id	sid	tid	token	lemma	pos
ma-115	1	1	2023	2023	NUM
ma-115	1	2	ada	ada	PROPN
ma-115	1	3	academica	academica	PROPN
ma-115	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-115	1	5	.	.	PUNCT
ma-115	2	1	j.	j.	PROPN
ma-115	2	2	math	math	PROPN
ma-115	2	3	.	.	PUNCT
ma-115	3	1	anal	anal	ADJ
ma-115	3	2	.	.	PUNCT
ma-115	4	1	3	3	NUM
ma-115	4	2	(	(	PUNCT
ma-115	4	3	2023	2023	NUM
ma-115	4	4	)	)	PUNCT
ma-115	4	5	6doi	6doi	NOUN
ma-115	4	6	:	:	PUNCT
ma-115	4	7	10.28924	10.28924	NUM
ma-115	4	8	/	/	SYM
ma-115	4	9	ada	ada	PROPN
ma-115	4	10	/	/	SYM
ma-115	4	11	ma.3.6	ma.3.6	PROPN
ma-115	4	12	fractionalization	fractionalization	NOUN
ma-115	4	13	of	of	ADP
ma-115	4	14	hankel	hankel	NOUN
ma-115	4	15	type	type	NOUN
ma-115	4	16	integral	integral	ADJ
ma-115	4	17	transforms	transform	NOUN
ma-115	4	18	and	and	CCONJ
ma-115	4	19	their	their	PRON
ma-115	4	20	relevance	relevance	NOUN
ma-115	4	21	b.	b.	PROPN
ma-115	4	22	b.	b.	PROPN
ma-115	4	23	waphare∗	waphare∗	PROPN
ma-115	4	24	,	,	PUNCT
ma-115	4	25	r.	r.	PROPN
ma-115	4	26	z.	z.	PROPN
ma-115	4	27	shaikh	shaikh	PROPN
ma-115	4	28	mit	mit	PROPN
ma-115	4	29	arts	art	NOUN
ma-115	4	30	,	,	PUNCT
ma-115	4	31	commerce	commerce	NOUN
ma-115	4	32	and	and	CCONJ
ma-115	4	33	science	science	PROPN
ma-115	4	34	college	college	PROPN
ma-115	4	35	,	,	PUNCT
ma-115	4	36	alandi(d	alandi(d	PROPN
ma-115	4	37	)	)	PUNCT
ma-115	4	38	,	,	PUNCT
ma-115	4	39	pune	pune	NOUN
ma-115	4	40	,	,	PUNCT
ma-115	4	41	maharashtra	maharashtra	PROPN
ma-115	4	42	,	,	PUNCT
ma-115	4	43	india	india	PROPN
ma-115	4	44	balasahebwaphare@gmail.com	balasahebwaphare@gmail.com	PROPN
ma-115	4	45	,	,	PUNCT
ma-115	4	46	shaikhrahilanaz@gmail.com	shaikhrahilanaz@gmail.com	X
ma-115	5	1	∗correspondence	∗correspondence	NOUN
ma-115	5	2	:	:	PUNCT
ma-115	5	3	balasahebwaphare@gmail.com	balasahebwaphare@gmail.com	X
ma-115	6	1	abstract	abstract	ADJ
ma-115	6	2	.	.	PUNCT
ma-115	7	1	in	in	ADP
ma-115	7	2	this	this	DET
ma-115	7	3	paper	paper	NOUN
ma-115	7	4	,	,	PUNCT
ma-115	7	5	the	the	DET
ma-115	7	6	fractionalization	fractionalization	NOUN
ma-115	7	7	of	of	ADP
ma-115	7	8	certain	certain	ADJ
ma-115	7	9	types	type	NOUN
ma-115	7	10	of	of	ADP
ma-115	7	11	hankel	hankel	NOUN
ma-115	7	12	transforms	transform	VERB
ma-115	7	13	is	be	AUX
ma-115	7	14	suggested.barut	suggested.barut	NUM
ma-115	7	15	-	-	PUNCT
ma-115	7	16	girardello	girardello	NOUN
ma-115	7	17	type	type	NOUN
ma-115	7	18	transforms	transform	NOUN
ma-115	7	19	are	be	AUX
ma-115	7	20	then	then	ADV
ma-115	7	21	introduced	introduce	VERB
ma-115	7	22	along	along	ADP
ma-115	7	23	with	with	ADP
ma-115	7	24	the	the	DET
ma-115	7	25	relevant	relevant	ADJ
ma-115	7	26	fractional	fractional	ADJ
ma-115	7	27	order	order	NOUN
ma-115	7	28	forms.finally	forms.finally	ADV
ma-115	7	29	some	some	DET
ma-115	7	30	further	further	ADJ
ma-115	7	31	generalizations	generalization	NOUN
ma-115	7	32	are	be	AUX
ma-115	7	33	suggested	suggest	VERB
ma-115	7	34	.	.	PUNCT
ma-115	8	1	1	1	X
ma-115	8	2	.	.	X
ma-115	8	3	introduction	introduction	NOUN
ma-115	8	4	the	the	DET
ma-115	8	5	theory	theory	NOUN
ma-115	8	6	of	of	ADP
ma-115	8	7	hankel	hankel	NOUN
ma-115	8	8	transforms	transform	VERB
ma-115	8	9	is	be	AUX
ma-115	8	10	very	very	ADV
ma-115	8	11	vast	vast	ADJ
ma-115	8	12	and	and	CCONJ
ma-115	8	13	it	it	PRON
ma-115	8	14	is	be	AUX
ma-115	8	15	studied	study	VERB
ma-115	8	16	by	by	ADP
ma-115	8	17	many	many	ADJ
ma-115	8	18	researchers	researcher	NOUN
ma-115	8	19	in	in	ADP
ma-115	8	20	recent	recent	ADJ
ma-115	8	21	aswell	aswell	NOUN
ma-115	8	22	as	as	ADP
ma-115	8	23	in	in	ADP
ma-115	8	24	past	past	NOUN
ma-115	8	25	.	.	PUNCT
ma-115	9	1	the	the	DET
ma-115	9	2	forward	forward	ADJ
ma-115	9	3	and	and	CCONJ
ma-115	9	4	inverse	inverse	NOUN
ma-115	9	5	transforms	transform	NOUN
ma-115	9	6	are	be	AUX
ma-115	9	7	completely	completely	ADV
ma-115	9	8	symmetric	symmetric	ADJ
ma-115	9	9	and	and	CCONJ
ma-115	9	10	resemble	resemble	VERB
ma-115	9	11	thefourier	thefouri	ADJ
ma-115	9	12	transform	transform	NOUN
ma-115	9	13	,	,	PUNCT
ma-115	9	14	with	with	ADP
ma-115	9	15	the	the	DET
ma-115	9	16	complex	complex	ADJ
ma-115	9	17	exponent	exponent	NOUN
ma-115	9	18	as	as	ADP
ma-115	9	19	kernal	kernal	ADJ
ma-115	9	20	being	be	AUX
ma-115	9	21	replaced	replace	VERB
ma-115	9	22	by	by	ADP
ma-115	9	23	the	the	DET
ma-115	9	24	bessel	bessel	NOUN
ma-115	9	25	function	function	NOUN
ma-115	9	26	offirst	offirst	ADV
ma-115	9	27	kind	kind	ADV
ma-115	9	28	jα−β	jα−β	NOUN
ma-115	9	29	of	of	ADP
ma-115	9	30	order	order	NOUN
ma-115	9	31	α−	α−	ADP
ma-115	9	32	β	β	X
ma-115	9	33	≥	≥	X
ma-115	9	34	−12	−12	NOUN
ma-115	9	35	.the	.the	DET
ma-115	9	36	formal	formal	ADJ
ma-115	9	37	equivalence	equivalence	NOUN
ma-115	9	38	between	between	ADP
ma-115	9	39	the	the	DET
ma-115	9	40	zeroth	zeroth	ADJ
ma-115	9	41	-	-	PUNCT
ma-115	9	42	order	order	NOUN
ma-115	9	43	hankel	hankel	NOUN
ma-115	9	44	transform	transform	NOUN
ma-115	9	45	and	and	CCONJ
ma-115	9	46	the	the	DET
ma-115	9	47	abel	abel	PROPN
ma-115	9	48	transform	transform	VERB
ma-115	9	49	fol	fol	NOUN
ma-115	9	50	-	-	PUNCT
ma-115	9	51	lowed	low	VERB
ma-115	9	52	by	by	ADP
ma-115	9	53	the	the	DET
ma-115	9	54	fourier	fourier	NOUN
ma-115	9	55	transform	transform	NOUN
ma-115	9	56	is	be	AUX
ma-115	9	57	used	use	VERB
ma-115	9	58	as	as	ADP
ma-115	9	59	basis	basis	NOUN
ma-115	9	60	for	for	ADP
ma-115	9	61	developing	develop	VERB
ma-115	9	62	fast	fast	ADJ
ma-115	9	63	algorithms	algorithm	NOUN
ma-115	9	64	for	for	ADP
ma-115	9	65	the	the	DET
ma-115	9	66	computationof	computationof	NOUN
ma-115	9	67	the	the	DET
ma-115	9	68	zeroth	zeroth	ADJ
ma-115	9	69	-	-	PUNCT
ma-115	9	70	order	order	NOUN
ma-115	9	71	hankel	hankel	NOUN
ma-115	9	72	transform	transform	VERB
ma-115	9	73	[	[	X
ma-115	9	74	5	5	NUM
ma-115	9	75	]	]	PUNCT
ma-115	9	76	.	.	PUNCT
ma-115	10	1	algorithms	algorithm	NOUN
ma-115	10	2	for	for	ADP
ma-115	10	3	the	the	DET
ma-115	10	4	computation	computation	NOUN
ma-115	10	5	of	of	ADP
ma-115	10	6	the	the	DET
ma-115	10	7	hankel	hankel	NOUN
ma-115	10	8	transformof	transformof	ADP
ma-115	10	9	integer	integer	NOUN
ma-115	10	10	order	order	NOUN
ma-115	10	11	n	n	DET
ma-115	10	12	>	>	X
ma-115	10	13	0	0	NUM
ma-115	10	14	have	have	AUX
ma-115	10	15	been	be	AUX
ma-115	10	16	proposed	propose	VERB
ma-115	10	17	.	.	PUNCT
ma-115	11	1	on	on	ADP
ma-115	11	2	the	the	DET
ma-115	11	3	basis	basis	NOUN
ma-115	11	4	of	of	ADP
ma-115	11	5	the	the	DET
ma-115	11	6	general	general	ADJ
ma-115	11	7	relation	relation	NOUN
ma-115	11	8	involving	involve	VERB
ma-115	11	9	thehankel	thehankel	NOUN
ma-115	11	10	transform	transform	NOUN
ma-115	11	11	of	of	ADP
ma-115	11	12	integer	integer	NOUN
ma-115	11	13	order	order	NOUN
ma-115	11	14	n	n	CCONJ
ma-115	11	15	>	>	PUNCT
ma-115	11	16	0	0	PUNCT
ma-115	12	1	and	and	CCONJ
ma-115	12	2	the	the	DET
ma-115	12	3	abel	abel	PROPN
ma-115	12	4	transform	transform	NOUN
ma-115	12	5	,	,	PUNCT
ma-115	12	6	whose	whose	DET
ma-115	12	7	kernel	kernel	NOUN
ma-115	12	8	is	be	AUX
ma-115	12	9	modulated	modulate	VERB
ma-115	12	10	by	by	ADP
ma-115	12	11	thechebyshev	thechebyshev	PROPN
ma-115	12	12	polynomial	polynomial	NOUN
ma-115	12	13	of	of	ADP
ma-115	12	14	the	the	DET
ma-115	12	15	first	first	ADJ
ma-115	12	16	kind	kind	NOUN
ma-115	12	17	of	of	ADP
ma-115	12	18	order	order	NOUN
ma-115	12	19	n	n	CCONJ
ma-115	12	20	,	,	PUNCT
ma-115	12	21	followed	follow	VERB
ma-115	12	22	by	by	ADP
ma-115	12	23	the	the	DET
ma-115	12	24	fourier	fourier	ADJ
ma-115	12	25	sine	sine	NOUN
ma-115	12	26	or	or	CCONJ
ma-115	12	27	cosine	cosine	NOUN
ma-115	12	28	transformaccording	transformaccording	NOUN
ma-115	12	29	to	to	ADP
ma-115	12	30	whether	whether	SCONJ
ma-115	12	31	n	n	PRON
ma-115	12	32	is	be	AUX
ma-115	12	33	odd	odd	ADJ
ma-115	12	34	or	or	CCONJ
ma-115	12	35	even	even	ADV
ma-115	12	36	[	[	X
ma-115	12	37	5	5	NUM
ma-115	12	38	,	,	PUNCT
ma-115	12	39	13].it	13].it	NUM
ma-115	12	40	has	have	AUX
ma-115	12	41	been	be	AUX
ma-115	12	42	evidenced	evidence	VERB
ma-115	12	43	in	in	ADP
ma-115	12	44	[	[	X
ma-115	12	45	18	18	NUM
ma-115	12	46	]	]	PUNCT
ma-115	12	47	the	the	DET
ma-115	12	48	formal	formal	ADJ
ma-115	12	49	equivalence	equivalence	NOUN
ma-115	12	50	between	between	ADP
ma-115	12	51	the	the	DET
ma-115	12	52	hankel	hankel	NOUN
ma-115	12	53	transform	transform	NOUN
ma-115	12	54	of	of	ADP
ma-115	12	55	order	order	NOUN
ma-115	12	56	α−	α−	ADP
ma-115	12	57	βand	βand	NOUN
ma-115	12	58	the	the	DET
ma-115	12	59	erdelyi	erdelyi	PROPN
ma-115	12	60	-	-	PUNCT
ma-115	12	61	kober	kober	NOUN
ma-115	12	62	fractional	fractional	PROPN
ma-115	12	63	integral	integral	ADJ
ma-115	12	64	of	of	ADP
ma-115	12	65	order	order	NOUN
ma-115	12	66	(	(	PUNCT
ma-115	12	67	α	α	NOUN
ma-115	12	68	−	−	NOUN
ma-115	12	69	β	β	NOUN
ma-115	13	1	+	+	NOUN
ma-115	13	2	1	1	NUM
ma-115	13	3	2	2	NUM
ma-115	13	4	)	)	PUNCT
ma-115	13	5	followed	follow	VERB
ma-115	13	6	by	by	ADP
ma-115	13	7	the	the	DET
ma-115	13	8	fourier	fourier	NOUN
ma-115	13	9	cosinetransform	cosinetransform	NOUN
ma-115	13	10	,	,	PUNCT
ma-115	13	11	with	with	SCONJ
ma-115	13	12	both	both	PRON
ma-115	13	13	acted	act	VERB
ma-115	13	14	on	on	ADP
ma-115	13	15	function	function	NOUN
ma-115	13	16	and	and	CCONJ
ma-115	13	17	the	the	DET
ma-115	13	18	resulting	result	VERB
ma-115	13	19	transform	transform	NOUN
ma-115	13	20	being	be	AUX
ma-115	13	21	modulated	modulate	VERB
ma-115	13	22	by	by	ADP
ma-115	13	23	properly	properly	ADV
ma-115	13	24	α−	α−	ADP
ma-115	13	25	β	β	X
ma-115	13	26	dependent	dependent	ADJ
ma-115	13	27	power	power	NOUN
ma-115	13	28	functions	function	NOUN
ma-115	13	29	of	of	ADP
ma-115	13	30	the	the	DET
ma-115	13	31	inherent	inherent	ADJ
ma-115	13	32	variables.notably	variables.notably	NOUN
ma-115	13	33	such	such	ADJ
ma-115	13	34	as	as	ADP
ma-115	13	35	equivalence	equivalence	NOUN
ma-115	13	36	suggests	suggest	VERB
ma-115	13	37	a	a	DET
ma-115	13	38	tool	tool	NOUN
ma-115	13	39	for	for	ADP
ma-115	13	40	the	the	DET
ma-115	13	41	optical	optical	ADJ
ma-115	13	42	computation	computation	NOUN
ma-115	13	43	of	of	ADP
ma-115	13	44	erdelyi	erdelyi	NOUN
ma-115	13	45	-	-	PUNCT
ma-115	13	46	kober	kober	NOUN
ma-115	13	47	typefractional	typefractional	ADJ
ma-115	13	48	integrals	integral	NOUN
ma-115	13	49	of	of	ADP
ma-115	13	50	order	order	NOUN
ma-115	13	51	(	(	PUNCT
ma-115	13	52	n	n	NOUN
ma-115	13	53	+	+	CCONJ
ma-115	13	54	1	1	NUM
ma-115	13	55	2	2	NUM
ma-115	13	56	)	)	PUNCT
ma-115	13	57	,	,	PUNCT
ma-115	13	58	n	n	DET
ma-115	13	59	integer	integer	NOUN
ma-115	13	60	,	,	PUNCT
ma-115	13	61	through	through	ADP
ma-115	13	62	the	the	DET
ma-115	13	63	optical	optical	ADJ
ma-115	13	64	implementation	implementation	NOUN
ma-115	13	65	of	of	ADP
ma-115	13	66	the	the	DET
ma-115	13	67	hankeland	hankeland	NOUN
ma-115	14	1	i	i	PROPN
ma-115	14	2	d	d	PROPN
ma-115	14	3	fourier	fourier	NOUN
ma-115	14	4	transforms	transform	VERB
ma-115	14	5	.	.	PUNCT
ma-115	15	1	in	in	ADP
ma-115	15	2	a	a	DET
ma-115	15	3	sense	sense	NOUN
ma-115	15	4	,	,	PUNCT
ma-115	15	5	the	the	DET
ma-115	15	6	erdelyi	erdelyi	NOUN
ma-115	15	7	-	-	PUNCT
ma-115	15	8	kober	kober	PROPN
ma-115	15	9	type	type	NOUN
ma-115	15	10	fractional	fractional	ADJ
ma-115	15	11	integrals	integral	NOUN
ma-115	15	12	of	of	ADP
ma-115	15	13	order	order	NOUN
ma-115	15	14	n	n	X
ma-115	15	15	+	+	CCONJ
ma-115	15	16	1	1	NUM
ma-115	15	17	2	2	NUM
ma-115	15	18	received	receive	VERB
ma-115	15	19	:	:	PUNCT
ma-115	15	20	4	4	NUM
ma-115	15	21	jun	jun	PROPN
ma-115	15	22	2022	2022	NUM
ma-115	15	23	.	.	PUNCT
ma-115	16	1	key	key	ADJ
ma-115	16	2	words	word	NOUN
ma-115	16	3	and	and	CCONJ
ma-115	16	4	phrases	phrase	NOUN
ma-115	16	5	.	.	PUNCT
ma-115	17	1	hankel	hankel	NOUN
ma-115	17	2	type	type	NOUN
ma-115	17	3	transform	transform	NOUN
ma-115	17	4	;	;	PUNCT
ma-115	17	5	barut	barut	NOUN
ma-115	17	6	-	-	PUNCT
ma-115	17	7	girardello	girardello	NOUN
ma-115	17	8	transform	transform	NOUN
ma-115	17	9	;	;	PUNCT
ma-115	17	10	fractional	fractional	ADJ
ma-115	17	11	transform	transform	NOUN
ma-115	17	12	;	;	PUNCT
ma-115	17	13	erdelyi	erdelyi	NOUN
ma-115	17	14	-	-	PUNCT
ma-115	17	15	kobertransform	kobertransform	NOUN
ma-115	17	16	.	.	PUNCT
ma-115	18	1	1	1	NUM
ma-115	19	1	https://adac.ee	https://adac.ee	PROPN
ma-115	19	2	https://doi.org/10.28924/ada/ma.3.6	https://doi.org/10.28924/ada/ma.3.6	PROPN
ma-115	19	3	eur	eur	PROPN
ma-115	19	4	.	.	PUNCT
ma-115	20	1	j.	j.	PROPN
ma-115	20	2	math	math	PROPN
ma-115	20	3	.	.	PUNCT
ma-115	21	1	anal	anal	PROPN
ma-115	21	2	.	.	PUNCT
ma-115	22	1	10.28924	10.28924	NUM
ma-115	22	2	/	/	SYM
ma-115	22	3	ada	ada	PROPN
ma-115	22	4	/	/	SYM
ma-115	22	5	ma.3.6	ma.3.6	PROPN
ma-115	22	6	2can	2can	PROPN
ma-115	22	7	be	be	AUX
ma-115	22	8	regarded	regard	VERB
ma-115	22	9	as	as	ADP
ma-115	22	10	the	the	DET
ma-115	22	11	(	(	PUNCT
ma-115	22	12	2n	2n	NUM
ma-115	22	13	+	+	CCONJ
ma-115	22	14	1)-plane	1)-plane	NUM
ma-115	22	15	abe1	abe1	NOUN
ma-115	22	16	transform	transform	NOUN
ma-115	22	17	on	on	ADP
ma-115	22	18	rm	rm	PROPN
ma-115	22	19	,	,	PUNCT
ma-115	22	20	with	with	ADP
ma-115	22	21	0	0	NUM
ma-115	22	22	<	<	X
ma-115	22	23	2n	2n	NUM
ma-115	23	1	+	+	CCONJ
ma-115	23	2	1	1	NUM
ma-115	23	3	<	<	X
ma-115	23	4	m.various	m.various	ADJ
ma-115	23	5	forms	form	NOUN
ma-115	23	6	of	of	ADP
ma-115	23	7	hankel	hankel	NOUN
ma-115	23	8	like	like	ADP
ma-115	23	9	integral	integral	ADJ
ma-115	23	10	transforms	transform	NOUN
ma-115	23	11	have	have	AUX
ma-115	23	12	been	be	AUX
ma-115	23	13	considered	consider	VERB
ma-115	23	14	in	in	ADP
ma-115	23	15	detail	detail	NOUN
