	japan	japan	PROPN
easat-10856	817	4	:	:	PUNCT
easat-10856	817	5	springer	springer	NOUN
easat-10856	817	6	,	,	PUNCT
easat-10856	817	7	2014	2014	NUM
easat-10856	817	8	.	.	PUNCT
easat-10856	818	1	[	[	X
easat-10856	818	2	22	22	NUM
easat-10856	818	3	]	]	PUNCT
easat-10856	818	4	s.	s.	PROPN
easat-10856	818	5	murray	murray	PROPN
easat-10856	818	6	,	,	PUNCT
easat-10856	818	7	manual	manual	NOUN
easat-10856	818	8	of	of	ADP
easat-10856	818	9	mathematical	mathematical	ADJ
easat-10856	818	10	formulas	formula	NOUN
easat-10856	818	11	and	and	CCONJ
easat-10856	818	12	tables	table	NOUN
easat-10856	818	13	.	.	PUNCT
easat-10856	819	1	new	new	PROPN
easat-10856	819	2	york	york	PROPN
easat-10856	819	3	:	:	PUNCT
easat-10856	819	4	mcgraw	mcgraw	PROPN
easat-10856	819	5	-	-	PUNCT
easat-10856	819	6	hill	hill	PROPN
easat-10856	819	7	,	,	PUNCT
easat-10856	819	8	inc	inc	PROPN
easat-10856	819	9	,	,	PUNCT
easat-10856	819	10	1970	1970	NUM
easat-10856	819	11	.	.	PUNCT
easat-10856	820	1	[	[	X
easat-10856	820	2	23	23	NUM
easat-10856	820	3	]	]	X
easat-10856	820	4	g.	g.	PROPN
easat-10856	820	5	f.	f.	PROPN
easat-10856	820	6	simmons	simmons	PROPN
easat-10856	820	7	,	,	PUNCT
easat-10856	820	8	differential	differential	ADJ
easat-10856	820	9	equations	equation	NOUN
easat-10856	820	10	:	:	PUNCT
easat-10856	820	11	with	with	ADP
easat-10856	820	12	applications	application	NOUN
easat-10856	820	13	and	and	CCONJ
easat-10856	820	14	historical	historical	ADJ
easat-10856	820	15	notes	note	NOUN
easat-10856	820	16	,	,	PUNCT
easat-10856	820	17	2nd	2nd	ADJ
easat-10856	820	18	ed	ed	NOUN
easat-10856	820	19	.	.	PUNCT
easat-10856	821	1	madrid	madrid	PROPN
easat-10856	821	2	,	,	PUNCT
easat-10856	821	3	españa	españa	PROPN
easat-10856	821	4	:	:	PUNCT
easat-10856	821	5	mcgrawhill	mcgrawhill	PROPN
easat-10856	821	6	/	/	SYM
easat-10856	821	7	interamericana	interamericana	PROPN
easat-10856	821	8	de	de	PROPN
easat-10856	821	9	españa	españa	PROPN
easat-10856	821	10	,	,	PUNCT
easat-10856	821	11	s.a.u	s.a.u	NOUN
easat-10856	821	12	,	,	PUNCT
easat-10856	821	13	1998	1998	NUM
easat-10856	821	14	.	.	PUNCT
easat-10856	822	1	https://doi.org/10.55996/dekamuagropec.v3i1.70	https://doi.org/10.55996/dekamuagropec.v3i1.70	NOUN
easat-10856	822	2	https://doi.org/10.31381/biotempo.v20i2.5945	https://doi.org/10.31381/biotempo.v20i2.5945	NUM