ma-115	23	16	in	in	ADP
ma-115	23	17	a	a	DET
ma-115	23	18	series	series	NOUN
ma-115	23	19	of	of	ADP
ma-115	23	20	pa	pa	PROPN
ma-115	23	21	-	-	PUNCT
ma-115	23	22	pers	per	NOUN
ma-115	23	23	[	[	X
ma-115	23	24	6,7,10–12,22	6,7,10–12,22	NOUN
ma-115	23	25	]	]	PUNCT
ma-115	23	26	.	.	PUNCT
ma-115	24	1	we	we	PRON
ma-115	24	2	will	will	AUX
ma-115	24	3	be	be	AUX
ma-115	24	4	concerned	concern	VERB
ma-115	24	5	here	here	ADV
ma-115	24	6	with	with	ADP
ma-115	24	7	certain	certain	ADJ
ma-115	24	8	hankel	hankel	NOUN
ma-115	24	9	type	type	NOUN
ma-115	24	10	transform	transform	NOUN
ma-115	24	11	having	have	VERB
ma-115	24	12	relevanceamong	relevanceamong	ADJ
ma-115	24	13	others	other	NOUN
ma-115	24	14	,	,	PUNCT
ma-115	24	15	in	in	ADP
ma-115	24	16	connection	connection	NOUN
ma-115	24	17	with	with	ADP
ma-115	24	18	the	the	DET
ma-115	24	19	solution	solution	NOUN
ma-115	24	20	to	to	ADP
ma-115	24	21	evolution	evolution	NOUN
ma-115	24	22	problems	problem	NOUN
ma-115	24	23	involving	involve	VERB
ma-115	24	24	the	the	DET
ma-115	24	25	bessel	bessel	ADJ
ma-115	24	26	type	type	NOUN
ma-115	24	27	differ	differ	VERB
ma-115	24	28	-	-	PUNCT
ma-115	24	29	ential	ential	ADJ
ma-115	24	30	operators	operator	NOUN
ma-115	24	31	xα+3β−1	xα+3β−1	PUNCT
ma-115	25	1	(	(	PUNCT
ma-115	25	2	∂∂x	∂∂x	PROPN
ma-115	25	3	)	)	PUNCT
ma-115	25	4	x2(α−β)+1	x2(α−β)+1	PUNCT
ma-115	26	1	(	(	PUNCT
ma-115	26	2	∂∂x	∂∂x	PROPN
ma-115	26	3	)	)	PUNCT
ma-115	27	1	x−3α−β	x−3α−β	PROPN
ma-115	27	2	and	and	CCONJ
ma-115	27	3	x−3α−β	x−3α−β	PROPN
ma-115	28	1	(	(	PUNCT
ma-115	28	2	∂∂x	∂∂x	PROPN
ma-115	28	3	)	)	PUNCT
ma-115	28	4	x2(α−β)+1	x2(α−β)+1	PUNCT
ma-115	29	1	(	(	PUNCT
ma-115	29	2	∂∂x	∂∂x	PROPN
ma-115	29	3	)	)	PUNCT
ma-115	30	1	xα+3β−1with	xα+3β−1with	PROPN
ma-115	30	2	α−	α−	ADP
ma-115	30	3	β	β	X
ma-115	30	4	≥	≥	X
ma-115	30	5	−12	−12	NOUN
ma-115	30	6	and	and	CCONJ
ma-115	30	7	−2(α+	−2(α+	NUM
ma-115	30	8	β	β	X
ma-115	30	9	)	)	PUNCT
ma-115	30	10	real	real	ADJ
ma-115	30	11	parameter	parameter	NOUN
ma-115	31	1	[	[	X
ma-115	31	2	6	6	NUM
ma-115	31	3	,	,	PUNCT
ma-115	31	4	11	11	NUM
ma-115	31	5	]	]	PUNCT
ma-115	31	6	.	.	PUNCT
ma-115	32	1	we	we	PRON
ma-115	32	2	introduced	introduce	VERB
ma-115	32	3	the	the	DET
ma-115	32	4	fractional	fractional	ADJ
ma-115	32	5	order	order	NOUN
ma-115	32	6	formsof	formsof	VERB
ma-115	32	7	such	such	ADJ
ma-115	32	8	hankel	hankel	NOUN
ma-115	32	9	-	-	PUNCT
ma-115	32	10	type	type	NOUN
ma-115	32	11	transforms	transform	VERB
ma-115	32	12	by	by	ADP
ma-115	32	13	following	follow	VERB
ma-115	32	14	the	the	DET
ma-115	32	15	lines	line	NOUN
ma-115	32	16	of	of	ADP
ma-115	32	17	the	the	DET
ma-115	32	18	fractionalization	fractionalization	NOUN
ma-115	32	19	of	of	ADP
ma-115	32	20	the	the	DET
ma-115	32	21	conventionalhankel	conventionalhankel	ADJ
ma-115	32	22	transform	transform	NOUN
ma-115	32	23	[	[	X
ma-115	32	24	9	9	NUM
ma-115	32	25	,	,	PUNCT
ma-115	32	26	16].work	16].work	PROPN
ma-115	32	27	of	of	ADP
ma-115	32	28	torre	torre	PROPN
ma-115	33	1	[	[	X
ma-115	33	2	17	17	NUM
ma-115	33	3	]	]	PUNCT
ma-115	33	4	motivated	motivate	VERB
ma-115	33	5	us	we	PRON
ma-115	33	6	to	to	PART
ma-115	33	7	prepare	prepare	VERB
ma-115	33	8	this	this	DET
ma-115	33	9	paper	paper	NOUN
ma-115	33	10	.	.	PUNCT
ma-115	34	1	2	2	X
ma-115	34	2	.	.	X
ma-115	34	3	hankel	hankel	NOUN
ma-115	34	4	type	type	NOUN
ma-115	34	5	transforms	transform	VERB
ma-115	34	6	:	:	PUNCT
ma-115	34	7	the	the	DET
ma-115	34	8	first	first	ADJ
ma-115	34	9	and	and	CCONJ
ma-115	34	10	second	second	ADJ
ma-115	34	11	hankel	hankel	NOUN
ma-115	34	12	-	-	PUNCT
ma-115	34	13	type	type	NOUN
ma-115	34	14	transforms	transform	NOUN
ma-115	34	15	of	of	ADP
ma-115	34	16	bessel	bessel	ADJ
ma-115	34	17	order	order	NOUN
ma-115	34	18	α−	α−	ADP
ma-115	34	19	β	β	NOUN
ma-115	34	20	,	,	PUNCT
ma-115	34	21	depending	depend	VERB
ma-115	34	22	on	on	ADP
ma-115	34	23	an	an	DET
ma-115	34	24	arbitraryreal	arbitraryreal	NOUN
ma-115	34	25	parameter	parameter	NOUN
ma-115	34	26	−2(α+	−2(α+	NUM
ma-115	34	27	β	β	NOUN
ma-115	34	28	)	)	PUNCT
ma-115	34	29	,	,	PUNCT
ma-115	34	30	respectively	respectively	ADV
ma-115	34	31	defined	define	VERB
ma-115	34	32	by	by	ADP
ma-115	34	33	the	the	DET
ma-115	34	34	operational	operational	ADJ
ma-115	34	35	relations	relation	NOUN
ma-115	34	36	[	[	X
ma-115	34	37	6	6	NUM
ma-115	34	38	,	,	PUNCT
ma-115	34	39	11	11	NUM
ma-115	34	40	]	]	PUNCT
ma-115	34	41	.	.	PUNCT
ma-115	35	1	f̃1,α	f̃1,α	NOUN
ma-115	35	2	,	,	PUNCT
ma-115	35	3	β(y	β(y	NUM
ma-115	35	4	)	)	PUNCT
ma-115	35	5	=	=	PRON
ma-115	36	1	[	[	PUNCT
ma-115	36	2	h1,α−β,−2(α+β)f	h1,α−β,−2(α+β)f	NOUN
ma-115	36	3	]	]	PUNCT
ma-115	36	4	(	(	PUNCT
ma-115	36	5	y	y	NOUN
ma-115	36	6	)	)	PUNCT
ma-115	36	7	=	=	SYM
ma-115	36	8	y1−4(α+β	y1−4(α+β	NOUN
ma-115	36	9	)	)	PUNCT
ma-115	36	10	∫	∫	PROPN
ma-115	37	1	∞	∞	PROPN
ma-115	37	2	0	0	NUM
ma-115	37	3	(	(	PUNCT
ma-115	37	4	xy)2(α+β)jα−β(xy)f	xy)2(α+β)jα−β(xy)f	NOUN
ma-115	37	5	(	(	PUNCT
ma-115	37	6	x)dx	x)dx	PROPN
ma-115	37	7	(	(	PUNCT
ma-115	37	8	1	1	NUM
ma-115	37	9	)	)	PUNCT
ma-115	37	10	f̃2,α	f̃2,α	PROPN
ma-115	37	11	,	,	PUNCT
ma-115	37	12	β(y	β(y	NUM
ma-115	37	13	)	)	PUNCT
ma-115	37	14	=	=	NOUN
ma-115	38	1	[	[	X
ma-115	38	2	h2,α−β,−2(α+β)f	h2,α−β,−2(α+β)f	NOUN
ma-115	38	3	]	]	X
ma-115	38	4	(	(	PUNCT
ma-115	38	5	y	y	NOUN
ma-115	38	6	)	)	PUNCT
ma-115	38	7	=	=	SYM
ma-115	39	1	∫	∫	PROPN
ma-115	39	2	∞	∞	PROPN
ma-115	39	3	0	0	NUM
ma-115	40	1	x1−4(α+β)(xy)2(α+β)jα−β(xy)f	x1−4(α+β)(xy)2(α+β)jα−β(xy)f	PROPN
ma-115	40	2	(	(	PUNCT
ma-115	40	3	x)dx	x)dx	PROPN
ma-115	40	4	(	(	PUNCT
ma-115	40	5	2	2	NUM
ma-115	40	6	)	)	PUNCT
ma-115	40	7	where	where	SCONJ
ma-115	40	8	jα−β	jα−β	PROPN
ma-115	40	9	is	be	AUX
ma-115	40	10	the	the	DET
ma-115	40	11	bessel	bessel	ADJ
ma-115	40	12	type	type	NOUN
ma-115	40	13	function	function	NOUN
ma-115	40	14	of	of	ADP
ma-115	40	15	the	the	DET
ma-115	40	16	first	first	ADJ
ma-115	40	17	kind	kind	NOUN
ma-115	40	18	and	and	CCONJ
ma-115	40	19	order	order	NOUN
ma-115	40	20	(	(	PUNCT
ma-115	40	21	α−β	α−β	PROPN
ma-115	40	22	)	)	PUNCT
ma-115	40	23	≥	≥	PROPN
ma-115	40	24	−12	−12	NOUN
ma-115	40	25	.	.	PUNCT
ma-115	41	1	here	here	ADV
ma-115	41	2	f	f	PROPN
ma-115	41	3	∈	∈	PROPN
ma-115	41	4	l2(r+)the	l2(r+)the	NOUN
ma-115	41	5	space	space	NOUN
ma-115	41	6	of	of	ADP
ma-115	41	7	the	the	DET
ma-115	41	8	complex	complex	ADV
ma-115	41	9	-	-	PUNCT
ma-115	41	10	valued	value	VERB
ma-115	41	11	functions	function	NOUN
ma-115	41	12	which	which	PRON
ma-115	41	13	are	be	AUX
ma-115	41	14	lebesgue	lebesgue	NOUN
ma-115	41	15	integrable	integrable	ADJ
ma-115	41	16	on	on	ADP
ma-115	41	17	r+	r+	NOUN
ma-115	41	18	=	=	PUNCT
ma-115	41	19	(	(	PUNCT
ma-115	41	20	0,+∞).thetransform	0,+∞).thetransform	NOUN
ma-115	41	21	[	[	X
ma-115	41	22	h2,α−β,−2(α+β)f	h2,α−β,−2(α+β)f	NOUN
ma-115	41	23	]	]	X
ma-115	41	24	(	(	PUNCT
ma-115	41	25	y	y	NOUN
ma-115	41	26	)	)	PUNCT
ma-115	41	27	for	for	ADP
ma-115	41	28	α	α	NOUN
ma-115	41	29	=	=	SYM
ma-115	41	30	−1	−1	NOUN
ma-115	41	31	3	3	NUM
ma-115	41	32	β	β	NOUN
ma-115	41	33	was	be	AUX
ma-115	41	34	originally	originally	ADV
ma-115	41	35	considered	consider	VERB
ma-115	41	36	in	in	ADP
ma-115	41	37	[	[	X
ma-115	41	38	15	15	NUM
ma-115	41	39	]	]	PUNCT
ma-115	41	40	,	,	PUNCT
ma-115	41	41	where	where	SCONJ
ma-115	41	42	the	the	DET
ma-115	41	43	relevantcondition	relevantcondition	NOUN
ma-115	41	44	for	for	ADP
ma-115	41	45	its	its	PRON
ma-115	41	46	inversion	inversion	NOUN
ma-115	41	47	were	be	AUX
ma-115	41	48	established	establish	VERB
ma-115	41	49	.	.	PUNCT
ma-115	42	1	also	also	ADV
ma-115	42	2	(	(	PUNCT
ma-115	42	3	1	1	X
ma-115	42	4	)	)	PUNCT
ma-115	42	5	and	and	CCONJ
ma-115	42	6	(	(	PUNCT
ma-115	42	7	2	2	X
ma-115	42	8	)	)	PUNCT
ma-115	42	9	relate	relate	VERB
ma-115	42	10	to	to	ADP
ma-115	42	11	the	the	DET
ma-115	42	12	hankel	hankel	NOUN
ma-115	42	13	type	type	NOUN
ma-115	42	14	cliffordtransforms	cliffordtransform	NOUN
ma-115	42	15	[	[	X
ma-115	42	16	10].for	10].for	NUM
ma-115	42	17	suitable	suitable	ADJ
ma-115	42	18	values	value	NOUN
ma-115	42	19	of	of	ADP
ma-115	42	20	α	α	PRON
ma-115	42	21	,	,	PUNCT
ma-115	42	22	β	β	X
ma-115	42	23	the	the	DET
ma-115	42	24	able	able	ADJ
ma-115	42	25	transforms	transform	NOUN
ma-115	42	26	can	can	AUX
ma-115	42	27	be	be	AUX
ma-115	42	28	framed	frame	VERB
ma-115	42	29	within	within	ADP
ma-115	42	30	the	the	DET
ma-115	42	31	formalism	formalism	NOUN
ma-115	42	32	,	,	PUNCT
ma-115	42	33	developedin	developedin	PROPN
ma-115	43	1	[	[	X
ma-115	43	2	20	20	NUM
ma-115	43	3	,	,	PUNCT
ma-115	43	4	21	21	NUM
ma-115	43	5	]	]	PUNCT
ma-115	43	6	concerning	concern	VERB
ma-115	43	7	the	the	DET
ma-115	43	8	integral	integral	ADJ
ma-115	43	9	transforms	transform	NOUN
ma-115	43	10	associated	associate	VERB
ma-115	43	11	with	with	ADP
ma-115	43	12	complex	complex	ADJ
ma-115	43	13	linear	linear	ADJ
ma-115	43	14	transformations	transformation	NOUN
ma-115	43	15	inquantum	inquantum	NOUN
ma-115	43	16	mechanics	mechanic	NOUN
ma-115	43	17	,	,	PUNCT
ma-115	43	18	which	which	PRON
ma-115	43	19	maps	map	VERB
ma-115	43	20	the	the	DET
ma-115	43	21	position	position	NOUN
ma-115	43	22	and	and	CCONJ
ma-115	43	23	momentum	momentum	NOUN
ma-115	43	24	operators	operator	NOUN
ma-115	43	25	to	to	PART
ma-115	43	26	canonically	canonically	ADV
ma-115	43	27	conjugate	conjugate	VERB
ma-115	43	28	,	,	PUNCT
ma-115	43	29	but	but	CCONJ
ma-115	43	30	not	not	PART
ma-115	43	31	necessarily	necessarily	ADV
ma-115	43	32	hermitian	hermitian	ADJ
ma-115	43	33	operator	operator	NOUN
ma-115	43	34	.	.	PUNCT
ma-115	44	1	thus	thus	ADV
ma-115	44	2	according	accord	VERB
ma-115	44	3	to	to	ADP
ma-115	44	4	that	that	DET
ma-115	44	5	formalism	formalism	NOUN
ma-115	44	6	,	,	PUNCT
ma-115	44	7	the	the	DET
ma-115	44	8	able	able	ADJ
ma-115	44	9	transformscan	transformscan	NOUN
ma-115	44	10	be	be	AUX
ma-115	44	11	seen	see	VERB
ma-115	44	12	as	as	ADP
ma-115	44	13	the	the	DET
ma-115	44	14	radial	radial	ADJ
ma-115	44	15	parts	part	NOUN
ma-115	44	16	of	of	ADP
ma-115	44	17	n	n	CCONJ
ma-115	44	18	-	-	PUNCT
ma-115	44	19	dimentional	dimentional	ADJ
ma-115	44	20	linear	linear	ADJ
ma-115	44	21	cannonical	cannonical	ADJ
ma-115	44	22	transformations	transformation	NOUN
ma-115	44	23	,	,	PUNCT
ma-115	44	24	specificallyrepresenting	specificallyrepresente	VERB
ma-115	44	25	a	a	DET
ma-115	44	26	π/2	π/2	NUM
ma-115	44	27	-	-	PUNCT
ma-115	44	28	rotation	rotation	NOUN
ma-115	44	29	for	for	ADP
ma-115	44	30	each	each	DET
ma-115	44	31	pair	pair	NOUN
ma-115	44	32	of	of	ADP
ma-115	44	33	the	the	DET
ma-115	44	34	cannonically	cannonically	ADV
ma-115	44	35	conjugate	conjugate	ADJ
ma-115	44	36	operators	operator	NOUN
ma-115	44	37	in	in	ADP
ma-115	44	38	the	the	DET
ma-115	44	39	respec	respec	NOUN
ma-115	44	40	-	-	PUNCT
ma-115	44	41	tive	tive	PROPN
ma-115	44	42	n	n	CCONJ
ma-115	44	43	-	-	PUNCT
ma-115	44	44	component	component	NOUN
ma-115	44	45	position	position	NOUN
ma-115	44	46	and	and	CCONJ
ma-115	44	47	momentum	momentum	NOUN
ma-115	44	48	operator	operator	NOUN
ma-115	44	49	vectors	vector	NOUN
ma-115	44	50	.	.	PUNCT
ma-115	45	1	precisely	precisely	ADV
ma-115	45	2	,	,	PUNCT
ma-115	45	3	n	n	PROPN
ma-115	45	4	=	=	SYM
ma-115	45	5	4(α	4(α	NUM
ma-115	45	6	+	+	CCONJ
ma-115	45	7	β	β	X
ma-115	45	8	)	)	PUNCT
ma-115	45	9	for	for	ADP
ma-115	45	10	(	(	PUNCT
ma-115	45	11	1	1	NUM
ma-115	45	12	)	)	PUNCT
ma-115	45	13	and	and	CCONJ
ma-115	45	14	n	n	NOUN
ma-115	45	15	=	=	SYM
ma-115	45	16	2[1−	2[1−	PRON
ma-115	45	17	2(α+	2(α+	NUM
ma-115	45	18	β	β	NOUN
ma-115	45	19	)	)	PUNCT
ma-115	45	20	]	]	PUNCT
ma-115	46	1	=	=	PUNCT
ma-115	46	2	2−	2−	NUM
ma-115	46	3	4(α+	4(α+	NUM
ma-115	46	4	β	β	X
ma-115	46	5	)	)	PUNCT
ma-115	46	6	for	for	ADP
ma-115	46	7	(	(	PUNCT
ma-115	46	8	2).the	2).the	PRON
ma-115	46	9	order	order	NOUN
ma-115	46	10	α−β	α−β	PROPN
ma-115	46	11	of	of	ADP
ma-115	46	12	the	the	DET
ma-115	46	13	bessel	bessel	ADJ
ma-115	46	14	type	type	NOUN
ma-115	46	15	function	function	NOUN
ma-115	46	16	relates	relate	VERB
ma-115	46	17	to	to	ADP
ma-115	46	18	the	the	DET
ma-115	46	19	eigen	eigen	PROPN
ma-115	46	20	value	value	NOUN
ma-115	46	21	λ	λ	PROPN
ma-115	46	22	=	=	SYM
ma-115	46	23	−l(l+n−2	−l(l+n−2	PROPN
ma-115	46	24	)	)	PUNCT
ma-115	46	25	,	,	PUNCT
ma-115	46	26	l	l	NOUN
ma-115	46	27	=	=	SYM
ma-115	46	28	0	0	NUM
ma-115	46	29	,	,	PUNCT
ma-115	46	30	1	1	NUM
ma-115	46	31	,	,	PUNCT
ma-115	46	32	2	2	NUM
ma-115	46	33	,	,	PUNCT
ma-115	46	34	...	...	PUNCT
ma-115	46	35	of	of	ADP
ma-115	46	36	the	the	DET
ma-115	46	37	angular	angular	ADJ
ma-115	46	38	momentum	momentum	NOUN
ma-115	46	39	;	;	PUNCT
ma-115	46	40	specifically	specifically	ADV
ma-115	46	41	,	,	PUNCT
ma-115	46	42	it	it	PRON
ma-115	46	43	turns	turn	VERB
ma-115	46	44	out	out	ADP
ma-115	46	45	that	that	SCONJ
ma-115	46	46	l	l	NOUN
ma-115	46	47	=	=	PUNCT
ma-115	47	1	α−β−	α−β−	PROPN
ma-115	47	2	n	n	NOUN
ma-115	47	3	2	2	NUM
ma-115	47	4	+	+	NUM
ma-115	47	5	1	1	NUM
ma-115	47	6	,	,	PUNCT
ma-115	47	7	and	and	CCONJ
ma-115	47	8	so	so	ADV
ma-115	47	9	l	l	NOUN
ma-115	48	1	=	=	PUNCT
ma-115	48	2	−(α+	−(α+	NUM
ma-115	48	3	3β−1)for	3β−1)for	PROPN
ma-115	48	4	(	(	PUNCT
ma-115	48	5	1	1	NUM
ma-115	48	6	)	)	PUNCT
ma-115	48	7	and	and	CCONJ
ma-115	48	8	l	l	NOUN
ma-115	48	9	=	=	SYM
ma-115	48	10	3α+	3α+	NUM
ma-115	48	11	β	β	NOUN
ma-115	48	12	for	for	ADP
ma-115	48	13	(	(	PUNCT
ma-115	48	14	2	2	NUM
ma-115	48	15	)	)	PUNCT
ma-115	48	16	,	,	PUNCT
ma-115	48	17	thus	thus	ADV
ma-115	48	18	respectively	respectively	ADV
ma-115	48	19	yeilding	yeilde	VERB
ma-115	48	20	λ	λ	X
ma-115	48	21	=	=	VERB
ma-115	48	22	3(α2	3(α2	NUM
ma-115	48	23	+	+	CCONJ
ma-115	48	24	β2	β2	VERB
ma-115	48	25	)	)	PUNCT
ma-115	48	26	+	+	NUM
ma-115	48	27	10αβ	10αβ	ADJ
ma-115	48	28	−	−	ADP
ma-115	48	29	4(α+	4(α+	NUM
ma-115	48	30	β	β	NOUN
ma-115	48	31	)	)	PUNCT
ma-115	49	1	+	+	PROPN
ma-115	49	2	1and	1and	NUM
ma-115	49	3	λ	λ	NOUN
ma-115	49	4	=	=	PUNCT
ma-115	49	5	3(α2	3(α2	NUM
ma-115	49	6	+	+	CCONJ
ma-115	49	7	β2	β2	VERB
ma-115	49	8	)	)	PUNCT
ma-115	49	9	+	+	NUM
ma-115	49	10	10αβ	10αβ	ADJ
ma-115	49	11	.	.	PUNCT
ma-115	50	1	when	when	SCONJ
ma-115	50	2	α+	α+	PRON
ma-115	50	3	β	β	X
ma-115	50	4	=	=	SYM
ma-115	50	5	1	1	NUM
ma-115	50	6	4	4	NUM
ma-115	50	7	,	,	PUNCT
ma-115	50	8	n	n	NOUN
ma-115	50	9	=	=	SYM
ma-115	50	10	1	1	NUM
ma-115	50	11	in	in	ADP
ma-115	50	12	both	both	DET
ma-115	50	13	cases	case	NOUN
ma-115	50	14	,	,	PUNCT
ma-115	50	15	and	and	CCONJ
ma-115	50	16	accordingly	accordingly	ADV
ma-115	50	17	both	both	DET
ma-115	50	18	trans	tran	NOUN
ma-115	50	19	-	-	NOUN
ma-115	50	20	forms	form	NOUN
ma-115	50	21	yield	yield	VERB
ma-115	50	22	the	the	DET
ma-115	50	23	conventional	conventional	ADJ
ma-115	50	24	hankel	hankel	NOUN
ma-115	50	25	type	type	NOUN
ma-115	50	26	transform	transform	NOUN
ma-115	50	27	.	.	PUNCT
ma-115	51	1	the	the	DET
ma-115	51	2	symmetry	symmetry	NOUN
ma-115	51	3	of	of	ADP
ma-115	51	4	(	(	PUNCT
ma-115	51	5	1	1	NUM
ma-115	51	6	)	)	PUNCT
ma-115	51	7	and	and	CCONJ
ma-115	51	8	(	(	PUNCT
ma-115	51	9	2	2	X
ma-115	51	10	)	)	PUNCT
ma-115	51	11	reflects	reflect	VERB
ma-115	51	12	into	into	ADP
ma-115	51	13	therelation	therelation	NOUN
ma-115	51	14	between	between	ADP
ma-115	51	15	the	the	DET
ma-115	51	16	respective	respective	ADJ
ma-115	51	17	integral	integral	ADJ
ma-115	51	18	kernels	kernel	NOUN
ma-115	51	19	k1,α−β,−2(α+β)(x	k1,α−β,−2(α+β)(x	PROPN
ma-115	51	20	,	,	PUNCT
ma-115	51	21	y	y	PROPN
ma-115	51	22	)	)	PUNCT
ma-115	51	23	and	and	CCONJ
ma-115	51	24	k2,α−β,−2(α+β)(y	k2,α−β,−2(α+β)(y	NOUN
ma-115	51	25	,	,	PUNCT
ma-115	51	26	x);i.e	x);i.e	PRON
ma-115	51	27	.	.	PUNCT
ma-115	52	1	k1,α−β,−2(α+β)(x	k1,α−β,−2(α+β)(x	PROPN
ma-115	52	2	,	,	PUNCT
ma-115	52	3	y	y	NOUN
ma-115	52	4	)	)	PUNCT
ma-115	52	5	=	=	SYM
ma-115	52	6	y1−2(α+β	y1−2(α+β	NOUN
ma-115	52	7	)	)	PUNCT
ma-115	52	8	x2(α+β	x2(α+β	NUM
ma-115	52	9	)	)	PUNCT
ma-115	52	10	jα−β(xy	jα−β(xy	ADJ
ma-115	52	11	)	)	PUNCT
ma-115	52	12	=	=	NOUN
ma-115	52	13	k2,α−β,−2(α+β)(y	k2,α−β,−2(α+β)(y	NOUN
ma-115	52	14	,	,	PUNCT
ma-115	52	15	x	x	NOUN
ma-115	52	16	)	)	PUNCT
ma-115	52	17	.	.	PUNCT
ma-115	53	1	https://doi.org/10.28924/ada/ma.3.6	https://doi.org/10.28924/ada/ma.3.6	PROPN
ma-115	53	2	eur	eur	PROPN
ma-115	53	3	.	.	PUNCT
ma-115	54	1	j.	j.	PROPN
ma-115	54	2	math	math	PROPN
ma-115	54	3	.	.	PUNCT
ma-115	55	1	anal	anal	PROPN
ma-115	55	2	.	.	PUNCT
ma-115	56	1	10.28924	10.28924	NUM
ma-115	56	2	/	/	SYM
ma-115	56	3	ada	ada	PROPN
ma-115	56	4	/	/	SYM
ma-115	56	5	ma.3.6	ma.3.6	PROPN
ma-115	56	6	3as	3as	PROPN
ma-115	56	7	a	a	DET
ma-115	56	8	consequence	consequence	NOUN
ma-115	56	9	of	of	ADP
ma-115	56	10	well	well	ADV
ma-115	56	11	known	know	VERB
ma-115	56	12	orthogonality	orthogonality	NOUN
ma-115	56	13	relation	relation	NOUN
ma-115	56	14	of	of	ADP
ma-115	56	15	the	the	DET
ma-115	56	16	bessel	bessel	ADJ
ma-115	56	17	functions	function	NOUN
ma-115	56	18	,	,	PUNCT
ma-115	56	19	both	both	PRON
ma-115	56	20	transforms	transform	VERB
ma-115	56	21	(	(	PUNCT
ma-115	56	22	1)and	1)and	NUM
ma-115	56	23	(	(	PUNCT
ma-115	56	24	2	2	NUM
ma-115	56	25	)	)	PUNCT
ma-115	56	26	are	be	AUX
ma-115	56	27	self	self	NOUN
ma-115	56	28	reciprocal	reciprocal	ADJ
ma-115	56	29	.	.	PUNCT
ma-115	57	1	h−1	h−1	PROPN
ma-115	57	2	1,α−β,−2(α+β	1,α−β,−2(α+β	NUM
ma-115	57	3	)	)	PUNCT
ma-115	57	4	=	=	SYM
ma-115	57	5	h1,α−β,−2(α+β	h1,α−β,−2(α+β	NOUN
ma-115	57	6	)	)	PUNCT
ma-115	57	7	,	,	PUNCT
ma-115	57	8	h−1	h−1	PROPN
ma-115	57	9	2,α−β,−2(α+β	2,α−β,−2(α+β	NUM
ma-115	57	10	)	)	PUNCT
ma-115	57	11	=	=	PUNCT
ma-115	57	12	h2,α−β,−2(α+β	h2,α−β,−2(α+β	NOUN
ma-115	57	13	)	)	PUNCT
ma-115	57	14	.	.	PUNCT
ma-115	58	1	(	(	PUNCT
ma-115	58	2	3	3	X
ma-115	58	3	)	)	PUNCT
ma-115	58	4	interestingly	interestingly	ADV
ma-115	58	5	,	,	PUNCT
ma-115	58	6	the	the	DET
ma-115	58	7	adjoint	adjoint	NOUN
ma-115	58	8	operator	operator	NOUN
ma-115	58	9	of	of	ADP
ma-115	58	10	h1,α−β,−2(α+β	h1,α−β,−2(α+β	NOUN
ma-115	58	11	)	)	PUNCT
ma-115	58	12	is	be	AUX
ma-115	58	13	h2,α−β,−2(α+β	h2,α−β,−2(α+β	VERB
ma-115	58	14	)	)	PUNCT
ma-115	58	15	and	and	CCONJ
ma-115	58	16	so	so	ADV
ma-115	58	17	h∗1,α−β,−2(α+β	h∗1,α−β,−2(α+β	NOUN
ma-115	58	18	)	)	PUNCT
ma-115	58	19	=	=	PRON
ma-115	59	1	h2,α−β,−2(α+β	h2,α−β,−2(α+β	NOUN
ma-115	59	2	)	)	PUNCT
ma-115	59	3	,	,	PUNCT
ma-115	59	4	h∗2,α−β,−2(α+β	h∗2,α−β,−2(α+β	PROPN
ma-115	59	5	)	)	PUNCT
ma-115	59	6	=	=	SYM
ma-115	59	7	h1,α−β,−2(α+β	h1,α−β,−2(α+β	NOUN
ma-115	59	8	)	)	PUNCT
ma-115	59	9	.	.	PUNCT
ma-115	60	1	(	(	PUNCT
ma-115	60	2	4	4	X
ma-115	60	3	)	)	PUNCT
ma-115	60	4	also	also	ADV
ma-115	60	5	one	one	PRON
ma-115	60	6	can	can	AUX
ma-115	60	7	prove	prove	VERB
ma-115	60	8	for	for	ADP
ma-115	60	9	the	the	DET
ma-115	60	10	operator	operator	NOUN
ma-115	60	11	h1,α−β,−2(α+β	h1,α−β,−2(α+β	NOUN
ma-115	60	12	)	)	PUNCT
ma-115	60	13	and	and	CCONJ
ma-115	60	14	h2,α−β,−2(α+β	h2,α−β,−2(α+β	VERB
ma-115	60	15	)	)	PUNCT
ma-115	60	16	the	the	DET
ma-115	60	17	parsevel	parsevel	ADJ
ma-115	60	18	equalities	equality	NOUN
ma-115	60	19	[	[	X
ma-115	60	20	12]∫	12]∫	NUM
ma-115	60	21	∞	∞	NUM
ma-115	60	22	0	0	PUNCT
ma-115	61	1	x−1	x−1	PROPN
ma-115	61	2	+	+	PROPN
ma-115	61	3	4(α+β	4(α+β	PROPN
ma-115	61	4	)	)	PUNCT
ma-115	61	5	f	f	PROPN
ma-115	61	6	∗(x	∗(x	PROPN
ma-115	61	7	)	)	PUNCT
ma-115	61	8	g(x)dx	g(x)dx	PART
ma-115	62	1	=	=	PUNCT
ma-115	62	2	∫	∫	PROPN
ma-115	62	3	∞	∞	PROPN
ma-115	62	4	0	0	PUNCT
ma-115	63	1	x−1	x−1	PROPN
ma-115	63	2	+	+	PROPN
ma-115	63	3	4(α+β	4(α+β	PROPN
ma-115	63	4	)	)	PUNCT
ma-115	63	5	f̃	f̃	PROPN
ma-115	63	6	∗1,α−β,−2(α+β	∗1,α−β,−2(α+β	NOUN
ma-115	63	7	)	)	PUNCT
ma-115	63	8	g̃1,α−β,−2(α+β)(x)dx,∫	g̃1,α−β,−2(α+β)(x)dx,∫	NOUN
ma-115	63	9	∞	∞	PROPN
ma-115	63	10	0	0	NUM
ma-115	63	11	x1−4(α+β	x1−4(α+β	PROPN
ma-115	63	12	)	)	PUNCT
ma-115	63	13	f	f	PROPN
ma-115	63	14	∗(x	∗(x	PROPN
ma-115	63	15	)	)	PUNCT
ma-115	63	16	g(x)dx	g(x)dx	PART
ma-115	63	17	=	=	PUNCT
ma-115	64	1	∫	∫	PROPN
ma-115	64	2	∞	∞	PROPN
ma-115	64	3	0	0	NUM
ma-115	64	4	x1−4(α+β	x1−4(α+β	PROPN
ma-115	64	5	)	)	PUNCT
ma-115	64	6	f̃	f̃	PROPN
ma-115	64	7	∗2,α−β,−2(α+β	∗2,α−β,−2(α+β	NOUN
ma-115	64	8	)	)	PUNCT
ma-115	64	9	g̃2,α−β,−2(α+β)(x)dx	g̃2,α−β,−2(α+β)(x)dx	NOUN
ma-115	64	10	(	(	PUNCT
ma-115	64	11	5	5	X
ma-115	64	12	)	)	PUNCT
ma-115	64	13	both	both	PRON
ma-115	64	14	containing	contain	VERB
ma-115	64	15	a	a	DET
ma-115	64	16	weight	weight	NOUN
ma-115	64	17	function	function	NOUN
ma-115	64	18	i.e.	i.e.	X
ma-115	64	19	x−1	x−1	X
ma-115	64	20	+	+	PROPN
ma-115	64	21	4(α+β	4(α+β	NUM
ma-115	64	22	)	)	PUNCT
ma-115	64	23	and	and	CCONJ
ma-115	64	24	x1−4(α+β	x1−4(α+β	NOUN
ma-115	64	25	)	)	PUNCT
ma-115	64	26	respectively	respectively	ADV
ma-115	64	27	.	.	PUNCT
ma-115	65	1	a	a	DET
ma-115	65	2	mixed	mixed	ADJ
ma-115	65	3	parsevelrelation	parsevelrelation	NOUN
ma-115	65	4	holds	hold	VERB
ma-115	65	5	as	as	ADV
ma-115	65	6	well	well	ADV
ma-115	65	7	,	,	PUNCT
ma-115	65	8	which	which	PRON
ma-115	65	9	writes	write	VERB
ma-115	65	10	as∫	as∫	PROPN
ma-115	65	11	∞	∞	PROPN
ma-115	65	12	0	0	PUNCT
ma-115	65	13	f	f	PROPN
ma-115	65	14	∗(x	∗(x	PROPN
ma-115	65	15	)	)	PUNCT
ma-115	65	16	g(x)dx	g(x)dx	PART
ma-115	66	1	=	=	PUNCT
ma-115	66	2	∫	∫	PROPN
ma-115	66	3	∞	∞	NUM
ma-115	66	4	0	0	NUM
ma-115	67	1	f̃	f̃	PROPN
ma-115	67	2	∗2,α−β,−2(α+β	∗2,α−β,−2(α+β	NOUN
ma-115	67	3	)	)	PUNCT
ma-115	67	4	g̃2,α−β,−2(α+β)(x)dx	g̃2,α−β,−2(α+β)(x)dx	PROPN
ma-115	67	5	.	.	PUNCT
ma-115	68	1	(	(	PUNCT
ma-115	68	2	6	6	X
ma-115	68	3	)	)	PUNCT
ma-115	68	4	note	note	NOUN
ma-115	68	5	that	that	SCONJ
ma-115	68	6	it	it	PRON
ma-115	68	7	does	do	AUX
ma-115	68	8	not	not	PART
ma-115	68	9	contain	contain	VERB
ma-115	68	10	any	any	DET
ma-115	68	11	weight	weight	NOUN
ma-115	68	12	function	function	NOUN
ma-115	68	13	and	and	CCONJ
ma-115	68	14	involves	involve	VERB
ma-115	68	15	both	both	PRON
ma-115	68	16	transforms	transform	VERB
ma-115	68	17	[	[	X
ma-115	68	18	12].relations	12].relation	NOUN
ma-115	68	19	(	(	PUNCT
ma-115	68	20	4	4	NUM
ma-115	68	21	)	)	PUNCT
ma-115	68	22	and	and	CCONJ
ma-115	68	23	(	(	PUNCT
ma-115	68	24	6	6	X
ma-115	68	25	)	)	PUNCT
ma-115	68	26	express	express	VERB
ma-115	68	27	the	the	DET
ma-115	68	28	complementary	complementary	ADJ
ma-115	68	29	of	of	ADP
ma-115	68	30	(	(	PUNCT
ma-115	68	31	1	1	NUM
ma-115	68	32	)	)	PUNCT
ma-115	68	33	and	and	CCONJ
ma-115	68	34	(	(	PUNCT
ma-115	68	35	2).for	2).for	NUM
ma-115	68	36	α+	α+	X
ma-115	68	37	β	β	X
ma-115	68	38	=	=	SYM
ma-115	68	39	1	1	NUM
ma-115	68	40	4	4	NUM
ma-115	68	41	,	,	PUNCT
ma-115	68	42	we	we	PRON
ma-115	68	43	recover	recover	VERB
ma-115	68	44	the	the	DET
ma-115	68	45	conventional	conventional	ADJ
ma-115	68	46	hankel	hankel	NOUN
ma-115	68	47	type	type	NOUN
ma-115	68	48	transform	transform	NOUN
ma-115	68	49	of	of	ADP
ma-115	68	50	bessel	bessel	ADJ
ma-115	68	51	order	order	NOUN
ma-115	68	52	α−	α−	ADP
ma-115	68	53	β	β	NOUN
ma-115	68	54	;	;	PUNCT
ma-115	68	55	ĥ1,α−β,−1	ĥ1,α−β,−1	ADV
ma-115	68	56	2	2	NUM
ma-115	68	57	=	=	SYM
ma-115	68	58	ĥ2,α−β,−1	ĥ2,α−β,−1	NOUN
ma-115	68	59	2	2	NUM
ma-115	68	60	≡	≡	PROPN
ma-115	68	61	ĥα−β	ĥα−β	X
ma-115	68	62	with	with	ADP
ma-115	68	63	[	[	PUNCT
ma-115	68	64	ĥα−β,−2(α+β)f	ĥα−β,−2(α+β)f	NOUN
ma-115	68	65	]	]	X
ma-115	68	66	(	(	PUNCT
ma-115	68	67	y	y	NOUN
ma-115	68	68	)	)	PUNCT
ma-115	68	69	≡	≡	PROPN
ma-115	68	70	f̃α−β(y	f̃α−β(y	PROPN
ma-115	68	71	)	)	PUNCT
ma-115	68	72	=	=	SYM
ma-115	69	1	∫	∫	PROPN
ma-115	69	2	∞	∞	NUM
ma-115	69	3	0	0	NUM
ma-115	70	1	(	(	PUNCT
ma-115	70	2	xy)2(α+β)jα−β(xy)f	xy)2(α+β)jα−β(xy)f	NOUN
ma-115	70	3	(	(	PUNCT
ma-115	70	4	x)dx	x)dx	PROPN
ma-115	70	5	=	=	SYM
ma-115	70	6	∫	∫	PROPN
ma-115	71	1	∞	∞	PROPN
ma-115	71	2	0	0	NUM
ma-115	72	1	kα	kα	PROPN
ma-115	72	2	,	,	PUNCT
ma-115	72	3	β(x	β(x	NOUN
ma-115	72	4	,	,	PUNCT
ma-115	72	5	y)f	y)f	NOUN
ma-115	72	6	(	(	PUNCT
ma-115	72	7	x)dx	x)dx	PROPN
ma-115	72	8	(	(	PUNCT
ma-115	72	9	7	7	X
ma-115	72	10	)	)	PUNCT
ma-115	72	11	the	the	DET
ma-115	72	12	latter	latter	ADJ
ma-115	72	13	expressing	express	VERB
ma-115	72	14	the	the	DET
ma-115	72	15	transform	transform	NOUN
ma-115	72	16	in	in	ADP
ma-115	72	17	terms	term	NOUN
ma-115	72	18	of	of	ADP
ma-115	72	19	the	the	DET
ma-115	72	20	kernel	kernel	NOUN
ma-115	72	21	kα	kα	PROPN
ma-115	72	22	,	,	PUNCT
ma-115	72	23	β(x	β(x	PROPN
ma-115	72	24	,	,	PUNCT
ma-115	72	25	y	y	NOUN
ma-115	72	26	)	)	PUNCT
ma-115	72	27	=	=	PUNCT
ma-115	72	28	(	(	PUNCT
ma-115	72	29	xy)2(α+β	xy)2(α+β	NUM
ma-115	72	30	)	)	PUNCT
ma-115	72	31	jα−β(xy	jα−β(xy	ADJ
ma-115	72	32	)	)	PUNCT
ma-115	73	1	=	=	SYM
ma-115	73	2	kα	kα	PROPN
ma-115	73	3	,	,	PUNCT
ma-115	73	4	β(y	β(y	PROPN
ma-115	73	5	,	,	PUNCT
ma-115	73	6	x).now	x).now	PROPN
ma-115	73	7	we	we	PRON
ma-115	73	8	evidence	evidence	VERB
ma-115	73	9	the	the	DET
ma-115	73	10	similarity	similarity	NOUN
ma-115	73	11	transformations	transformation	NOUN
ma-115	73	12	like	like	ADP
ma-115	73	13	structure	structure	NOUN
ma-115	73	14	of	of	ADP
ma-115	73	15	the	the	DET
ma-115	73	16	transforms	transform	NOUN
ma-115	73	17	(	(	PUNCT
ma-115	73	18	1	1	NUM
ma-115	73	19	)	)	PUNCT
ma-115	73	20	and	and	CCONJ
ma-115	73	21	(	(	PUNCT
ma-115	73	22	2	2	NUM
ma-115	73	23	)	)	PUNCT
ma-115	73	24	,	,	PUNCT
ma-115	73	25	beingindeed	beingindeed	VERB
ma-115	73	26	[	[	PUNCT
ma-115	73	27	ĥ1,α−β,−2(α+β)f	ĥ1,α−β,−2(α+β)f	NOUN
ma-115	73	28	]	]	PUNCT
ma-115	73	29	(	(	PUNCT
ma-115	73	30	y	y	NOUN
ma-115	73	31	)	)	PUNCT
ma-115	73	32	=	=	SYM
ma-115	74	1	(	(	PUNCT
ma-115	74	2	y)−2(α+β)+1/2	y)−2(α+β)+1/2	PROPN
ma-115	74	3	∫	∫	PROPN
ma-115	74	4	∞	∞	PROPN
ma-115	74	5	0	0	NUM
ma-115	75	1	(	(	PUNCT
ma-115	75	2	x)2(α+β)−1/2	x)2(α+β)−1/2	PROPN
ma-115	75	3	kα	kα	PROPN
ma-115	75	4	,	,	PUNCT
ma-115	75	5	β(x	β(x	PROPN
ma-115	75	6	,	,	PUNCT
ma-115	75	7	y	y	NOUN
ma-115	75	8	)	)	PUNCT
ma-115	75	9	f	f	NOUN
ma-115	76	1	(	(	PUNCT
ma-115	76	2	x)dx	x)dx	PROPN
ma-115	76	3	=	=	SYM
ma-115	76	4	(	(	PUNCT
ma-115	76	5	y)−2(α+β)+1/2	y)−2(α+β)+1/2	PROPN
ma-115	76	6	[	[	PUNCT
ma-115	76	7	ĥα	ĥα	NOUN
ma-115	76	8	,	,	PUNCT
ma-115	76	9	β(x)2(α+β)−1/2f	β(x)2(α+β)−1/2f	NUM
ma-115	76	10	]	]	PUNCT
ma-115	76	11	(	(	PUNCT
ma-115	76	12	y	y	NOUN
ma-115	76	13	)	)	PUNCT
ma-115	76	14	[	[	PUNCT
ma-115	76	15	ĥ2,α−β,−2(α+β)f	ĥ2,α−β,−2(α+β)f	NOUN
ma-115	76	16	]	]	PUNCT
ma-115	76	17	(	(	PUNCT
ma-115	76	18	y	y	NOUN
ma-115	76	19	)	)	PUNCT
ma-115	76	20	=	=	PRON
ma-115	76	21	(	(	PUNCT
ma-115	76	22	y)2(α+β)−1/2	y)2(α+β)−1/2	PROPN
ma-115	76	23	∫	∫	PROPN
ma-115	76	24	∞	∞	PROPN
ma-115	76	25	0	0	NUM
ma-115	76	26	(	(	PUNCT
ma-115	76	27	x)−2(α+β)+1/2	x)−2(α+β)+1/2	PROPN
ma-115	76	28	kα	kα	PROPN
ma-115	76	29	,	,	PUNCT
ma-115	76	30	β(x	β(x	NOUN
ma-115	76	31	,	,	PUNCT
ma-115	76	32	y	y	NOUN
ma-115	76	33	)	)	PUNCT
ma-115	76	34	f	f	NOUN
ma-115	77	1	(	(	PUNCT
ma-115	77	2	x)dx	x)dx	PROPN
ma-115	77	3	=	=	SYM
ma-115	77	4	(	(	PUNCT
ma-115	77	5	y)2(α+β)−1/2	y)2(α+β)−1/2	PROPN
ma-115	77	6	[	[	PUNCT
ma-115	77	7	ĥα	ĥα	NOUN
ma-115	77	8	,	,	PUNCT
ma-115	77	9	β(x)−2(α+β)+1/2f	β(x)−2(α+β)+1/2f	NOUN
ma-115	77	10	]	]	PUNCT
ma-115	77	11	(	(	PUNCT
ma-115	77	12	y	y	NOUN
ma-115	77	13	)	)	PUNCT
ma-115	77	14	(	(	PUNCT
ma-115	77	15	8)	8)	NUM
ma-115	77	16	https://doi.org/10.28924/ada/ma.3.6	https://doi.org/10.28924/ada/ma.3.6	PROPN
ma-115	77	17	eur	eur	NOUN
ma-115	77	18	.	.	PUNCT
ma-115	78	1	j.	j.	PROPN
ma-115	78	2	math	math	PROPN
ma-115	78	3	.	.	PUNCT
ma-115	79	1	anal	anal	PROPN
ma-115	79	2	.	.	PUNCT
ma-115	80	1	10.28924	10.28924	NUM
ma-115	80	2	/	/	SYM
ma-115	80	3	ada	ada	PROPN
ma-115	80	4	/	/	SYM
ma-115	80	5	ma.3.6	ma.3.6	PROPN
ma-115	80	6	4and	4and	PROPN
ma-115	80	7	so	so	ADV
ma-115	80	8	for	for	ADP
ma-115	80	9	the	the	DET
ma-115	80	10	kernels	kernel	NOUN
ma-115	80	11	k1,α−β,−2(α+β)(x	k1,α−β,−2(α+β)(x	PROPN
ma-115	80	12	,	,	PUNCT
ma-115	80	13	y	y	PROPN
ma-115	80	14	)	)	PUNCT
ma-115	80	15	=	=	SYM
ma-115	80	16	(	(	PUNCT
ma-115	80	17	y)−2(α+β)+1/2	y)−2(α+β)+1/2	PROPN
ma-115	80	18	kα	kα	PROPN
ma-115	80	19	,	,	PUNCT
ma-115	80	20	β(x	β(x	NOUN
ma-115	80	21	,	,	PUNCT
ma-115	81	1	y)x2(α+β)−1/2	y)x2(α+β)−1/2	PROPN
ma-115	81	2	=	=	SYM
ma-115	81	3	k2,α−β,−2(α+β)(y	k2,α−β,−2(α+β)(y	NOUN
ma-115	81	4	,	,	PUNCT
ma-115	81	5	x	x	NOUN
ma-115	81	6	)	)	PUNCT
ma-115	81	7	.	.	PUNCT
ma-115	82	1	it	it	PRON
ma-115	82	2	can	can	AUX
ma-115	82	3	be	be	AUX
ma-115	82	4	easily	easily	ADV
ma-115	82	5	verified	verify	VERB
ma-115	82	6	that	that	SCONJ
ma-115	82	7	[	[	X
ma-115	82	8	6	6	NUM
ma-115	82	9	,	,	PUNCT
ma-115	82	10	11	11	NUM
ma-115	82	11	]	]	X
ma-115	82	12	[	[	PUNCT
ma-115	82	13	ĥ1,α−β,−2(α+β	ĥ1,α−β,−2(α+β	NOUN
ma-115	82	14	)	)	PUNCT
ma-115	82	15	b̂∗α−β,−2(α+β)f	b̂∗α−β,−2(α+β)f	NOUN
ma-115	82	16	]	]	PUNCT
ma-115	82	17	(	(	PUNCT
ma-115	82	18	y	y	NOUN
ma-115	82	19	)	)	PUNCT
ma-115	82	20	=	=	SYM
ma-115	82	21	−y2	−y2	PROPN
ma-115	82	22	[	[	PUNCT
ma-115	82	23	ĥ1,α−β,−2(α+β)f	ĥ1,α−β,−2(α+β)f	NOUN
ma-115	82	24	]	]	PUNCT
ma-115	82	25	(	(	PUNCT
ma-115	82	26	y	y	NOUN
ma-115	82	27	)	)	PUNCT
ma-115	82	28	[	[	PUNCT
ma-115	82	29	ĥ2,α−β,−2(α+β	ĥ2,α−β,−2(α+β	NOUN
ma-115	82	30	)	)	PUNCT
ma-115	82	31	b̂α−β,−2(α+β)f	b̂α−β,−2(α+β)f	PROPN
ma-115	82	32	]	]	PUNCT
ma-115	82	33	(	(	PUNCT
ma-115	82	34	y	y	NOUN
ma-115	82	35	)	)	PUNCT
ma-115	82	36	=	=	SYM
ma-115	82	37	−y2	−y2	PROPN
ma-115	82	38	[	[	PUNCT
ma-115	82	39	ĥ2,α−β,−2(α+β)f	ĥ2,α−β,−2(α+β)f	NOUN
ma-115	82	40	]	]	X
ma-115	82	41	(	(	PUNCT
ma-115	82	42	y	y	NOUN
ma-115	82	43	)	)	PUNCT
ma-115	82	44	(	(	PUNCT
ma-115	82	45	9	9	X
ma-115	82	46	)	)	PUNCT
ma-115	82	47	where	where	SCONJ
ma-115	82	48	b̂α−β,−2(α+β	b̂α−β,−2(α+β	NOUN
ma-115	82	49	)	)	PUNCT
ma-115	82	50	is	be	AUX
ma-115	82	51	the	the	DET
ma-115	82	52	bessel	bessel	ADJ
ma-115	82	53	type	type	NOUN
ma-115	82	54	differential	differential	NOUN
ma-115	82	55	operator	operator	NOUN
ma-115	82	56	b̂α−β,−2(α+β	b̂α−β,−2(α+β	NOUN
ma-115	82	57	)	)	PUNCT
ma-115	82	58	=	=	PUNCT
ma-115	82	59	xα+3β−1	xα+3β−1	PUNCT
ma-115	82	60	dxx	dxx	NOUN
ma-115	82	61	2(α−β)+1	2(α−β)+1	PROPN
ma-115	82	62	dxx	dxx	NOUN
ma-115	82	63	−3α−β	−3α−β	PUNCT
ma-115	83	1	=	=	PUNCT
ma-115	84	1	d2x	d2x	X
ma-115	84	2	+	+	CCONJ
ma-115	85	1	[	[	X
ma-115	85	2	1−	1−	NUM
ma-115	85	3	4(α+	4(α+	NUM
ma-115	85	4	β	β	NOUN
ma-115	85	5	)	)	PUNCT
ma-115	85	6	]	]	PUNCT
ma-115	85	7	1	1	NUM
ma-115	85	8	x	x	SYM
ma-115	85	9	dx	dx	PROPN
ma-115	85	10	+	+	CCONJ
ma-115	85	11	(	(	PUNCT
ma-115	85	12	3α+	3α+	NUM
ma-115	85	13	β)(α+	β)(α+	NUM
ma-115	85	14	3β	3β	NUM
ma-115	85	15	)	)	PUNCT
ma-115	86	1	x2	x2	PROPN
ma-115	86	2	(	(	PUNCT
ma-115	86	3	10	10	NUM
ma-115	86	4	)	)	PUNCT
ma-115	86	5	whose	whose	DET
ma-115	86	6	adjoint	adjoint	NOUN
ma-115	86	7	is	be	AUX
ma-115	86	8	then	then	ADV
ma-115	86	9	b̂∗α−β,−2(α+β	b̂∗α−β,−2(α+β	NOUN
ma-115	86	10	)	)	PUNCT
ma-115	86	11	=	=	SYM
ma-115	87	1	x−3α−β	x−3α−β	PROPN
ma-115	87	2	dxx	dxx	PROPN
ma-115	87	3	2(α−β)+1	2(α−β)+1	PROPN
ma-115	87	4	dxx	dxx	NOUN
ma-115	87	5	α+3β−1	α+3β−1	ADV
ma-115	87	6	=	=	PUNCT
ma-115	87	7	d2x	d2x	PROPN
ma-115	88	1	+	+	CCONJ
ma-115	88	2	[	[	X
ma-115	88	3	4(α+	4(α+	X
ma-115	88	4	β)−	β)−	PROPN
ma-115	88	5	1	1	NUM
ma-115	88	6	]	]	SYM
ma-115	88	7	1	1	NUM
ma-115	88	8	x	x	SYM
ma-115	88	9	dx	dx	PROPN
ma-115	88	10	+	+	CCONJ
ma-115	88	11	(	(	PUNCT
ma-115	88	12	α+	α+	PROPN
ma-115	88	13	3β	3β	NUM
ma-115	88	14	−	−	PROPN
ma-115	89	1	1)(3α+	1)(3α+	NUM
ma-115	89	2	β	β	NOUN
ma-115	89	3	−	−	NOUN
ma-115	89	4	1	1	X
ma-115	89	5	)	)	PUNCT
ma-115	89	6	x2	x2	NOUN
ma-115	89	7	(	(	PUNCT
ma-115	89	8	11	11	NUM
ma-115	89	9	)	)	PUNCT
ma-115	89	10	notice	notice	VERB
ma-115	89	11	that	that	SCONJ
ma-115	89	12	for	for	ADP
ma-115	89	13	α+	α+	PRON
ma-115	89	14	β	β	NOUN
ma-115	89	15	=	=	SYM
ma-115	89	16	1	1	NUM
ma-115	89	17	4	4	NUM
ma-115	89	18	both	both	DET
ma-115	89	19	operators	operator	NOUN
ma-115	89	20	turn	turn	VERB
ma-115	89	21	into	into	ADP
ma-115	89	22	the	the	DET
ma-115	89	23	self	self	NOUN
ma-115	89	24	-	-	PUNCT
ma-115	89	25	adjoint	adjoint	NOUN
ma-115	89	26	operator	operator	NOUN
ma-115	89	27	b̂α	b̂α	NOUN
ma-115	89	28	,	,	PUNCT
ma-115	89	29	β	β	X
ma-115	89	30	,	,	PUNCT
ma-115	89	31	being	be	AUX
ma-115	89	32	b̂α−β,−	b̂α−β,−	VERB
ma-115	89	33	1	1	NUM
ma-115	89	34	2	2	NUM
ma-115	89	35	=	=	SYM
ma-115	89	36	b̂∗	b̂∗	X
ma-115	89	37	α−β,−	α−β,−	NUM
ma-115	89	38	1	1	NUM
ma-115	89	39	2	2	NUM
ma-115	89	40	=	=	SYM
ma-115	90	1	d2x	d2x	PROPN
ma-115	90	2	+	+	CCONJ
ma-115	90	3	64αβ	64αβ	NOUN
ma-115	91	1	+	+	CCONJ
ma-115	91	2	3	3	NUM
ma-115	91	3	16	16	NUM
ma-115	91	4	x2	x2	PROPN
ma-115	91	5	≡	≡	PROPN
ma-115	91	6	b̂α−β	b̂α−β	PROPN
ma-115	91	7	.	.	PUNCT
ma-115	92	1	(	(	PUNCT
ma-115	92	2	12	12	NUM
ma-115	92	3	)	)	PUNCT
ma-115	92	4	from	from	ADP
ma-115	92	5	(	(	PUNCT
ma-115	92	6	9	9	X
ma-115	92	7	)	)	PUNCT
ma-115	92	8	it	it	PRON
ma-115	92	9	follows	follow	VERB
ma-115	92	10	,	,	PUNCT
ma-115	92	11	for	for	ADP
ma-115	92	12	instance	instance	NOUN
ma-115	92	13	,	,	PUNCT
ma-115	92	14	that	that	SCONJ
ma-115	92	15	the	the	DET
ma-115	92	16	solution	solution	NOUN
ma-115	92	17	of	of	ADP
ma-115	92	18	the	the	DET
ma-115	92	19	differential	differential	ADJ
ma-115	92	20	equation	equation	NOUN
ma-115	92	21	[	[	X
ma-115	92	22	6	6	NUM
ma-115	92	23	,	,	PUNCT
ma-115	92	24	11	11	NUM
ma-115	92	25	]	]	PUNCT
ma-115	92	26	.	.	PUNCT
ma-115	93	1	k	k	PROPN
ma-115	93	2	∂	∂	PROPN
ma-115	93	3	∂τ	∂τ	PROPN
ma-115	93	4	h(x	h(x	PROPN
ma-115	93	5	,	,	PUNCT
ma-115	93	6	τ	τ	PROPN
ma-115	93	7	)	)	PUNCT
ma-115	93	8	=	=	SYM
ma-115	93	9	b̂∗α−β,−2(α+β	b̂∗α−β,−2(α+β	NOUN
ma-115	93	10	)	)	PUNCT
ma-115	93	11	(	(	PUNCT
ma-115	93	12	13	13	NUM
ma-115	93	13	)	)	PUNCT
ma-115	93	14	satisfying	satisfy	VERB
ma-115	93	15	the	the	DET
ma-115	93	16	initial	initial	ADJ
ma-115	93	17	condition	condition	NOUN
ma-115	93	18	h(x	h(x	PROPN
ma-115	93	19	,	,	PUNCT
ma-115	93	20	0	0	NUM
ma-115	93	21	)	)	PUNCT
ma-115	93	22	=	=	SYM
ma-115	94	1	f	f	X
ma-115	94	2	(	(	PUNCT
ma-115	94	3	x	x	X
ma-115	94	4	)	)	PUNCT
ma-115	94	5	can	can	AUX
ma-115	94	6	be	be	AUX
ma-115	94	7	written	write	VERB
ma-115	94	8	into	into	ADP
ma-115	94	9	the	the	DET
ma-115	94	10	transform	transform	NOUN
ma-115	94	11	conjugate	conjugate	ADJ
ma-115	94	12	y	y	NOUN
ma-115	94	13	-	-	PUNCT
ma-115	94	14	space	space	NOUN
ma-115	94	15	as	as	ADP
ma-115	94	16	ĥ1,α−β,−2(α+β)(y	ĥ1,α−β,−2(α+β)(y	PROPN
ma-115	94	17	,	,	PUNCT
ma-115	94	18	τ	τ	X
ma-115	94	19	)	)	PUNCT
ma-115	94	20	=	=	PUNCT
ma-115	95	1	e−	e−	PROPN
ma-115	95	2	y2	y2	PROPN
ma-115	95	3	kτ	kτ	PROPN
ma-115	95	4	f̂1,α	f̂1,α	PROPN
ma-115	95	5	,	,	PUNCT
ma-115	95	6	β(y	β(y	NOUN
ma-115	95	7	)	)	PUNCT
ma-115	95	8	for	for	ADP
ma-115	95	9	any	any	DET
ma-115	95	10	value	value	NOUN
ma-115	95	11	of	of	ADP
ma-115	95	12	the	the	DET
ma-115	95	13	arbitrary	arbitrary	ADJ
ma-115	95	14	constant	constant	ADJ
ma-115	95	15	k	k	PROPN
ma-115	95	16	.	.	PUNCT
ma-115	96	1	then	then	ADV
ma-115	96	2	transformingback	transformingback	VERB
ma-115	96	3	to	to	ADP
ma-115	96	4	the	the	DET
ma-115	96	5	x	x	NOUN
ma-115	96	6	-	-	NOUN
ma-115	96	7	space	space	NOUN
ma-115	96	8	,	,	PUNCT
ma-115	96	9	one	one	PRON
ma-115	96	10	obtains	obtain	VERB
ma-115	96	11	h(x	h(x	PROPN
ma-115	96	12	,	,	PUNCT
ma-115	96	13	τ	τ	X
ma-115	96	14	)	)	PUNCT
ma-115	96	15	=	=	SYM
ma-115	96	16	k	k	PROPN
ma-115	96	17	2τ	2τ	PROPN
ma-115	96	18	x1−4(α+β	x1−4(α+β	PROPN
ma-115	96	19	)	)	PUNCT
ma-115	96	20	∫	∫	PROPN
ma-115	97	1	∞	∞	PROPN
ma-115	97	2	0	0	NUM
ma-115	97	3	(	(	PUNCT
ma-115	97	4	xy)2(α+β)−	xy)2(α+β)−	PROPN
ma-115	97	5	(	(	PUNCT
ma-115	97	6	k	k	ADJ
ma-115	97	7	4τ	4τ	NOUN
ma-115	97	8	)	)	PUNCT
ma-115	97	9	(	(	PUNCT
ma-115	97	10	x2+y2	x2+y2	NOUN
ma-115	97	11	)	)	PUNCT
ma-115	97	12	iα−β	iα−β	NOUN
ma-115	97	13	(	(	PUNCT
ma-115	97	14	k	k	PROPN
ma-115	97	15	2τ	2τ	NUM
ma-115	97	16	xy	xy	PROPN
ma-115	97	17	)	)	PUNCT
ma-115	98	1	f	f	PROPN
ma-115	98	2	(	(	PUNCT
ma-115	98	3	y)dy	y)dy	PROPN
ma-115	98	4	(	(	PUNCT
ma-115	98	5	14	14	NUM
ma-115	98	6	)	)	PUNCT
ma-115	98	7	under	under	ADP
ma-115	98	8	the	the	DET
ma-115	98	9	condition	condition	NOUN
ma-115	98	10	that	that	SCONJ
ma-115	98	11	|arg(τk	|arg(τk	PROPN
ma-115	98	12	)	)	PUNCT
ma-115	98	13	|	|	ADV
ma-115	98	14	≤	≤	NUM
ma-115	98	15	π	π	PROPN
ma-115	98	16	4	4	NUM
ma-115	98	17	,	,	PUNCT
ma-115	98	18	which	which	PRON
ma-115	98	19	for	for	ADP
ma-115	98	20	both	both	DET
ma-115	98	21	τ	τ	PROPN
ma-115	98	22	and	and	CCONJ
ma-115	98	23	k	k	PROPN
ma-115	98	24	real	real	ADV
ma-115	98	25	turns	turn	VERB
ma-115	98	26	into	into	ADP
ma-115	98	27	τ	τ	PROPN
ma-115	98	28	k	k	X
ma-115	98	29	>	>	X
ma-115	98	30	0	0	NUM
ma-115	98	31	.	.	NOUN
ma-115	99	1	3	3	X
ma-115	99	2	.	.	X
ma-115	99	3	hankel	hankel	NOUN
ma-115	99	4	-	-	PUNCT
ma-115	99	5	type	type	NOUN
ma-115	99	6	transforms	transform	NOUN
ma-115	99	7	of	of	ADP
ma-115	99	8	fractional	fractional	ADJ
ma-115	99	9	order	order	NOUN
ma-115	99	10	:	:	PUNCT
ma-115	99	11	it	it	PRON
ma-115	99	12	is	be	AUX
ma-115	99	13	well	well	ADV
ma-115	99	14	known	know	VERB
ma-115	99	15	that	that	SCONJ
ma-115	99	16	equation	equation	NOUN
ma-115	99	17	(	(	PUNCT
ma-115	99	18	13	13	NUM
ma-115	99	19	)	)	PUNCT
ma-115	99	20	has	have	VERB
ma-115	99	21	the	the	DET
ma-115	99	22	formal	formal	ADJ
ma-115	99	23	solution	solution	NOUN
ma-115	99	24	h(x	h(x	PROPN
ma-115	99	25	,	,	PUNCT
ma-115	99	26	τ	τ	X
ma-115	99	27	)	)	PUNCT
ma-115	99	28	=	=	PUNCT
ma-115	99	29	e	e	PROPN
ma-115	99	30	τ	τ	PROPN
ma-115	99	31	k	k	PROPN
ma-115	99	32	b̂∗α	b̂∗α	PROPN
ma-115	99	33	,	,	PUNCT
ma-115	99	34	βf	βf	PRON
ma-115	99	35	(	(	PUNCT
ma-115	99	36	x	x	NOUN
ma-115	99	37	)	)	PUNCT
ma-115	99	38	.	.	PUNCT
ma-115	100	1	equation(14	equation(14	NOUN
ma-115	100	2	)	)	PUNCT
ma-115	100	3	yields	yield	VERB
ma-115	100	4	an	an	DET
ma-115	100	5	explicit	explicit	ADJ
ma-115	100	6	functional	functional	ADJ
ma-115	100	7	representation	representation	NOUN
ma-115	100	8	of	of	ADP
ma-115	100	9	the	the	DET
ma-115	100	10	exponential	exponential	ADJ
ma-115	100	11	operator	operator	NOUN
ma-115	100	12	eb	eb	PROPN
ma-115	100	13	b̂∗α−β,−2(α+β	b̂∗α−β,−2(α+β	PROPN
ma-115	100	14	)	)	PUNCT
ma-115	100	15	:	:	PUNCT
ma-115	101	1	[	[	PUNCT
ma-115	101	2	e	e	X
ma-115	101	3	b	b	X
ma-115	101	4	b̂∗	b̂∗	X
ma-115	101	5	α−β,−2(α+β	α−β,−2(α+β	NOUN
ma-115	101	6	)	)	PUNCT
ma-115	101	7	]	]	PUNCT
ma-115	102	1	f	f	X
ma-115	102	2	(	(	PUNCT
ma-115	102	3	y	y	NOUN
ma-115	102	4	)	)	PUNCT
ma-115	102	5	=	=	SYM
ma-115	102	6	1	1	NUM
ma-115	102	7	2b	2b	NUM
ma-115	102	8	y1−4(α+β	y1−4(α+β	NOUN
ma-115	102	9	)	)	PUNCT
ma-115	102	10	∫	∫	PROPN
ma-115	103	1	∞	∞	PROPN
ma-115	103	2	0	0	NUM
ma-115	103	3	(	(	PUNCT
ma-115	103	4	xy)2(α+β	xy)2(α+β	NUM
ma-115	103	5	)	)	PUNCT
ma-115	103	6	e−	e−	PROPN
ma-115	103	7	(	(	PUNCT
ma-115	103	8	14b	14b	NUM
ma-115	103	9	)	)	PUNCT
ma-115	103	10	(	(	PUNCT
ma-115	103	11	x2+y2	x2+y2	NOUN
ma-115	103	12	)	)	PUNCT
ma-115	103	13	iα−β	iα−β	NOUN
ma-115	103	14	(	(	PUNCT
ma-115	103	15	xy	xy	PROPN
ma-115	103	16	2b	2b	NUM
ma-115	103	17	)	)	PUNCT
ma-115	103	18	f	f	PROPN
ma-115	104	1	(	(	PUNCT
ma-115	104	2	x)dx	x)dx	PROPN
ma-115	104	3	(	(	PUNCT
ma-115	104	4	15	15	NUM
ma-115	104	5	)	)	PUNCT
ma-115	104	6	where	where	SCONJ
ma-115	104	7	iα−β	iα−β	PROPN
ma-115	104	8	denotes	denote	VERB
ma-115	104	9	the	the	DET
ma-115	104	10	modified	modify	VERB
ma-115	104	11	bessel	bessel	NOUN
ma-115	104	12	function	function	NOUN
ma-115	104	13	of	of	ADP
ma-115	104	14	the	the	DET
ma-115	104	15	first	first	ADJ
ma-115	104	16	kind	kind	NOUN
ma-115	104	17	of	of	ADP
ma-115	104	18	order	order	NOUN
ma-115	104	19	α	α	NOUN
ma-115	104	20	−	−	NOUN
ma-115	104	21	β	β	NOUN
ma-115	104	22	:	:	PUNCT
ma-115	104	23	jα−β(ix	jα−β(ix	X
ma-115	104	24	)	)	PUNCT
ma-115	104	25	=	=	SYM
ma-115	104	26	iα−β	iα−β	PROPN
ma-115	104	27	iα−β(x).in	iα−β(x).in	PROPN
ma-115	104	28	particular	particular	ADJ
ma-115	104	29	,	,	PUNCT
ma-115	104	30	setting	set	VERB
ma-115	104	31	b	b	X
ma-115	104	32	=	=	SYM
ma-115	104	33	i	i	PRON
ma-115	104	34	2	2	NUM
ma-115	104	35	we	we	PRON
ma-115	104	36	obtain	obtain	VERB
ma-115	104	37	a	a	DET
ma-115	104	38	representation	representation	NOUN
ma-115	104	39	of	of	ADP
ma-115	104	40	ĥ1,α−β,−2(α+β	ĥ1,α−β,−2(α+β	NOUN
ma-115	104	41	)	)	PUNCT
ma-115	104	42	in	in	ADP
ma-115	104	43	the	the	DET
ma-115	104	44	form	form	NOUN
ma-115	104	45	of	of	ADP
ma-115	104	46	a	a	DET
ma-115	104	47	symmetricfractional	symmetricfractional	ADJ
ma-115	104	48	product	product	NOUN
ma-115	104	49	of	of	ADP
ma-115	104	50	the	the	DET
ma-115	104	51	exponential	exponential	NOUN
ma-115	104	52	of	of	ADP
ma-115	104	53	the	the	DET
ma-115	104	54	generators	generator	NOUN
ma-115	104	55	of	of	ADP
ma-115	104	56	the	the	DET
ma-115	104	57	su(1	su(1	NOUN
ma-115	104	58	,	,	PUNCT
ma-115	104	59	1	1	X
ma-115	104	60	)	)	PUNCT
ma-115	104	61	algebra	algebra	NOUN
ma-115	104	62	:	:	PUNCT
ma-115	104	63	ĥ1,α−β,−2(α+β	ĥ1,α−β,−2(α+β	NOUN
ma-115	104	64	)	)	PUNCT
ma-115	105	1	=	=	SYM
ma-115	105	2	iα−β+1e−	iα−β+1e−	NOUN
ma-115	105	3	(	(	PUNCT
ma-115	105	4	i	i	NOUN
ma-115	105	5	2	2	X
ma-115	105	6	)	)	PUNCT
ma-115	105	7	x2e	x2e	NOUN
ma-115	106	1	(	(	PUNCT
ma-115	106	2	i	i	NOUN
ma-115	106	3	2	2	X
ma-115	106	4	)	)	PUNCT
ma-115	106	5	b̂∗	b̂∗	NOUN
ma-115	106	6	α−β,−2(α+β)e−	α−β,−2(α+β)e−	NOUN
ma-115	106	7	(	(	PUNCT
ma-115	106	8	i	i	NOUN
ma-115	106	9	2	2	NUM
ma-115	106	10	)	)	PUNCT
ma-115	106	11	x2	x2	NOUN
ma-115	106	12	(	(	PUNCT
ma-115	106	13	16	16	NUM
ma-115	106	14	)	)	PUNCT
ma-115	106	15	https://doi.org/10.28924/ada/ma.3.6	https://doi.org/10.28924/ada/ma.3.6	PROPN
ma-115	106	16	eur	eur	PROPN
ma-115	106	17	.	.	PUNCT
ma-115	107	1	j.	j.	PROPN
ma-115	107	2	math	math	PROPN
ma-115	107	3	.	.	PUNCT
ma-115	108	1	anal	anal	PROPN
ma-115	108	2	.	.	PUNCT
ma-115	109	1	10.28924	10.28924	NUM
ma-115	109	2	/	/	SYM
ma-115	109	3	ada	ada	PROPN
ma-115	109	4	/	/	SYM
ma-115	109	5	ma.3.6	ma.3.6	PROPN
ma-115	109	6	5	5	NUM
ma-115	109	7	in	in	ADP
ma-115	109	8	this	this	DET
ma-115	109	9	connection	connection	NOUN
ma-115	109	10	,	,	PUNCT
ma-115	109	11	we	we	PRON
ma-115	109	12	may	may	AUX
ma-115	109	13	note	note	VERB
ma-115	109	14	that	that	SCONJ
ma-115	109	15	the	the	DET
ma-115	109	16	operators	operator	NOUN
ma-115	109	17	k̂	k̂	X
ma-115	109	18	(	(	PUNCT
ma-115	109	19	1	1	X
ma-115	109	20	)	)	PUNCT
ma-115	109	21	+	+	NOUN
ma-115	110	1	=	=	SYM
ma-115	110	2	1	1	NUM
ma-115	110	3	2	2	NUM
ma-115	110	4	x2	x2	NOUN
ma-115	110	5	,	,	PUNCT
ma-115	110	6	k̂	k̂	X
ma-115	110	7	(	(	PUNCT
ma-115	110	8	1	1	X
ma-115	110	9	)	)	PUNCT
ma-115	110	10	−	−	NOUN
ma-115	111	1	=	=	SYM
ma-115	111	2	−	−	PROPN
ma-115	111	3	1	1	NUM
ma-115	111	4	2	2	NUM
ma-115	111	5	b̂∗α−β,−2(α+β	b̂∗α−β,−2(α+β	NOUN
ma-115	111	6	)	)	PUNCT
ma-115	111	7	,	,	PUNCT
ma-115	111	8	k̂	k̂	X
ma-115	111	9	(	(	PUNCT
ma-115	111	10	1	1	X
ma-115	111	11	)	)	PUNCT
ma-115	111	12	3	3	NUM
ma-115	111	13	=	=	SYM
ma-115	111	14	−	−	NOUN
ma-115	112	1	i	i	PRON
ma-115	112	2	2	2	NUM
ma-115	112	3	(	(	PUNCT
ma-115	112	4	x	x	PROPN
ma-115	112	5	d	d	X
ma-115	112	6	dx	dx	PROPN
ma-115	112	7	+	+	CCONJ
ma-115	112	8	2(α+	2(α+	NUM
ma-115	112	9	β	β	NOUN
ma-115	112	10	)	)	PUNCT
ma-115	112	11	)	)	PUNCT
ma-115	112	12	(	(	PUNCT
ma-115	112	13	17	17	NUM
ma-115	112	14	)	)	PUNCT
ma-115	112	15	conjugate	conjugate	VERB
ma-115	112	16	a	a	DET
ma-115	112	17	non	non	ADJ
ma-115	112	18	self	self	NOUN
ma-115	112	19	-	-	PUNCT
ma-115	112	20	adjoint	adjoint	NOUN
ma-115	112	21	one	one	NUM
ma-115	112	22	variable	variable	ADJ
ma-115	112	23	realization	realization	NOUN
ma-115	112	24	of	of	ADP
ma-115	112	25	the	the	DET
ma-115	112	26	su(1	su(1	NOUN
ma-115	112	27	,	,	PUNCT
ma-115	112	28	1	1	X
ma-115	112	29	)	)	PUNCT
ma-115	112	30	algebra	algebra	NOUN
ma-115	112	31	generators	generator	NOUN
ma-115	112	32	accordingto	accordingto	NOUN
ma-115	112	33	the	the	DET
ma-115	112	34	inherent	inherent	ADJ
ma-115	112	35	commutation	commutation	NOUN
ma-115	112	36	relations	relation	NOUN
ma-115	112	37	[	[	PUNCT
ma-115	112	38	k̂	k̂	X
ma-115	112	39	(	(	PUNCT
ma-115	112	40	1	1	NUM
ma-115	112	41	)	)	PUNCT
ma-115	113	1	+	+	CCONJ
ma-115	113	2	,	,	PUNCT
ma-115	113	3	k̂	k̂	X
ma-115	113	4	(	(	PUNCT
ma-115	113	5	1	1	X
ma-115	113	6	)	)	PUNCT
ma-115	113	7	−	−	NOUN
ma-115	113	8	]	]	PUNCT
ma-115	114	1	=	=	PUNCT
ma-115	114	2	2i	2i	NUM
ma-115	114	3	k̂	k̂	X
ma-115	114	4	(	(	PUNCT
ma-115	114	5	1	1	X
ma-115	114	6	)	)	PUNCT
ma-115	114	7	3	3	NUM
ma-115	114	8	,	,	PUNCT
ma-115	114	9	[	[	PUNCT
ma-115	114	10	k̂	k̂	X
ma-115	114	11	(	(	PUNCT
ma-115	114	12	1	1	X
ma-115	114	13	)	)	PUNCT
ma-115	114	14	±	±	NOUN
ma-115	114	15	,	,	PUNCT
ma-115	114	16	k̂	k̂	X
ma-115	114	17	(	(	PUNCT
ma-115	114	18	1	1	X
ma-115	114	19	)	)	PUNCT
ma-115	114	20	3	3	NUM
ma-115	114	21	]	]	PUNCT
ma-115	114	22	=	=	PUNCT
ma-115	115	1	±i	±i	DET
ma-115	115	2	k̂(1)±	k̂(1)±	NOUN
ma-115	115	3	.	.	PUNCT
ma-115	116	1	(	(	PUNCT
ma-115	116	2	18	18	NUM
ma-115	116	3	)	)	PUNCT
ma-115	116	4	thus	thus	ADV
ma-115	116	5	(	(	PUNCT
ma-115	116	6	16	16	NUM
ma-115	116	7	)	)	PUNCT
ma-115	116	8	can	can	AUX
ma-115	116	9	be	be	AUX
ma-115	116	10	formally	formally	ADV
ma-115	116	11	be	be	AUX
ma-115	116	12	rewritten	rewrite	VERB
ma-115	116	13	in	in	ADP
ma-115	116	14	terms	term	NOUN
ma-115	116	15	of	of	ADP
ma-115	116	16	the	the	DET
ma-115	116	17	operators	operator	NOUN
ma-115	116	18	k̂(1)+	k̂(1)+	PROPN
ma-115	116	19	and	and	CCONJ
ma-115	116	20	k̂(1)−	k̂(1)−	PROPN
ma-115	116	21	,	,	PUNCT
ma-115	116	22	and	and	CCONJ
ma-115	116	23	further	far	ADV
ma-115	116	24	recastin	recastin	VERB
ma-115	116	25	the	the	DET
ma-115	116	26	single	single	ADJ
ma-115	116	27	exponential	exponential	ADJ
ma-115	116	28	form	form	NOUN
ma-115	116	29	ĥα−β,−2(α+β	ĥα−β,−2(α+β	NOUN
ma-115	116	30	)	)	PUNCT
ma-115	117	1	=	=	PUNCT
ma-115	118	1	iα−β+1	iα−β+1	ADJ
ma-115	118	2	e−i	e−i	NOUN
ma-115	118	3	π	π	PROPN
ma-115	118	4	2	2	NUM
ma-115	118	5	[	[	PUNCT
ma-115	118	6	k̂	k̂	X
ma-115	118	7	(	(	PUNCT
ma-115	118	8	1	1	NUM
ma-115	118	9	)	)	PUNCT
ma-115	118	10	+	+	CCONJ
ma-115	119	1	+	+	CCONJ
ma-115	119	2	k̂	k̂	X
ma-115	119	3	(	(	PUNCT
ma-115	119	4	1	1	NUM
ma-115	119	5	)	)	PUNCT
ma-115	119	6	−	−	NOUN
ma-115	119	7	]	]	PUNCT
ma-115	119	8	.	.	PUNCT
ma-115	120	1	(	(	PUNCT
ma-115	120	2	19	19	NUM
ma-115	120	3	)	)	PUNCT
ma-115	120	4	this	this	PRON
ma-115	120	5	is	be	AUX
ma-115	120	6	on	on	ADP
ma-115	120	7	account	account	NOUN
ma-115	120	8	of	of	ADP
ma-115	120	9	disentanglement	disentanglement	NOUN
ma-115	120	10	relation	relation	NOUN
ma-115	120	11	for	for	ADP
ma-115	120	12	the	the	DET
ma-115	120	13	su(1	su(1	NOUN
ma-115	120	14	,	,	PUNCT
ma-115	120	15	1	1	X
ma-115	120	16	)	)	PUNCT
ma-115	120	17	algebra	algebra	NOUN
ma-115	120	18	generators	generator	NOUN
ma-115	120	19	e	e	NOUN
ma-115	120	20	−iφ	−iφ	X
ma-115	120	21	[	[	PUNCT
ma-115	120	22	k̂	k̂	X
ma-115	120	23	(	(	PUNCT
ma-115	120	24	1	1	NUM
ma-115	120	25	)	)	PUNCT
ma-115	120	26	+	+	CCONJ
ma-115	121	1	+	+	X
ma-115	121	2	k̂	k̂	X
ma-115	121	3	(	(	PUNCT
ma-115	121	4	1	1	NUM
ma-115	121	5	)	)	PUNCT
ma-115	121	6	−	−	NOUN
ma-115	121	7	]	]	PUNCT
ma-115	122	1	=	=	PUNCT
ma-115	122	2	e−i	e−i	NOUN
ma-115	122	3	tan(φ/2)k̂	tan(φ/2)k̂	PROPN
ma-115	122	4	(	(	PUNCT
ma-115	122	5	1	1	NUM
ma-115	122	6	)	)	PUNCT
ma-115	122	7	+	+	NUM
ma-115	122	8	e−i	e−i	NOUN
ma-115	122	9	sinφk̂	sinφk̂	NOUN
ma-115	122	10	(	(	PUNCT
ma-115	122	11	1	1	NUM
ma-115	122	12	)	)	PUNCT
ma-115	122	13	−	−	NOUN
ma-115	122	14	e−i	e−i	NOUN
ma-115	122	15	tan(φ/2)k̂	tan(φ/2)k̂	X
ma-115	122	16	(	(	PUNCT
ma-115	122	17	1	1	NUM
ma-115	122	18	)	)	PUNCT
ma-115	122	19	+	+	CCONJ
ma-115	122	20	(	(	PUNCT
ma-115	122	21	20	20	X
ma-115	122	22	)	)	PUNCT
ma-115	122	23	holding	hold	VERB
ma-115	122	24	for	for	ADP
ma-115	122	25	−π	−π	PROPN
ma-115	122	26	<	<	X
ma-115	122	27	φ	φ	X
ma-115	122	28	<	<	X
ma-115	122	29	π	π	PROPN
ma-115	122	30	.	.	PUNCT
ma-115	123	1	expressing	express	VERB
ma-115	123	2	(	(	PUNCT
ma-115	123	3	19	19	NUM
ma-115	123	4	)	)	PUNCT
ma-115	123	5	corresponds	correspond	VERB
ma-115	123	6	to	to	ADP
ma-115	123	7	the	the	DET
ma-115	123	8	value	value	NOUN
ma-115	123	9	φ	φ	NOUN
ma-115	123	10	=	=	SYM
ma-115	123	11	(	(	PUNCT
ma-115	123	12	π/2).exploiting	π/2).exploite	VERB
ma-115	123	13	the	the	DET
ma-115	123	14	integral	integral	ADJ
ma-115	123	15	transform	transform	NOUN
ma-115	123	16	representation	representation	NOUN
ma-115	123	17	(	(	PUNCT
ma-115	123	18	15	15	NUM
ma-115	123	19	)	)	PUNCT
ma-115	123	20	of	of	ADP
ma-115	123	21	the	the	DET
ma-115	123	22	centred	centre	VERB
ma-115	123	23	operator	operator	NOUN
ma-115	123	24	in	in	ADP
ma-115	123	25	equation	equation	NOUN
ma-115	123	26	(	(	PUNCT
ma-115	123	27	20	20	NUM
ma-115	123	28	)	)	PUNCT
ma-115	123	29	,	,	PUNCT
ma-115	123	30	weobtain	weobtain	VERB
ma-115	123	31	an	an	DET
ma-115	123	32	expression	expression	NOUN
ma-115	123	33	for	for	ADP
ma-115	123	34	the	the	DET
ma-115	123	35	operator	operator	NOUN
ma-115	123	36	e−iφ[k̂(1)+	e−iφ[k̂(1)+	PROPN
ma-115	124	1	+	+	NOUN
ma-115	124	2	k̂(1)−	k̂(1)−	PROPN
ma-115	124	3	]	]	PUNCT
ma-115	124	4	in	in	ADP
ma-115	124	5	the	the	DET
ma-115	124	6	form	form	NOUN
ma-115	124	7	of	of	ADP
ma-115	124	8	a	a	DET
ma-115	124	9	hankel	hankel	NOUN
ma-115	124	10	-type	-type	NOUN
ma-115	124	11	integral	integral	ADJ
ma-115	124	12	transform.then	transform.then	NOUN
ma-115	124	13	writing	write	VERB
ma-115	124	14	φ	φ	NOUN
ma-115	124	15	=	=	SYM
ma-115	124	16	a(π/2	a(π/2	PROPN
ma-115	124	17	)	)	PUNCT
ma-115	124	18	and	and	CCONJ
ma-115	124	19	multiplying	multiply	VERB
ma-115	124	20	both	both	DET
ma-115	124	21	sides	side	NOUN
ma-115	124	22	by	by	ADP
ma-115	124	23	e	e	PROPN
ma-115	124	24	i(aπ/2)(α−β+1	i(aπ/2)(α−β+1	ADJ
ma-115	124	25	)	)	PUNCT
ma-115	124	26	,	,	PUNCT
ma-115	124	27	one	one	PRON
ma-115	124	28	ends	end	VERB
ma-115	124	29	up	up	ADP
ma-115	124	30	on	on	ADP
ma-115	124	31	the	the	DET
ma-115	124	32	l.h.s.with	l.h.s.with	PROPN
ma-115	124	33	the	the	DET
ma-115	124	34	ath	ath	NOUN
ma-115	124	35	power	power	NOUN
ma-115	124	36	of	of	ADP
ma-115	124	37	the	the	DET
ma-115	124	38	operator	operator	NOUN
ma-115	124	39	iα−β+1e−i	iα−β+1e−i	NOUN
ma-115	125	1	π2	π2	ADV
ma-115	126	1	[	[	X
ma-115	126	2	k̂(1)+	k̂(1)+	PROPN
ma-115	126	3	+	+	PROPN
ma-115	126	4	k̂(1)−	k̂(1)−	PROPN
ma-115	126	5	]	]	PUNCT
ma-115	126	6	and	and	CCONJ
ma-115	126	7	corresponding	correspond	VERB
ma-115	126	8	on	on	ADP
ma-115	126	9	the	the	DET
ma-115	126	10	r.h.s	r.h.s	NOUN
ma-115	126	11	.	.	PUNCT
ma-115	127	1	with	with	ADP
ma-115	127	2	ath	ath	NOUN
ma-115	127	3	power	power	NOUN
ma-115	127	4	of	of	ADP
ma-115	127	5	the	the	DET
ma-115	127	6	first	first	ADJ
ma-115	127	7	hankel	hankel	NOUN
ma-115	127	8	-	-	PUNCT
ma-115	127	9	type	type	NOUN
ma-115	127	10	transform	transform	NOUN
ma-115	127	11	,	,	PUNCT
ma-115	127	12	ĥa1,α−β,−2(α+β	ĥa1,α−β,−2(α+β	NOUN
ma-115	127	13	)	)	PUNCT
ma-115	127	14	,	,	PUNCT
ma-115	127	15	or	or	CCONJ
ma-115	127	16	the	the	DET
ma-115	127	17	first	first	ADJ
ma-115	127	18	hankel	hankel	NOUN
ma-115	127	19	-	-	PUNCT
ma-115	127	20	type	type	NOUN
ma-115	127	21	transform	transform	NOUN
ma-115	127	22	offractional	offractional	ADJ
ma-115	127	23	order	order	NOUN
ma-115	127	24	a.	a.	NOUN
ma-115	127	25	accordingly	accordingly	ADV
ma-115	127	26	,	,	PUNCT
ma-115	127	27	we	we	PRON
ma-115	127	28	can	can	AUX
ma-115	127	29	write	write	VERB
ma-115	127	30	[	[	PUNCT
ma-115	127	31	ĥa1,α−β,−2(α+β)f	ĥa1,α−β,−2(α+β)f	NOUN
ma-115	127	32	]	]	PUNCT
ma-115	127	33	(	(	PUNCT
ma-115	127	34	y	y	NOUN
ma-115	127	35	)	)	PUNCT
ma-115	127	36	=	=	SYM
ma-115	128	1	e	e	X
ma-115	128	2	i(α−β+1)(φ−π/2	i(α−β+1)(φ−π/2	PROPN
ma-115	128	3	)	)	PUNCT
ma-115	128	4	sinφ	sinφ	NOUN
ma-115	128	5	x1−4(α+β	x1−4(α+β	PROPN
ma-115	128	6	)	)	PUNCT
ma-115	128	7	∫	∫	PROPN
ma-115	129	1	∞	∞	PROPN
ma-115	129	2	0	0	NUM
ma-115	129	3	(	(	PUNCT
ma-115	129	4	xy)2(α+β	xy)2(α+β	NUM
ma-115	129	5	)	)	PUNCT
ma-115	130	1	e	e	NOUN
ma-115	130	2	i	i	PRON
ma-115	130	3	2	2	NUM
ma-115	130	4	cotφ[x2+y2	cotφ[x2+y2	NOUN
ma-115	130	5	]	]	PUNCT
ma-115	130	6	jα−β	jα−β	PROPN
ma-115	130	7	(	(	PUNCT
ma-115	130	8	xy	xy	PROPN
ma-115	130	9	sinφ	sinφ	PROPN
ma-115	130	10	)	)	PUNCT
ma-115	131	1	f	f	PROPN
ma-115	132	1	(	(	PUNCT
ma-115	132	2	x)dx	x)dx	PROPN
ma-115	132	3	(	(	PUNCT
ma-115	132	4	21	21	NUM
ma-115	132	5	)	)	PUNCT
ma-115	132	6	=	=	NOUN
ma-115	133	1	[	[	X
ma-115	133	2	e	e	X
ma-115	133	3	iφ(α−β+1	iφ(α−β+1	X
ma-115	133	4	)	)	PUNCT
ma-115	133	5	e	e	NOUN
ma-115	133	6	−iφ	−iφ	X
ma-115	133	7	[	[	PUNCT
ma-115	133	8	k̂	k̂	X
ma-115	133	9	(	(	PUNCT
ma-115	133	10	1	1	NUM
ma-115	133	11	)	)	PUNCT
ma-115	133	12	+	+	CCONJ
ma-115	134	1	+	+	X
ma-115	134	2	k̂	k̂	X
ma-115	134	3	(	(	PUNCT
ma-115	134	4	1	1	NUM
ma-115	134	5	)	)	PUNCT
ma-115	134	6	−	−	NOUN
ma-115	134	7	]	]	PUNCT
ma-115	135	1	f	f	X
ma-115	135	2	]	]	X
ma-115	135	3	(	(	PUNCT
ma-115	135	4	y	y	NOUN
ma-115	135	5	)	)	PUNCT
ma-115	135	6	=	=	SYM
ma-115	135	7	f̃	f̃	PROPN
ma-115	135	8	(	(	PUNCT
ma-115	135	9	a	a	NOUN
ma-115	135	10	)	)	PUNCT
ma-115	135	11	1,α	1,α	NOUN
ma-115	135	12	,	,	PUNCT
ma-115	135	13	β(y	β(y	NOUN
ma-115	135	14	)	)	PUNCT
ma-115	135	15	where	where	SCONJ
ma-115	135	16	φ	φ	PROPN
ma-115	135	17	=	=	NOUN
ma-115	135	18	a(π/2).we	a(π/2).we	NOUN
ma-115	135	19	can	can	AUX
ma-115	135	20	interpret	interpret	VERB
ma-115	135	21	it	it	PRON
ma-115	135	22	as	as	ADP
ma-115	135	23	the	the	DET
ma-115	135	24	functional	functional	ADJ
ma-115	135	25	representation	representation	NOUN
ma-115	135	26	of	of	ADP
ma-115	135	27	the	the	DET
ma-115	135	28	operator	operator	NOUN
ma-115	135	29	associated	associate	VERB
ma-115	135	30	with	with	ADP
ma-115	135	31	the	the	DET
ma-115	135	32	equation	equation	NOUN
ma-115	136	1	i	i	PRON
ma-115	136	2	∂	∂	NOUN
ma-115	136	3	∂τ	∂τ	PROPN
ma-115	136	4	h(x	h(x	PROPN
ma-115	136	5	,	,	PUNCT
ma-115	136	6	τ	τ	PROPN
ma-115	136	7	)	)	PUNCT
ma-115	136	8	=	=	SYM
ma-115	137	1	−	−	PROPN
ma-115	137	2	1	1	NUM
ma-115	137	3	2	2	NUM
ma-115	137	4	{	{	PUNCT
ma-115	137	5	∂2	∂2	NUM
ma-115	137	6	∂x2	∂x2	NOUN
ma-115	137	7	−	−	NOUN
ma-115	137	8	(	(	PUNCT
ma-115	137	9	1−	1−	NUM
ma-115	137	10	4(α+	4(α+	NUM
ma-115	137	11	β	β	NOUN
ma-115	137	12	)	)	PUNCT
ma-115	137	13	)	)	PUNCT
ma-115	137	14	1	1	NUM
ma-115	137	15	x	x	SYM
ma-115	137	16	∂	∂	NOUN
ma-115	137	17	∂x	∂x	PROPN
ma-115	137	18	+	+	CCONJ
ma-115	138	1	[	[	X
ma-115	138	2	1−	1−	NUM
ma-115	138	3	2(α+	2(α+	NUM
ma-115	138	4	β)2	β)2	ADV
ma-115	138	5	−	−	PROPN
ma-115	138	6	(	(	PUNCT
ma-115	138	7	α−	α−	ADP
ma-115	138	8	β)2	β)2	X
ma-115	138	9	]	]	X
ma-115	138	10	1	1	NUM
ma-115	138	11	x2	x2	NOUN
ma-115	138	12	−	−	PROPN
ma-115	138	13	x2	x2	PROPN
ma-115	138	14	+	+	CCONJ
ma-115	138	15	2(α−	2(α−	NUM
ma-115	138	16	β	β	X
ma-115	138	17	+	+	NOUN
ma-115	138	18	1	1	NUM
ma-115	138	19	)	)	PUNCT
ma-115	138	20	}	}	PUNCT
ma-115	138	21	h(x	h(x	PROPN
ma-115	138	22	,	,	PUNCT
ma-115	138	23	τ	τ	PROPN
ma-115	138	24	)	)	PUNCT
ma-115	138	25	(	(	PUNCT
ma-115	138	26	22	22	NUM
ma-115	138	27	)	)	PUNCT
ma-115	138	28	with	with	ADP
ma-115	138	29	the	the	DET
ma-115	138	30	relevant	relevant	ADJ
ma-115	138	31	initial	initial	ADJ
ma-115	138	32	condition	condition	NOUN
ma-115	138	33	h(x	h(x	PROPN
ma-115	138	34	,	,	PUNCT
ma-115	138	35	0	0	NUM
ma-115	138	36	)	)	PUNCT
ma-115	139	1	=	=	SYM
ma-115	139	2	f	f	X
ma-115	139	3	(	(	PUNCT
ma-115	139	4	x).the	x).the	PRON
ma-115	139	5	evolution	evolution	NOUN
ma-115	139	6	variable	variable	NOUN
ma-115	139	7	is	be	AUX
ma-115	139	8	here	here	ADV
ma-115	139	9	measured	measure	VERB
ma-115	139	10	in	in	ADP
ma-115	139	11	unitsof	unitsof	NOUN
ma-115	139	12	(	(	PUNCT
ma-115	139	13	π/2	π/2	NUM
ma-115	139	14	)	)	PUNCT
ma-115	139	15	:	:	PUNCT
ma-115	140	1	τ	τ	PROPN
ma-115	140	2	=	=	SYM
ma-115	140	3	a(π/2	a(π/2	PROPN
ma-115	140	4	)	)	PUNCT
ma-115	140	5	,	,	PUNCT
ma-115	140	6	and	and	CCONJ
ma-115	140	7	conventionally	conventionally	ADV
ma-115	140	8	denoted	denote	VERB
ma-115	140	9	by	by	ADP
ma-115	140	10	φ.we	φ.we	NOUN
ma-115	140	11	can	can	AUX
ma-115	140	12	also	also	ADV
ma-115	140	13	develop	develop	VERB
ma-115	140	14	similar	similar	ADJ
ma-115	140	15	results	result	NOUN
ma-115	140	16	in	in	ADP
ma-115	140	17	relation	relation	NOUN
ma-115	140	18	with	with	ADP
ma-115	140	19	the	the	DET
ma-115	140	20	second	second	ADJ
ma-115	140	21	hankel	hankel	NOUN
ma-115	140	22	-	-	PUNCT
ma-115	140	23	type	type	NOUN
ma-115	140	24	transform	transform	NOUN
ma-115	140	25	ĥ2,α−β,−2(α+β),the	ĥ2,α−β,−2(α+β),the	DET
ma-115	140	26	inherent	inherent	ADJ
ma-115	140	27	su(1	su(1	NOUN
ma-115	140	28	,	,	PUNCT
ma-115	140	29	1	1	X
ma-115	140	30	)	)	PUNCT
ma-115	140	31	algebra	algebra	NOUN
ma-115	140	32	generators	generator	NOUN
ma-115	140	33	being	be	AUX
ma-115	140	34	the	the	DET
ma-115	140	35	adjoint	adjoint	NOUN
ma-115	140	36	of	of	ADP
ma-115	140	37	equation	equation	NOUN
ma-115	140	38	(	(	PUNCT
ma-115	140	39	17	17	NUM
ma-115	140	40	)	)	PUNCT
ma-115	140	41	,	,	PUNCT
ma-115	140	42	namely	namely	ADV
ma-115	140	43	,	,	PUNCT
ma-115	140	44	k̂	k̂	X
ma-115	140	45	(	(	PUNCT
ma-115	140	46	2	2	X
ma-115	140	47	)	)	PUNCT
ma-115	140	48	+	+	NOUN
ma-115	140	49	=	=	SYM
ma-115	140	50	1	1	NUM
ma-115	140	51	2	2	NUM
ma-115	140	52	x2	x2	NOUN
ma-115	140	53	,	,	PUNCT
ma-115	140	54	k̂	k̂	X
ma-115	140	55	(	(	PUNCT
ma-115	140	56	2	2	NUM
ma-115	140	57	)	)	PUNCT
ma-115	140	58	−	−	NOUN
ma-115	141	1	=	=	SYM
ma-115	141	2	−	−	PROPN
ma-115	141	3	1	1	NUM
ma-115	141	4	2	2	NUM
ma-115	141	5	b̂α−β,−2(α+β	b̂α−β,−2(α+β	NOUN
ma-115	141	6	)	)	PUNCT
ma-115	141	7	,	,	PUNCT
ma-115	141	8	k̂	k̂	X
ma-115	141	9	(	(	PUNCT
ma-115	141	10	2	2	X
ma-115	141	11	)	)	PUNCT
ma-115	141	12	3	3	NUM
ma-115	141	13	=	=	SYM
ma-115	141	14	−	−	NOUN
ma-115	142	1	i	i	PRON
ma-115	142	2	2	2	NUM
ma-115	142	3	(	(	PUNCT
ma-115	142	4	x	x	PROPN
ma-115	142	5	d	d	X
ma-115	142	6	dx	dx	PROPN
ma-115	142	7	−	−	PROPN
ma-115	142	8	2(α+	2(α+	NUM
ma-115	142	9	β	β	NOUN
ma-115	142	10	)	)	PUNCT
ma-115	142	11	+	+	CCONJ
ma-115	142	12	1	1	NUM
ma-115	142	13	)	)	PUNCT
ma-115	142	14	.	.	PUNCT
ma-115	143	1	(	(	PUNCT
ma-115	143	2	23	23	NUM
ma-115	143	3	)	)	PUNCT
ma-115	143	4	https://doi.org/10.28924/ada/ma.3.6	https://doi.org/10.28924/ada/ma.3.6	PROPN
ma-115	143	5	eur	eur	PROPN
ma-115	143	6	.	.	PUNCT
ma-115	144	1	j.	j.	PROPN
ma-115	144	2	math	math	PROPN
ma-115	144	3	.	.	PUNCT
ma-115	145	1	anal	anal	PROPN
ma-115	145	2	.	.	PUNCT
ma-115	146	1	10.28924	10.28924	NUM
ma-115	146	2	/	/	SYM
ma-115	146	3	ada	ada	PROPN
ma-115	146	4	/	/	SYM
ma-115	146	5	ma.3.6	ma.3.6	PROPN
ma-115	146	6	6	6	NUM
ma-115	146	7	now	now	ADV
ma-115	146	8	we	we	PRON
ma-115	146	9	introduce	introduce	VERB
ma-115	146	10	the	the	DET
ma-115	146	11	second	second	ADJ
ma-115	146	12	hankel	hankel	NOUN
ma-115	146	13	-	-	PUNCT
ma-115	146	14	type	type	NOUN
ma-115	146	15	transform	transform	NOUN
ma-115	146	16	of	of	ADP
ma-115	146	17	fractional	fractional	ADJ
ma-115	146	18	order	order	NOUN
ma-115	146	19	a	a	DET
ma-115	146	20	,	,	PUNCT
ma-115	146	21	ĥa2,α−β,−2(α+β	ĥa2,α−β,−2(α+β	NOUN
ma-115	146	22	)	)	PUNCT
ma-115	146	23	as	as	ADP
ma-115	146	24	[	[	PUNCT
ma-115	146	25	ĥa2,α−β,−2(α+β)f	ĥa2,α−β,−2(α+β)f	NOUN
ma-115	146	26	]	]	PUNCT
ma-115	146	27	(	(	PUNCT
ma-115	146	28	y	y	NOUN
ma-115	146	29	)	)	PUNCT
ma-115	146	30	=	=	SYM
ma-115	146	31	e	e	X
ma-115	146	32	i(α−β+1)(φ−π/2	i(α−β+1)(φ−π/2	PROPN
ma-115	146	33	)	)	PUNCT
ma-115	146	34	sinφ	sinφ	NOUN
ma-115	146	35	∫	∫	PROPN
ma-115	146	36	∞	∞	PROPN
ma-115	146	37	0	0	PROPN
ma-115	146	38	x1−4(α+β	x1−4(α+β	PROPN
ma-115	146	39	)	)	PUNCT
ma-115	146	40	(	(	PUNCT
ma-115	146	41	xy)2(α+β	xy)2(α+β	X
ma-115	146	42	)	)	PUNCT
ma-115	146	43	e	e	NOUN
ma-115	147	1	i	i	PRON
ma-115	147	2	2	2	NUM
ma-115	147	3	cotφ[x2+y2	cotφ[x2+y2	NOUN
ma-115	147	4	]	]	PUNCT
ma-115	147	5	jα−β	jα−β	PROPN
ma-115	147	6	(	(	PUNCT
ma-115	147	7	xy	xy	PROPN
ma-115	147	8	sinφ	sinφ	PROPN
ma-115	147	9	)	)	PUNCT
ma-115	148	1	f	f	PROPN
ma-115	149	1	(	(	PUNCT
ma-115	149	2	x)dx	x)dx	PROPN
ma-115	149	3	(	(	PUNCT
ma-115	149	4	24	24	NUM
ma-115	149	5	)	)	PUNCT
ma-115	149	6	=	=	NOUN
ma-115	150	1	[	[	PUNCT
ma-115	150	2	e	e	X
ma-115	150	3	iφ(α−β+1	iφ(α−β+1	X
ma-115	150	4	)	)	PUNCT
ma-115	150	5	e	e	NOUN
ma-115	150	6	−iφ	−iφ	X
ma-115	150	7	[	[	PUNCT
ma-115	150	8	k̂	k̂	X
ma-115	150	9	(	(	PUNCT
ma-115	150	10	2	2	NUM
ma-115	150	11	)	)	PUNCT
ma-115	150	12	+	+	CCONJ
ma-115	151	1	+	+	X
ma-115	151	2	k̂	k̂	X
ma-115	151	3	(	(	PUNCT
ma-115	151	4	2	2	NUM
ma-115	151	5	)	)	PUNCT
ma-115	151	6	−	−	NOUN
ma-115	151	7	]	]	PUNCT
ma-115	152	1	f	f	X
ma-115	152	2	]	]	X
ma-115	152	3	(	(	PUNCT
ma-115	152	4	y	y	NOUN
ma-115	152	5	)	)	PUNCT
ma-115	152	6	=	=	SYM
ma-115	152	7	f̃	f̃	PROPN
ma-115	152	8	(	(	PUNCT
ma-115	152	9	a	a	NOUN
ma-115	152	10	)	)	PUNCT
ma-115	152	11	2,α−β,−2(α+β)(y	2,α−β,−2(α+β)(y	NUM
ma-115	152	12	)	)	PUNCT
ma-115	152	13	,	,	PUNCT
ma-115	152	14	φ	φ	PROPN
ma-115	152	15	=	=	SYM
ma-115	152	16	a(π/2	a(π/2	PROPN
ma-115	152	17	)	)	PUNCT
ma-115	152	18	.	.	PUNCT
ma-115	153	1	this	this	PRON
ma-115	153	2	yields	yield	VERB
ma-115	153	3	the	the	DET
ma-115	153	4	functional	functional	ADJ
ma-115	153	5	representation	representation	NOUN
ma-115	153	6	of	of	ADP
ma-115	153	7	the	the	DET
ma-115	153	8	evolution	evolution	NOUN
ma-115	153	9	operator	operator	NOUN
ma-115	153	10	for	for	ADP
ma-115	153	11	the	the	DET
ma-115	153	12	equation	equation	NOUN
ma-115	153	13	i	i	PRON
ma-115	153	14	∂	∂	NOUN
ma-115	153	15	∂τ	∂τ	PROPN
ma-115	153	16	h(x	h(x	PROPN
ma-115	153	17	,	,	PUNCT
ma-115	153	18	τ	τ	PROPN
ma-115	153	19	)	)	PUNCT
ma-115	153	20	=	=	SYM
ma-115	154	1	−	−	PROPN
ma-115	154	2	1	1	NUM
ma-115	154	3	2	2	NUM
ma-115	154	4	{	{	PUNCT
ma-115	154	5	∂2	∂2	NUM
ma-115	154	6	∂x2	∂x2	NOUN
ma-115	154	7	+	+	CCONJ
ma-115	154	8	(	(	PUNCT
ma-115	154	9	1−	1−	NUM
ma-115	154	10	2(α+	2(α+	NUM
ma-115	154	11	β	β	NOUN
ma-115	154	12	)	)	PUNCT
ma-115	154	13	)	)	PUNCT
ma-115	154	14	1	1	NUM
ma-115	154	15	x	x	SYM
ma-115	154	16	∂	∂	NOUN
ma-115	154	17	∂x	∂x	PROPN
ma-115	155	1	+	+	CCONJ
ma-115	156	1	[	[	X
ma-115	156	2	−2(α+	−2(α+	X
ma-115	156	3	β)2	β)2	ADV
ma-115	156	4	−	−	PROPN
ma-115	156	5	(	(	PUNCT
ma-115	156	6	α−	α−	ADP
ma-115	156	7	β)2	β)2	X
ma-115	156	8	]	]	X
ma-115	156	9	1	1	NUM
ma-115	156	10	x2	x2	NOUN
ma-115	156	11	−	−	PROPN
ma-115	156	12	x2	x2	PROPN
ma-115	157	1	+	+	CCONJ
ma-115	157	2	2(α−	2(α−	NUM
ma-115	157	3	β	β	X
ma-115	157	4	+	+	NOUN
ma-115	157	5	1	1	NUM
ma-115	157	6	)	)	PUNCT
ma-115	157	7	}	}	PUNCT
ma-115	157	8	h(x	h(x	PROPN
ma-115	157	9	,	,	PUNCT
ma-115	157	10	τ	τ	PROPN
ma-115	157	11	)	)	PUNCT
ma-115	157	12	(	(	PUNCT
ma-115	157	13	25	25	NUM
ma-115	157	14	)	)	PUNCT
ma-115	157	15	with	with	ADP
ma-115	157	16	the	the	DET
ma-115	157	17	initial	initial	ADJ
ma-115	157	18	condition	condition	NOUN
ma-115	157	19	h(x	h(x	PROPN
ma-115	157	20	,	,	PUNCT
ma-115	157	21	0	0	NUM
ma-115	157	22	)	)	PUNCT
ma-115	158	1	=	=	SYM
ma-115	158	2	f	f	X
ma-115	158	3	(	(	PUNCT
ma-115	158	4	x).the	x).the	DET
ma-115	158	5	evolution	evolution	PROPN
ma-115	158	6	variable	variable	NOUN
ma-115	158	7	parameterized	parameterized	ADJ
ma-115	158	8	as	as	ADP
ma-115	158	9	τ	τ	PROPN
ma-115	158	10	=	=	SYM
ma-115	158	11	a(π/2	a(π/2	PROPN
ma-115	158	12	)	)	PUNCT
ma-115	158	13	.	.	PUNCT
ma-115	159	1	for	for	ADP
ma-115	159	2	α+β	α+β	NUM
ma-115	159	3	=	=	SYM
ma-115	159	4	1	1	NUM
ma-115	159	5	4	4	NUM
ma-115	159	6	,	,	PUNCT
ma-115	159	7	both	both	DET
ma-115	159	8	equations	equation	NOUN
ma-115	159	9	(	(	PUNCT
ma-115	159	10	21	21	NUM
ma-115	159	11	)	)	PUNCT
ma-115	159	12	and	and	CCONJ
ma-115	159	13	(	(	PUNCT
ma-115	159	14	24	24	NUM
ma-115	159	15	)	)	PUNCT
ma-115	159	16	yields	yield	VERB
ma-115	159	17	the	the	DET
ma-115	159	18	expression	expression	NOUN
ma-115	159	19	of	of	ADP
ma-115	159	20	the	the	DET
ma-115	159	21	conventional	conventional	ADJ
ma-115	159	22	hankel	hankel	NOUN
ma-115	159	23	transform	transform	VERB
ma-115	159	24	offractional	offractional	ADJ
ma-115	159	25	order	order	NOUN
ma-115	159	26	,	,	PUNCT
ma-115	159	27	originally	originally	ADV
ma-115	159	28	introduced	introduce	VERB
ma-115	159	29	by	by	ADP
ma-115	159	30	namia	namia	NOUN
ma-115	160	1	[	[	X
ma-115	160	2	9	9	NUM
ma-115	160	3	]	]	PUNCT
ma-115	160	4	and	and	CCONJ
ma-115	160	5	further	far	ADV
ma-115	160	6	investigated	investigate	VERB
ma-115	160	7	in	in	ADP
ma-115	160	8	[	[	X
ma-115	160	9	16,21].in	16,21].in	X
ma-115	160	10	particular	particular	ADJ
ma-115	160	11	,	,	PUNCT
ma-115	160	12	for	for	ADP
ma-115	160	13	α+	α+	PRON
ma-115	160	14	β	β	X
ma-115	160	15	=	=	SYM
ma-115	160	16	1	1	NUM
ma-115	160	17	4	4	NUM
ma-115	160	18	,	,	PUNCT
ma-115	160	19	equations	equation	NOUN
ma-115	160	20	(	(	PUNCT
ma-115	160	21	17	17	NUM
ma-115	160	22	)	)	PUNCT
ma-115	160	23	and	and	CCONJ
ma-115	160	24	(	(	PUNCT
ma-115	160	25	23	23	X
ma-115	160	26	)	)	PUNCT
ma-115	160	27	turn	turn	VERB
ma-115	160	28	into	into	ADP
ma-115	160	29	the	the	DET
ma-115	160	30	same	same	ADJ
ma-115	160	31	set	set	NOUN
ma-115	160	32	of	of	ADP
ma-115	160	33	self	self	NOUN
ma-115	160	34	-	-	PUNCT
ma-115	160	35	adjoint	adjoint	NOUN
ma-115	160	36	operators	operator	NOUN
ma-115	160	37	k̂+	k̂+	NOUN
ma-115	161	1	=	=	NOUN
ma-115	161	2	1	1	NUM
ma-115	161	3	2	2	NUM
ma-115	161	4	x2	x2	NOUN
ma-115	161	5	,	,	PUNCT
ma-115	161	6	k̂−	k̂−	PROPN
ma-115	161	7	=	=	PUNCT
ma-115	162	1	−	−	PROPN
ma-115	162	2	1	1	NUM
ma-115	162	3	2	2	NUM
ma-115	162	4	b̂α−β	b̂α−β	NOUN
ma-115	162	5	,	,	PUNCT
ma-115	162	6	k̂3	k̂3	NOUN
ma-115	162	7	=	=	PUNCT
ma-115	163	1	−	−	NOUN
ma-115	163	2	i	i	PRON
ma-115	163	3	2	2	NUM
ma-115	163	4	(	(	PUNCT
ma-115	163	5	x	x	PROPN
ma-115	163	6	d	d	NOUN
ma-115	163	7	dx	dx	PROPN
ma-115	163	8	+	+	NOUN
ma-115	163	9	1	1	NUM
ma-115	163	10	2	2	NUM
ma-115	163	11	)	)	PUNCT
ma-115	163	12	(	(	PUNCT
ma-115	163	13	26	26	NUM
ma-115	163	14	)	)	PUNCT
ma-115	163	15	which	which	PRON
ma-115	163	16	pertain	pertain	VERB
ma-115	163	17	to	to	ADP
ma-115	163	18	the	the	DET
ma-115	163	19	conventional	conventional	ADJ
ma-115	163	20	hankel	hankel	NOUN
ma-115	163	21	transform	transform	NOUN
ma-115	163	22	(	(	PUNCT
ma-115	163	23	7).thus	7).thu	NOUN
ma-115	163	24	we	we	PRON
ma-115	163	25	have	have	VERB
ma-115	163	26	ĥα−β	ĥα−β	X
ma-115	163	27	=	=	SYM
ma-115	163	28	iα−β+1e	iα−β+1e	PROPN
ma-115	163	29	i	i	PRON
ma-115	163	30	(	(	PUNCT
ma-115	163	31	π2	π2	ADV
ma-115	163	32	)	)	PUNCT
ma-115	163	33	[	[	PUNCT
ma-115	163	34	d2	d2	PROPN
ma-115	163	35	dx2	dx2	PROPN
ma-115	163	36	−(α−β)2−	−(α−β)2−	PROPN
ma-115	163	37	(	(	PUNCT
ma-115	163	38	1/4	1/4	NUM
ma-115	163	39	)	)	PUNCT
ma-115	164	1	x2	x2	NOUN
ma-115	165	1	−	−	PUNCT
ma-115	166	1	x2	x2	INTJ
ma-115	166	2	2	2	X
ma-115	166	3	]	]	PUNCT
ma-115	166	4	(	(	PUNCT
ma-115	166	5	27	27	NUM
ma-115	166	6	)	)	PUNCT
ma-115	166	7	and	and	CCONJ
ma-115	166	8	corresponding	correspond	VERB
ma-115	166	9	for	for	ADP
ma-115	166	10	the	the	DET
ma-115	166	11	transform	transform	NOUN
ma-115	166	12	of	of	ADP
ma-115	166	13	fractional	fractional	ADJ
ma-115	166	14	order	order	NOUN
ma-115	166	15	a	a	DET
ma-115	166	16	ĥaα−β	ĥaα−β	NOUN
ma-115	166	17	=	=	SYM
ma-115	166	18	e	e	X
ma-115	166	19	i	i	PRON
ma-115	166	20	(	(	PUNCT
ma-115	166	21	aπ	aπ	PROPN
ma-115	166	22	2	2	NUM
ma-115	166	23	)	)	PUNCT
ma-115	166	24	(	(	PUNCT
ma-115	166	25	α−β+1)e	α−β+1)e	NOUN
ma-115	166	26	i	i	NOUN
ma-115	166	27	(	(	PUNCT
ma-115	166	28	aπ2	aπ2	X
ma-115	166	29	)	)	PUNCT
ma-115	166	30	[	[	PUNCT
ma-115	166	31	d2	d2	PROPN
ma-115	166	32	dx2	dx2	PROPN
ma-115	166	33	−(α−β)2−	−(α−β)2−	PROPN
ma-115	166	34	(	(	PUNCT
ma-115	166	35	1/4	1/4	NUM
ma-115	166	36	)	)	PUNCT
ma-115	167	1	x2	x2	NOUN
ma-115	167	2	−	−	PUNCT
ma-115	168	1	x2	x2	INTJ
ma-115	168	2	2	2	X
ma-115	168	3	]	]	PUNCT
ma-115	168	4	(	(	PUNCT
ma-115	168	5	28	28	NUM
ma-115	168	6	)	)	PUNCT
ma-115	168	7	whose	whose	DET
ma-115	168	8	fractional	fractional	ADJ
ma-115	168	9	equation	equation	NOUN
ma-115	168	10	is	be	AUX
ma-115	168	11	[	[	X
ma-115	168	12	9	9	NUM
ma-115	168	13	,	,	PUNCT
ma-115	168	14	16,21	16,21	PROPN
ma-115	168	15	]	]	X
ma-115	168	16	[	[	PUNCT
ma-115	168	17	ĥaα−βf	ĥaα−βf	NOUN
ma-115	168	18	]	]	PUNCT
ma-115	168	19	(	(	PUNCT
ma-115	168	20	y	y	NOUN
ma-115	168	21	)	)	PUNCT
ma-115	168	22	≡	≡	PROPN
ma-115	168	23	f̃	f̃	PROPN
ma-115	168	24	(	(	PUNCT
ma-115	168	25	a)α−β(y	a)α−β(y	PROPN
ma-115	168	26	)	)	PUNCT
ma-115	168	27	=	=	PUNCT
ma-115	168	28	e	e	X
ma-115	168	29	i(α−β+1)(φ−π/2	i(α−β+1)(φ−π/2	PROPN
ma-115	168	30	)	)	PUNCT
ma-115	168	31	sinφ	sinφ	NOUN
ma-115	168	32	∫	∫	PROPN
ma-115	168	33	∞	∞	PROPN
ma-115	168	34	0	0	NUM
ma-115	168	35	(	(	PUNCT
ma-115	168	36	xy	xy	NOUN
ma-115	168	37	)	)	PUNCT
ma-115	168	38	(	(	PUNCT
ma-115	168	39	1	1	NUM
ma-115	168	40	2	2	NUM
ma-115	168	41	)	)	PUNCT
ma-115	169	1	e	e	NOUN
ma-115	169	2	i	i	PROPN
ma-115	169	3	2	2	NUM
ma-115	169	4	cotφ[x2+y2	cotφ[x2+y2	NOUN
ma-115	169	5	]	]	PUNCT
ma-115	169	6	jα−β	jα−β	PROPN
ma-115	169	7	(	(	PUNCT
ma-115	169	8	xy	xy	PROPN
ma-115	169	9	sinφ	sinφ	PROPN
ma-115	169	10	)	)	PUNCT
ma-115	170	1	f	f	PROPN
ma-115	171	1	(	(	PUNCT
ma-115	171	2	x)dx	x)dx	PROPN
ma-115	171	3	(	(	PUNCT
ma-115	171	4	29	29	NUM
ma-115	171	5	)	)	PUNCT
ma-115	171	6	since	since	SCONJ
ma-115	171	7	(	(	PUNCT
ma-115	171	8	1	1	NUM
ma-115	171	9	)	)	PUNCT
ma-115	171	10	and	and	CCONJ
ma-115	171	11	(	(	PUNCT
ma-115	171	12	2	2	NUM
ma-115	171	13	)	)	PUNCT
ma-115	171	14	,	,	PUNCT
ma-115	171	15	also	also	ADV
ma-115	171	16	ĥa1,α−β,−2(α+β	ĥa1,α−β,−2(α+β	NOUN
ma-115	171	17	)	)	PUNCT
ma-115	171	18	and	and	CCONJ
ma-115	171	19	ĥa2,α−β,−2(α+β	ĥa2,α−β,−2(α+β	NUM
ma-115	171	20	)	)	PUNCT
ma-115	171	21	can	can	AUX
ma-115	171	22	be	be	AUX
ma-115	171	23	framed	frame	VERB
ma-115	171	24	for	for	ADP
ma-115	171	25	suitable	suitable	ADJ
ma-115	171	26	values	value	NOUN
ma-115	171	27	of	of	ADP
ma-115	171	28	α	α	PROPN
ma-115	171	29	,	,	PUNCT
ma-115	171	30	β	β	X
ma-115	171	31	,	,	PUNCT
ma-115	171	32	within	within	ADP
ma-115	171	33	the	the	DET
ma-115	171	34	formalism	formalism	NOUN
ma-115	171	35	of	of	ADP
ma-115	171	36	[	[	X
ma-115	171	37	20	20	NUM
ma-115	171	38	,	,	PUNCT
ma-115	171	39	21	21	NUM
ma-115	171	40	]	]	PUNCT
ma-115	171	41	,	,	PUNCT
ma-115	171	42	the	the	DET
ma-115	171	43	relevant	relevant	ADJ
ma-115	171	44	canonical	canonical	ADJ
ma-115	171	45	transformation	transformation	NOUN
ma-115	171	46	being	be	AUX
ma-115	171	47	now	now	ADV
ma-115	171	48	the	the	DET
ma-115	171	49	rotation	rotation	NOUN
ma-115	171	50	bythe	bythe	ADP
ma-115	171	51	angle	angle	PROPN
ma-115	171	52	φ	φ	PROPN
ma-115	171	53	for	for	ADP
ma-115	171	54	each	each	DET
ma-115	171	55	pair	pair	NOUN
ma-115	171	56	of	of	ADP
ma-115	171	57	corresponding	correspond	VERB
ma-115	171	58	canonically	canonically	ADV
ma-115	171	59	conjugate	conjugate	ADJ
ma-115	171	60	position	position	NOUN
ma-115	171	61	and	and	CCONJ
ma-115	171	62	momentum	momentum	NOUN
ma-115	171	63	operatorsin	operatorsin	NOUN
ma-115	171	64	the	the	DET
ma-115	171	65	relevant	relevant	ADJ
ma-115	171	66	n	n	NUM
ma-115	171	67	-	-	PUNCT
ma-115	171	68	component	component	NOUN
ma-115	171	69	operator	operator	NOUN
ma-115	171	70	vectors	vector	NOUN
ma-115	171	71	.	.	PUNCT
ma-115	172	1	4	4	X
ma-115	172	2	.	.	X
ma-115	172	3	properties	property	NOUN
ma-115	172	4	of	of	ADP
ma-115	172	5	ĥa1,α−β,−2(α+β	ĥa1,α−β,−2(α+β	NOUN
ma-115	172	6	)	)	PUNCT
ma-115	172	7	and	and	CCONJ
ma-115	172	8	ĥa2,α−β,−2(α+β):the	ĥa2,α−β,−2(α+β):the	DET
ma-115	172	9	fractionalization	fractionalization	NOUN
ma-115	172	10	of	of	ADP
ma-115	172	11	order	order	NOUN
ma-115	172	12	a	a	PRON
ma-115	172	13	of	of	ADP
ma-115	172	14	an	an	DET
ma-115	172	15	integral	integral	ADJ
ma-115	172	16	transform	transform	NOUN
ma-115	172	17	t̂	t̂	PRON
ma-115	172	18	is	be	AUX
ma-115	172	19	intended	intend	VERB
ma-115	172	20	to	to	PART
ma-115	172	21	produce	produce	VERB
ma-115	172	22	an	an	DET
ma-115	172	23	integraltransform	integraltransform	NOUN
ma-115	172	24	t̂	t̂	ADP
ma-115	172	25	a	a	PRON
ma-115	172	26	which	which	PRON
ma-115	172	27	satisfy	satisfy	VERB
ma-115	172	28	specific	specific	ADJ
ma-115	172	29	properties	property	NOUN
ma-115	172	30	;	;	PUNCT
ma-115	172	31	more	more	ADV
ma-115	172	32	precisely	precisely	ADV
ma-115	172	33	we	we	PRON
ma-115	172	34	need	need	VERB
ma-115	172	35	that(1	that(1	NOUN
ma-115	172	36	)	)	PUNCT
ma-115	172	37	t̂	t̂	ADP
ma-115	173	1	a	a	PRON
ma-115	173	2	is	be	AUX
ma-115	173	3	continuous	continuous	ADJ
ma-115	173	4	with	with	ADP
ma-115	173	5	respect	respect	NOUN
ma-115	173	6	to	to	ADP
ma-115	173	7	the	the	DET
ma-115	173	8	order	order	NOUN
ma-115	173	9	,	,	PUNCT
ma-115	173	10	i.e.	i.e.	X
ma-115	173	11	t̂	t̂	PRON
ma-115	173	12	b	b	X
ma-115	173	13	−→	−→	NOUN
ma-115	173	14	t̂	t̂	NOUN
ma-115	173	15	a	a	DET
ma-115	173	16	as	as	ADP
ma-115	173	17	b	b	NOUN
ma-115	173	18	−→	−→	NOUN
ma-115	173	19	a	a	DET
ma-115	173	20	https://doi.org/10.28924/ada/ma.3.6	https://doi.org/10.28924/ada/ma.3.6	PROPN
ma-115	173	21	eur	eur	NOUN
ma-115	173	22	.	.	PUNCT
ma-115	174	1	j.	j.	PROPN
ma-115	174	2	math	math	PROPN
ma-115	174	3	.	.	PUNCT
ma-115	175	1	anal	anal	PROPN
ma-115	175	2	.	.	PUNCT
ma-115	176	1	10.28924	10.28924	NUM
ma-115	176	2	/	/	SYM
ma-115	176	3	ada	ada	PROPN
ma-115	176	4	/	/	SYM
ma-115	176	5	ma.3.6	ma.3.6	PROPN
ma-115	176	6	7	7	NUM
ma-115	176	7	(	(	PUNCT
ma-115	176	8	2	2	NUM
ma-115	176	9	)	)	PUNCT
ma-115	176	10	t̂	t̂	NOUN
ma-115	176	11	a	a	DET
ma-115	176	12	obeys	obey	NOUN
ma-115	176	13	the	the	DET
ma-115	176	14	semigroup	semigroup	PROPN
ma-115	176	15	property	property	NOUN
ma-115	176	16	,	,	PUNCT
ma-115	176	17	so	so	SCONJ
ma-115	176	18	that	that	SCONJ
ma-115	176	19	composing	compose	VERB
ma-115	176	20	two	two	NUM
ma-115	176	21	fractional	fractional	ADJ
ma-115	176	22	transform	transform	NOUN
ma-115	176	23	of	of	ADP
ma-115	176	24	order	order	NOUN
ma-115	176	25	a1and	a1and	PROPN
ma-115	176	26	a2	a2	PROPN
ma-115	176	27	yeilds	yeild	VERB
ma-115	176	28	the	the	DET
ma-115	176	29	fractional	fractional	ADJ
ma-115	176	30	transform	transform	NOUN
ma-115	176	31	of	of	ADP
ma-115	176	32	order	order	NOUN
ma-115	176	33	a1	a1	NOUN
ma-115	176	34	+	+	CCONJ
ma-115	176	35	a2	a2	PROPN
ma-115	176	36	t̂	t̂	PRON
ma-115	176	37	a1	a1	NOUN
ma-115	177	1	t̂	t̂	PROPN
ma-115	177	2	a2	a2	PROPN
ma-115	177	3	=	=	SYM
ma-115	177	4	t̂	t̂	PROPN
ma-115	177	5	a2	a2	PROPN
ma-115	177	6	t̂	t̂	PRON
ma-115	177	7	a1	a1	NOUN
ma-115	177	8	=	=	PUNCT
ma-115	177	9	t̂	t̂	X
ma-115	177	10	a1+a2	a1+a2	PROPN
ma-115	177	11	,	,	PUNCT
ma-115	177	12	(	(	PUNCT
ma-115	177	13	3	3	NUM
ma-115	177	14	)	)	PUNCT
ma-115	177	15	t̂	t̂	NOUN
ma-115	177	16	a	a	DET
ma-115	177	17	reduces	reduce	NOUN
ma-115	177	18	to	to	ADP
ma-115	177	19	the	the	DET
ma-115	177	20	identity	identity	NOUN
ma-115	177	21	operator	operator	NOUN
ma-115	177	22	with	with	ADP
ma-115	177	23	a	a	DET
ma-115	177	24	=	=	NOUN
ma-115	177	25	0	0	NUM
ma-115	177	26	and	and	CCONJ
ma-115	177	27	to	to	ADP
ma-115	177	28	the	the	DET
ma-115	177	29	ordinary	ordinary	ADJ
ma-115	177	30	transform	transform	NOUN
ma-115	177	31	for	for	ADP
ma-115	177	32	a	a	DET
ma-115	177	33	=	=	SYM
ma-115	177	34	1	1	NUM
ma-115	177	35	;	;	PUNCT
ma-115	177	36	insymbols	insymbol	NOUN
ma-115	177	37	:	:	PUNCT
ma-115	177	38	t̂	t̂	NUM
ma-115	177	39	0	0	X
ma-115	177	40	=	=	SYM
ma-115	177	41	1̂	1̂	NUM
ma-115	177	42	and	and	CCONJ
ma-115	177	43	t̂	t̂	NUM
ma-115	177	44	1	1	NUM
ma-115	177	45	=	=	SYM
ma-115	177	46	t̂	t̂	NOUN
ma-115	177	47	.from	.from	ADP
ma-115	177	48	the	the	DET
ma-115	177	49	procedure	procedure	NOUN
ma-115	177	50	we	we	PRON
ma-115	177	51	followed	follow	VERB
ma-115	177	52	to	to	PART
ma-115	177	53	introduced	introduce	VERB
ma-115	177	54	the	the	DET
ma-115	177	55	fractional	fractional	ADJ
ma-115	177	56	order	order	NOUN
ma-115	177	57	transforms	transform	VERB
ma-115	177	58	ĥa1,α−β,−2(α+β	ĥa1,α−β,−2(α+β	NOUN
ma-115	177	59	)	)	PUNCT
ma-115	177	60	and	and	CCONJ
ma-115	177	61	ĥa2,α−β,−2(α+β	ĥa2,α−β,−2(α+β	NUM
ma-115	177	62	)	)	PUNCT
ma-115	177	63	,	,	PUNCT
ma-115	177	64	it	it	PRON
ma-115	177	65	is	be	AUX
ma-115	177	66	clear	clear	ADJ
ma-115	177	67	that	that	SCONJ
ma-115	177	68	both	both	PRON
ma-115	177	69	transforms	transform	VERB
ma-115	177	70	satisfy	satisfy	VERB
ma-115	177	71	the	the	PRON
ma-115	177	72	above	above	ADV
ma-115	177	73	properties.thus	properties.thus	PRON
ma-115	177	74	the	the	DET
ma-115	177	75	additivityproperties	additivitypropertie	NOUN
ma-115	177	76	follows	follow	VERB
ma-115	177	77	from	from	ADP
ma-115	177	78	ĥa1,α−β,−2(α+β	ĥa1,α−β,−2(α+β	NOUN
ma-115	177	79	)	)	PUNCT
ma-115	177	80	=	=	SYM
ma-115	177	81	[	[	PUNCT
ma-115	177	82	ĥ1,α−β,−2(α+β	ĥ1,α−β,−2(α+β	NOUN
ma-115	177	83	)	)	PUNCT
ma-115	178	1	]	]	PUNCT
ma-115	178	2	a	a	DET
ma-115	178	3	,	,	PUNCT
ma-115	178	4	ĥa2,α−β,−2(α+β	ĥa2,α−β,−2(α+β	NOUN
ma-115	178	5	)	)	PUNCT
ma-115	179	1	=	=	NOUN
ma-115	179	2	[	[	PUNCT
ma-115	179	3	ĥ2,α−β,−2(α+β	ĥ2,α−β,−2(α+β	NOUN
ma-115	179	4	)	)	PUNCT
ma-115	179	5	]	]	PUNCT
ma-115	179	6	a	a	PRON
ma-115	179	7	(	(	PUNCT
ma-115	179	8	30	30	NUM
ma-115	179	9	)	)	PUNCT
ma-115	179	10	which	which	PRON
ma-115	179	11	in	in	ADP
ma-115	179	12	turn	turn	NOUN
ma-115	179	13	implies	imply	VERB
ma-115	179	14	that	that	SCONJ
ma-115	179	15	ĥ01,α−β,−2(α+β	ĥ01,α−β,−2(α+β	VERB
ma-115	179	16	)	)	PUNCT
ma-115	179	17	=	=	SYM
ma-115	179	18	1̂	1̂	NOUN
ma-115	179	19	,	,	PUNCT
ma-115	179	20	ĥ02,α−β,−2(α+β	ĥ02,α−β,−2(α+β	NOUN
ma-115	179	21	)	)	PUNCT
ma-115	179	22	=	=	PUNCT
ma-115	180	1	1̂.	1̂.	NUM
ma-115	180	2	(	(	PUNCT
ma-115	180	3	31	31	NUM
ma-115	180	4	)	)	PUNCT
ma-115	180	5	in	in	ADP
ma-115	180	6	our	our	PRON
ma-115	180	7	case	case	NOUN
ma-115	180	8	,	,	PUNCT
ma-115	180	9	the	the	DET
ma-115	180	10	ordinary	ordinary	ADJ
ma-115	180	11	transform	transform	NOUN
ma-115	180	12	ĥa1,α−β,−2(α+β	ĥa1,α−β,−2(α+β	NOUN
ma-115	180	13	)	)	PUNCT
ma-115	180	14	and	and	CCONJ
ma-115	180	15	ĥa2,α−β,−2(α+β	ĥa2,α−β,−2(α+β	NUM
ma-115	180	16	)	)	PUNCT
ma-115	180	17	are	be	AUX
ma-115	180	18	recovered	recover	VERB
ma-115	180	19	for	for	ADP
ma-115	180	20	a	a	DET
ma-115	180	21	=	=	SYM
ma-115	180	22	±1	±1	NOUN
ma-115	180	23	:	:	PUNCT
ma-115	180	24	ĥ11,α−β,−2(α+β	ĥ11,α−β,−2(α+β	NOUN
ma-115	180	25	)	)	PUNCT
ma-115	180	26	=	=	SYM
ma-115	180	27	ĥ1,α−β,−2(α+β	ĥ1,α−β,−2(α+β	NOUN
ma-115	180	28	)	)	PUNCT
ma-115	180	29	,	,	PUNCT
ma-115	180	30	ĥ−1	ĥ−1	PROPN
ma-115	180	31	1,α−β,−2(α+β	1,α−β,−2(α+β	NUM
ma-115	180	32	)	)	PUNCT
ma-115	180	33	=	=	SYM
ma-115	180	34	ĥ1,α−β,−2(α+β	ĥ1,α−β,−2(α+β	NOUN
ma-115	180	35	)	)	PUNCT
ma-115	180	36	ĥ12,α−β,−2(α+β	ĥ12,α−β,−2(α+β	NOUN
ma-115	180	37	)	)	PUNCT
ma-115	180	38	=	=	SYM
ma-115	180	39	ĥ2,α−β,−2(α+β	ĥ2,α−β,−2(α+β	NOUN
ma-115	180	40	)	)	PUNCT
ma-115	180	41	,	,	PUNCT
ma-115	180	42	ĥ−1	ĥ−1	PROPN
ma-115	180	43	2,α−β,−2(α+β	2,α−β,−2(α+β	NUM
ma-115	180	44	)	)	PUNCT
ma-115	180	45	=	=	SYM
ma-115	180	46	ĥ2,α−β,−2(α+β	ĥ2,α−β,−2(α+β	NOUN
ma-115	180	47	)	)	PUNCT
ma-115	180	48	.	.	PUNCT
ma-115	181	1	(	(	PUNCT
ma-115	181	2	32	32	NUM
ma-115	181	3	)	)	PUNCT
ma-115	181	4	this	this	PRON
ma-115	181	5	confirms	confirm	VERB
ma-115	181	6	to	to	ADP
ma-115	181	7	the	the	DET
ma-115	181	8	self	self	NOUN
ma-115	181	9	-	-	PUNCT
ma-115	181	10	reciprocal	reciprocal	ADJ
ma-115	181	11	property	property	NOUN
ma-115	181	12	(	(	PUNCT
ma-115	181	13	3	3	NUM
ma-115	181	14	)	)	PUNCT
ma-115	181	15	of	of	ADP
ma-115	181	16	the	the	DET
ma-115	181	17	ordinary	ordinary	ADJ
ma-115	181	18	transform	transform	NOUN
ma-115	181	19	.	.	PUNCT
ma-115	182	1	we	we	PRON
ma-115	182	2	have	have	VERB
ma-115	182	3	ĥ−a	ĥ−a	NOUN
ma-115	182	4	1,α−β,−2(α+β	1,α−β,−2(α+β	NUM
ma-115	182	5	)	)	PUNCT
ma-115	182	6	=	=	NOUN
ma-115	182	7	[	[	PUNCT
ma-115	182	8	ĥa1,α−β,−2(α+β	ĥa1,α−β,−2(α+β	NOUN
ma-115	182	9	)	)	PUNCT
ma-115	182	10	]	]	X
ma-115	182	11	−1	−1	NOUN
ma-115	182	12	,	,	PUNCT
ma-115	182	13	ĥ−a	ĥ−a	NOUN
ma-115	182	14	2,α−β,−2(α+β	2,α−β,−2(α+β	NUM
ma-115	182	15	)	)	PUNCT
ma-115	183	1	=	=	NOUN
ma-115	183	2	[	[	PUNCT
ma-115	183	3	ĥa2,α−β,−2(α+β	ĥa2,α−β,−2(α+β	NOUN
ma-115	183	4	)	)	PUNCT
ma-115	183	5	]	]	X
ma-115	183	6	−1	−1	NOUN
ma-115	183	7	.	.	PUNCT
ma-115	184	1	(	(	PUNCT
ma-115	184	2	33	33	NUM
ma-115	184	3	)	)	PUNCT
ma-115	184	4	in	in	ADP
ma-115	184	5	fact	fact	NOUN
ma-115	184	6	,	,	PUNCT
ma-115	184	7	both	both	PRON
ma-115	184	8	transforms	transform	VERB
ma-115	184	9	are	be	AUX
ma-115	184	10	periodic	periodic	ADJ
ma-115	184	11	with	with	ADP
ma-115	184	12	respect	respect	NOUN
ma-115	184	13	to	to	ADP
ma-115	184	14	order	order	NOUN
ma-115	184	15	parameter	parameter	NOUN
ma-115	184	16	a	a	DET
ma-115	184	17	i.e.	i.e.	X
ma-115	184	18	ĥa+2j	ĥa+2j	SYM
ma-115	184	19	1,α−β,−2(α+β	1,α−β,−2(α+β	NUM
ma-115	184	20	)	)	PUNCT
ma-115	184	21	=	=	SYM
ma-115	184	22	ĥa1,α−β,−2(α+β	ĥa1,α−β,−2(α+β	NOUN
ma-115	184	23	)	)	PUNCT
ma-115	184	24	,	,	PUNCT
ma-115	184	25	ĥa+2j	ĥa+2j	PROPN
ma-115	184	26	2,α−β,−2(α+β	2,α−β,−2(α+β	NUM
ma-115	184	27	)	)	PUNCT
ma-115	184	28	=	=	SYM
ma-115	184	29	ĥa2,α−β,−2(α+β	ĥa2,α−β,−2(α+β	NOUN
ma-115	184	30	)	)	PUNCT
ma-115	184	31	(	(	PUNCT
ma-115	184	32	34	34	NUM
ma-115	184	33	)	)	PUNCT
ma-115	184	34	so	so	SCONJ
ma-115	184	35	that	that	SCONJ
ma-115	184	36	a	a	PRON
ma-115	184	37	can	can	AUX
ma-115	184	38	be	be	AUX
ma-115	184	39	taken	take	VERB
ma-115	184	40	in	in	ADP
ma-115	184	41	[	[	X
ma-115	184	42	-1,1].intrestingly	-1,1].intrestingly	ADV
ma-115	184	43	,	,	PUNCT
ma-115	184	44	for	for	ADP
ma-115	184	45	the	the	DET
ma-115	184	46	adjoint	adjoint	NOUN
ma-115	184	47	operator	operator	NOUN
ma-115	184	48	,	,	PUNCT
ma-115	184	49	we	we	PRON
ma-115	184	50	find	find	VERB
ma-115	184	51	the	the	DET
ma-115	184	52	cross	cross	NOUN
ma-115	184	53	-	-	NOUN
ma-115	184	54	relations	relation	NOUN
ma-115	184	55	:	:	PUNCT
ma-115	184	56	[	[	PUNCT
ma-115	184	57	ĥa1,α−β,−2(α+β	ĥa1,α−β,−2(α+β	NOUN
ma-115	184	58	)	)	PUNCT
ma-115	184	59	]	]	PUNCT
ma-115	184	60	∗	∗	NOUN
ma-115	184	61	=	=	PUNCT
ma-115	184	62	ĥ−a	ĥ−a	NOUN
ma-115	184	63	2,α−β,−2(α+β	2,α−β,−2(α+β	NUM
ma-115	184	64	)	)	PUNCT
ma-115	184	65	,	,	PUNCT
ma-115	184	66	[	[	PUNCT
ma-115	184	67	ĥa2,α−β,−2(α+β	ĥa2,α−β,−2(α+β	NOUN
ma-115	184	68	)	)	PUNCT
ma-115	184	69	]	]	PUNCT
ma-115	184	70	∗	∗	NOUN
ma-115	184	71	=	=	SYM
ma-115	184	72	ĥ−a	ĥ−a	NOUN
ma-115	184	73	1,α−β,−2(α+β	1,α−β,−2(α+β	NUM
ma-115	184	74	)	)	PUNCT
ma-115	184	75	(	(	PUNCT
ma-115	184	76	35	35	NUM
ma-115	184	77	)	)	PUNCT
ma-115	184	78	which	which	PRON
ma-115	184	79	reproduce	reproduce	VERB
ma-115	184	80	(	(	PUNCT
ma-115	184	81	4	4	NUM
ma-115	184	82	)	)	PUNCT
ma-115	184	83	for	for	ADP
ma-115	184	84	a	a	DET
ma-115	184	85	=	=	SYM
ma-115	184	86	±1.parsevel	±1.parsevel	NOUN
ma-115	184	87	’s	’s	PART
ma-115	184	88	equalities	equality	NOUN
ma-115	184	89	separately	separately	ADV
ma-115	184	90	pertaining	pertain	VERB
ma-115	184	91	to	to	ADP
ma-115	184	92	ĥa1,α−β,−2(α+β	ĥa1,α−β,−2(α+β	NOUN
ma-115	184	93	)	)	PUNCT
ma-115	184	94	and	and	CCONJ
ma-115	184	95	ĥa2,α−β,−2(α+β	ĥa2,α−β,−2(α+β	NUM
ma-115	184	96	)	)	PUNCT
ma-115	184	97	are	be	AUX
ma-115	184	98	easily	easily	ADV
ma-115	184	99	proceedi.e.∫	proceedi.e.∫	ADJ
ma-115	184	100	∞	∞	NOUN
ma-115	184	101	0	0	PUNCT
ma-115	185	1	x−1	x−1	PROPN
ma-115	185	2	+	+	PROPN
ma-115	185	3	4(α+β)f	4(α+β)f	NUM
ma-115	185	4	(	(	PUNCT
ma-115	185	5	x)∗g(x)dx	x)∗g(x)dx	X
ma-115	185	6	=	=	SYM
ma-115	185	7	∫	∫	PROPN
ma-115	185	8	∞	∞	NOUN
ma-115	185	9	0	0	NUM
ma-115	186	1	x1	x1	PROPN
ma-115	186	2	+	+	NOUN
ma-115	186	3	2(α+β	2(α+β	NUM
ma-115	186	4	)	)	PUNCT
ma-115	186	5	[	[	PUNCT
ma-115	186	6	f̃	f̃	PROPN
ma-115	186	7	(	(	PUNCT
ma-115	186	8	a	a	PRON
ma-115	186	9	)	)	PUNCT
ma-115	186	10	1,α−β,−2(α+β)(x	1,α−β,−2(α+β)(x	NUM
ma-115	186	11	)	)	PUNCT
ma-115	186	12	]	]	PUNCT
ma-115	186	13	∗	∗	X
ma-115	186	14	g̃	g̃	PROPN
ma-115	186	15	(	(	PUNCT
ma-115	186	16	a	a	NOUN
ma-115	186	17	)	)	PUNCT
ma-115	186	18	1,α−β,−2(α+β)(x)dx∫	1,α−β,−2(α+β)(x)dx∫	NUM
ma-115	186	19	∞	∞	PROPN
ma-115	186	20	0	0	NUM
ma-115	186	21	x1−2(α+β)f	x1−2(α+β)f	PROPN
ma-115	186	22	(	(	PUNCT
ma-115	186	23	x)∗g(x)dx	x)∗g(x)dx	PROPN
ma-115	186	24	=	=	SYM
ma-115	186	25	∫	∫	PROPN
ma-115	186	26	∞	∞	PROPN
ma-115	186	27	0	0	NUM
ma-115	186	28	x1−4(α+β	x1−4(α+β	PROPN
ma-115	186	29	)	)	PUNCT
ma-115	186	30	[	[	PUNCT
ma-115	186	31	f̃	f̃	PROPN
ma-115	186	32	(	(	PUNCT
ma-115	186	33	a	a	NOUN
ma-115	186	34	)	)	PUNCT
ma-115	186	35	2,α−β,−2(α+β)(x	2,α−β,−2(α+β)(x	NUM
ma-115	186	36	)	)	PUNCT
ma-115	186	37	]	]	PUNCT
ma-115	186	38	∗	∗	X
ma-115	186	39	g̃	g̃	PROPN
ma-115	186	40	(	(	PUNCT
ma-115	186	41	a	a	NOUN
ma-115	186	42	)	)	PUNCT
ma-115	186	43	2,α−β,−2(α+β)(x)dx	2,α−β,−2(α+β)(x)dx	NOUN
ma-115	186	44	(	(	PUNCT
ma-115	186	45	36	36	NUM
ma-115	186	46	)	)	PUNCT
ma-115	186	47	as	as	ADV
ma-115	186	48	well	well	ADV
ma-115	186	49	as	as	ADP
ma-115	186	50	the	the	DET
ma-115	186	51	mixed	mixed	ADJ
ma-115	186	52	parsevel	parsevel	NOUN
ma-115	186	53	’s	’s	PART
ma-115	187	1	relation:∫	relation:∫	PROPN
ma-115	187	2	∞	∞	PROPN
ma-115	187	3	0	0	NUM
ma-115	187	4	f	f	NOUN
ma-115	187	5	(	(	PUNCT
ma-115	187	6	x)∗g(x)dx	x)∗g(x)dx	PROPN
ma-115	187	7	=	=	SYM
ma-115	187	8	∫	∫	PROPN
ma-115	187	9	∞	∞	NUM
ma-115	187	10	0	0	PUNCT
ma-115	188	1	[	[	PUNCT
ma-115	188	2	f̃	f̃	PROPN
ma-115	188	3	(	(	PUNCT
ma-115	188	4	a	a	PRON
ma-115	188	5	)	)	PUNCT
ma-115	188	6	1,α−β,−2(α+β)(x	1,α−β,−2(α+β)(x	NUM
ma-115	188	7	)	)	PUNCT
ma-115	188	8	]	]	PUNCT
ma-115	188	9	∗	∗	X
ma-115	188	10	g̃	g̃	PROPN
ma-115	188	11	(	(	PUNCT
ma-115	188	12	a	a	NOUN
ma-115	188	13	)	)	PUNCT
ma-115	188	14	2,α−β,−2(α+β)(x)dx	2,α−β,−2(α+β)(x)dx	NOUN
ma-115	188	15	.	.	PUNCT
ma-115	189	1	(	(	PUNCT
ma-115	189	2	37	37	NUM
ma-115	189	3	)	)	PUNCT
ma-115	189	4	https://doi.org/10.28924/ada/ma.3.6	https://doi.org/10.28924/ada/ma.3.6	PROPN
ma-115	189	5	eur	eur	NOUN
ma-115	189	6	.	.	PUNCT
ma-115	190	1	j.	j.	PROPN
ma-115	190	2	math	math	PROPN
ma-115	190	3	.	.	PUNCT
ma-115	191	1	anal	anal	PROPN
ma-115	191	2	.	.	PUNCT
ma-115	192	1	10.28924	10.28924	NUM
ma-115	192	2	/	/	SYM
ma-115	192	3	ada	ada	PROPN
ma-115	192	4	/	/	PROPN
ma-115	192	5	ma.3.6	ma.3.6	PROPN
ma-115	193	1	8for	8for	NUM
ma-115	193	2	α	α	PROPN
ma-115	194	1	+	+	X
ma-115	194	2	β	β	X
ma-115	194	3	=	=	SYM
ma-115	194	4	1	1	NUM
ma-115	194	5	4	4	NUM
ma-115	194	6	,	,	PUNCT
ma-115	194	7	the	the	DET
ma-115	194	8	above	above	ADJ
ma-115	194	9	equalities	equality	NOUN
ma-115	194	10	turn	turn	VERB
ma-115	194	11	into	into	ADP
ma-115	194	12	the	the	DET
ma-115	194	13	energy	energy	NOUN
ma-115	194	14	preserving	preserve	VERB
ma-115	194	15	relation	relation	NOUN
ma-115	194	16	of	of	ADP
ma-115	194	17	the	the	DET
ma-115	194	18	conventionaltransform	conventionaltransform	NOUN
ma-115	194	19	:	:	PUNCT
ma-115	194	20	∫	∫	PROPN
ma-115	195	1	∞	∞	PROPN
ma-115	195	2	0	0	NUM
ma-115	196	1	f	f	PROPN
ma-115	196	2	(	(	PUNCT
ma-115	196	3	x)∗g(x)dx	x)∗g(x)dx	PROPN
ma-115	196	4	=	=	SYM
ma-115	196	5	∫	∫	PROPN
ma-115	196	6	∞	∞	NUM
ma-115	196	7	0	0	PUNCT
ma-115	197	1	[	[	PUNCT
ma-115	197	2	f̃	f̃	PROPN
ma-115	197	3	(	(	PUNCT
ma-115	197	4	a	a	NOUN
ma-115	197	5	)	)	PUNCT
ma-115	197	6	α−β(x	α−β(x	NOUN
ma-115	197	7	)	)	PUNCT
ma-115	197	8	]	]	PUNCT
ma-115	197	9	∗	∗	X
ma-115	197	10	g̃	g̃	PROPN
ma-115	197	11	(	(	PUNCT
ma-115	197	12	a	a	NOUN
ma-115	197	13	)	)	PUNCT
ma-115	197	14	α−β(x)dx	α−β(x)dx	PROPN
ma-115	197	15	.	.	PUNCT
ma-115	198	1	operational	operational	ADJ
ma-115	198	2	rules	rule	NOUN
ma-115	198	3	similar	similar	ADJ
ma-115	198	4	to	to	ADP
ma-115	198	5	(	(	PUNCT
ma-115	198	6	9	9	NUM
ma-115	198	7	)	)	PUNCT
ma-115	198	8	can	can	AUX
ma-115	198	9	be	be	AUX
ma-115	198	10	stated	state	VERB
ma-115	198	11	for	for	ADP
ma-115	198	12	the	the	DET
ma-115	198	13	fractional	fractional	ADJ
ma-115	198	14	transforms	transform	NOUN
ma-115	198	15	,	,	PUNCT
ma-115	198	16	involving	involve	VERB
ma-115	198	17	of	of	ADP
ma-115	198	18	courseappropriate	courseappropriate	ADJ
ma-115	198	19	bessel	bessel	NOUN
ma-115	198	20	-	-	PUNCT
ma-115	198	21	type	type	NOUN
ma-115	198	22	differential	differential	ADJ
ma-115	198	23	operators	operator	NOUN
ma-115	198	24	.	.	PUNCT
ma-115	199	1	indeed	indeed	ADV
ma-115	199	2	we	we	PRON
ma-115	199	3	see	see	VERB
ma-115	199	4	that	that	SCONJ
ma-115	199	5	[	[	PUNCT
ma-115	199	6	ĥa1,α−β,−2(α+β	ĥa1,α−β,−2(α+β	NOUN
ma-115	199	7	)	)	PUNCT
ma-115	199	8	b̂	b̂	NOUN
ma-115	199	9	∗	∗	NOUN
ma-115	199	10	α−β,−2(α+β),af	α−β,−2(α+β),af	PRON
ma-115	199	11	]	]	PUNCT
ma-115	199	12	(	(	PUNCT
ma-115	199	13	y	y	NOUN
ma-115	199	14	)	)	PUNCT
ma-115	199	15	=	=	SYM
ma-115	200	1	−	−	PROPN
ma-115	200	2	y2	y2	PROPN
ma-115	200	3	sin2	sin2	PROPN
ma-115	200	4	φ	φ	PROPN
ma-115	200	5	[	[	PUNCT
ma-115	200	6	ĥa1,α−β,−2(α+β)f	ĥa1,α−β,−2(α+β)f	X
ma-115	200	7	]	]	PUNCT
ma-115	200	8	(	(	PUNCT
ma-115	200	9	y	y	NOUN
ma-115	200	10	)	)	PUNCT
ma-115	200	11	,	,	PUNCT
ma-115	200	12	[	[	PUNCT
ma-115	200	13	ĥa2,α−β,−2(α+β	ĥa2,α−β,−2(α+β	NOUN
ma-115	200	14	)	)	PUNCT
ma-115	200	15	b̂	b̂	NOUN
ma-115	200	16	∗	∗	NOUN
ma-115	200	17	α−β,−2(α+β),af	α−β,−2(α+β),af	PRON
ma-115	200	18	]	]	PUNCT
ma-115	200	19	(	(	PUNCT
ma-115	200	20	y	y	NOUN
ma-115	200	21	)	)	PUNCT
ma-115	200	22	=	=	SYM
ma-115	201	1	−	−	PROPN
ma-115	201	2	y2	y2	PROPN
ma-115	201	3	sin2	sin2	PROPN
ma-115	201	4	φ	φ	PROPN
ma-115	201	5	[	[	PUNCT
ma-115	201	6	ĥa2,α−β,−2(α+β)f	ĥa2,α−β,−2(α+β)f	NOUN
ma-115	201	7	]	]	PUNCT
ma-115	201	8	(	(	PUNCT
ma-115	201	9	y	y	NOUN
ma-115	201	10	)	)	PUNCT
ma-115	201	11	,	,	PUNCT
ma-115	201	12	(	(	PUNCT
ma-115	201	13	38	38	NUM
ma-115	201	14	)	)	PUNCT
ma-115	201	15	with	with	ADP
ma-115	201	16	b̂α−β,−2(α+β),a	b̂α−β,−2(α+β),a	PROPN
ma-115	201	17	=	=	SYM
ma-115	201	18	−2k̂	−2k̂	PROPN
ma-115	201	19	(	(	PUNCT
ma-115	201	20	2	2	NUM
ma-115	201	21	)	)	PUNCT
ma-115	201	22	−	−	NOUN
ma-115	201	23	−	−	PROPN
ma-115	201	24	2	2	NUM
ma-115	201	25	cot2	cot2	NOUN
ma-115	201	26	φk̂	φk̂	PROPN
ma-115	201	27	(	(	PUNCT
ma-115	201	28	2	2	NUM
ma-115	201	29	)	)	PUNCT
ma-115	201	30	+	+	CCONJ
ma-115	201	31	−	−	PROPN
ma-115	201	32	4	4	NUM
ma-115	201	33	cotφk̂	cotφk̂	NOUN
ma-115	201	34	(	(	PUNCT
ma-115	201	35	2	2	NUM
ma-115	201	36	)	)	PUNCT
ma-115	201	37	3	3	NUM
ma-115	201	38	,	,	PUNCT
ma-115	201	39	(	(	PUNCT
ma-115	201	40	39	39	NUM
ma-115	201	41	)	)	PUNCT
ma-115	201	42	and	and	CCONJ
ma-115	201	43	in	in	ADP
ma-115	201	44	particular	particular	ADJ
ma-115	201	45	b̂α−β	b̂α−β	NOUN
ma-115	201	46	,	,	PUNCT
ma-115	201	47	a	a	DET
ma-115	201	48	≡	≡	PROPN
ma-115	201	49	b̂α−β,−	b̂α−β,−	PROPN
ma-115	201	50	(	(	PUNCT
ma-115	201	51	1	1	NUM
ma-115	201	52	2	2	NUM
ma-115	201	53	)	)	PUNCT
ma-115	201	54	,	,	PUNCT
ma-115	201	55	a	a	DET
ma-115	201	56	=	=	X
ma-115	201	57	b̂∗	b̂∗	ADJ
ma-115	201	58	α−β,−	α−β,−	PROPN
ma-115	201	59	(	(	PUNCT
ma-115	201	60	1	1	NUM
ma-115	201	61	2	2	NUM
ma-115	201	62	)	)	PUNCT
ma-115	201	63	,	,	PUNCT
ma-115	201	64	a	a	DET
ma-115	201	65	=	=	NOUN
ma-115	201	66	−2k̂−	−2k̂−	NOUN
ma-115	201	67	−	−	PROPN
ma-115	201	68	2	2	NUM
ma-115	201	69	cot2	cot2	NOUN
ma-115	201	70	φk̂+	φk̂+	ADV
ma-115	201	71	−	−	PROPN
ma-115	201	72	4	4	NUM
ma-115	201	73	cotφk̂3	cotφk̂3	NOUN
ma-115	201	74	.	.	PUNCT
ma-115	202	1	(	(	PUNCT
ma-115	202	2	40	40	NUM
ma-115	202	3	)	)	PUNCT
ma-115	202	4	relation	relation	NOUN
ma-115	202	5	(	(	PUNCT
ma-115	202	6	38	38	NUM
ma-115	202	7	)	)	PUNCT
ma-115	202	8	gives	give	VERB
ma-115	202	9	the	the	DET
ma-115	202	10	relevance	relevance	NOUN
ma-115	202	11	of	of	ADP
ma-115	202	12	the	the	DET
ma-115	202	13	fractional	fractional	ADJ
ma-115	202	14	transforms	transform	VERB
ma-115	202	15	for	for	ADP
ma-115	202	16	the	the	DET
ma-115	202	17	solution	solution	NOUN
ma-115	202	18	of	of	ADP
ma-115	202	19	differential	differential	NOUN
ma-115	202	20	equationsinvolving	equationsinvolve	VERB
ma-115	202	21	the	the	DET
ma-115	202	22	operators	operator	NOUN
ma-115	202	23	b̂∗α−β,−2(α+β),a	b̂∗α−β,−2(α+β),a	VERB
ma-115	202	24	and	and	CCONJ
ma-115	202	25	b̂α−β,−2(α+β),a	b̂α−β,−2(α+β),a	VERB
ma-115	202	26	like	like	INTJ
ma-115	202	27	,	,	PUNCT
ma-115	202	28	for	for	ADP
ma-115	202	29	instance	instance	NOUN
ma-115	202	30	,	,	PUNCT
ma-115	202	31	the	the	DET
ma-115	202	32	evolution	evolution	NOUN
ma-115	202	33	equation	equation	NOUN
ma-115	202	34	k	k	PROPN
ma-115	202	35	∂	∂	PROPN
ma-115	202	36	∂τ	∂τ	PROPN
ma-115	202	37	h(x	h(x	PROPN
ma-115	202	38	,	,	PUNCT
ma-115	202	39	τ	τ	X
ma-115	202	40	)	)	PUNCT
ma-115	203	1	=	=	SYM
ma-115	203	2	b̂∗α−β,−2(α+β),a	b̂∗α−β,−2(α+β),a	PROPN
ma-115	203	3	h(x	h(x	PROPN
ma-115	203	4	,	,	PUNCT
ma-115	203	5	τ	τ	PROPN
ma-115	203	6	)	)	PUNCT
ma-115	203	7	,	,	PUNCT
ma-115	203	8	(	(	PUNCT
ma-115	203	9	41	41	NUM
ma-115	203	10	)	)	PUNCT
ma-115	203	11	or	or	CCONJ
ma-115	203	12	,	,	PUNCT
ma-115	203	13	more	more	ADJ
ma-115	203	14	in	in	ADP
ma-115	203	15	general	general	ADJ
ma-115	203	16	,	,	PUNCT
ma-115	203	17	the	the	DET
ma-115	203	18	following	follow	VERB
ma-115	203	19	k	k	PROPN
ma-115	203	20	∂	∂	NOUN
ma-115	203	21	∂τ	∂τ	PROPN
ma-115	203	22	h(x	h(x	PROPN
ma-115	203	23	,	,	PUNCT
ma-115	203	24	τ	τ	X
ma-115	203	25	)	)	PUNCT
ma-115	203	26	=	=	SYM
ma-115	204	1	p	p	X
ma-115	204	2	(	(	PUNCT
ma-115	204	3	b̂∗α−β,−2(α+β),a	b̂∗α−β,−2(α+β),a	PROPN
ma-115	204	4	)	)	PUNCT
ma-115	204	5	h(x	h(x	PROPN
ma-115	204	6	,	,	PUNCT
ma-115	204	7	τ	τ	PROPN
ma-115	204	8	)	)	PUNCT
ma-115	204	9	(	(	PUNCT
ma-115	204	10	42	42	NUM
ma-115	204	11	)	)	PUNCT
ma-115	204	12	involving	involve	VERB
ma-115	204	13	polynomial	polynomial	ADJ
ma-115	204	14	function	function	NOUN
ma-115	204	15	of	of	ADP
ma-115	204	16	b̂∗α−β,−2(α+β),a	b̂∗α−β,−2(α+β),a	PROPN
ma-115	204	17	(	(	PUNCT
ma-115	204	18	or	or	CCONJ
ma-115	204	19	the	the	DET
ma-115	204	20	adjoint	adjoint	NOUN
ma-115	204	21	involving	involve	VERB
ma-115	204	22	a	a	DET
ma-115	204	23	polynomial	polynomial	NOUN
ma-115	204	24	of	of	ADP
ma-115	204	25	b̂α−β,−2(α+β),a).then	b̂α−β,−2(α+β),a).then	NOUN
ma-115	204	26	considering	consider	VERB
ma-115	204	27	equation	equation	NOUN
ma-115	204	28	(	(	PUNCT
ma-115	204	29	41	41	NUM
ma-115	204	30	)	)	PUNCT
ma-115	204	31	,	,	PUNCT
ma-115	204	32	we	we	PRON
ma-115	204	33	note	note	VERB
ma-115	204	34	that	that	SCONJ
ma-115	204	35	the	the	DET
ma-115	204	36	solution	solution	NOUN
ma-115	204	37	turns	turn	VERB
ma-115	204	38	out	out	ADP
ma-115	204	39	to	to	PART
ma-115	204	40	be	be	AUX
ma-115	204	41	h(x	h(x	PROPN
ma-115	204	42	,	,	PUNCT
ma-115	204	43	τ	τ	X
ma-115	204	44	)	)	PUNCT
ma-115	204	45	=	=	PUNCT
ma-115	205	1	[	[	PUNCT
ma-115	205	2	ĥ−a	ĥ−a	NOUN
ma-115	205	3	1,α−β,−2(α+β	1,α−β,−2(α+β	NUM
ma-115	205	4	)	)	PUNCT
ma-115	205	5	ĥ	ĥ	X
ma-115	205	6	a	a	DET
ma-115	205	7	α−β,−2(α+β),a(y	α−β,−2(α+β),a(y	PROPN
ma-115	205	8	,	,	PUNCT
ma-115	205	9	τ	τ	PROPN
ma-115	205	10	)	)	PUNCT
ma-115	205	11	]	]	PUNCT
ma-115	205	12	(	(	PUNCT
ma-115	205	13	x	x	X
ma-115	205	14	,	,	PUNCT
ma-115	205	15	τ	τ	X
ma-115	205	16	)	)	PUNCT
ma-115	205	17	(	(	PUNCT
ma-115	205	18	43	43	NUM
ma-115	205	19	)	)	PUNCT
ma-115	205	20	before	before	ADP
ma-115	205	21	giving	give	VERB
ma-115	205	22	details	detail	NOUN
ma-115	205	23	of	of	ADP
ma-115	205	24	the	the	DET
ma-115	205	25	expression	expression	NOUN
ma-115	205	26	of	of	ADP
ma-115	205	27	h(x	h(x	PROPN
ma-115	205	28	,	,	PUNCT
ma-115	205	29	τ	τ	PROPN
ma-115	205	30	)	)	PUNCT
ma-115	205	31	from	from	ADP
ma-115	205	32	the	the	DET
ma-115	205	33	above	above	ADJ
ma-115	205	34	scheme	scheme	NOUN
ma-115	205	35	,	,	PUNCT
ma-115	205	36	let	let	VERB
ma-115	205	37	us	we	PRON
ma-115	205	38	note	note	VERB
ma-115	205	39	that	that	SCONJ
ma-115	205	40	theoperators	theoperator	NOUN
ma-115	205	41	b̂α−β,−2(α+β),a	b̂α−β,−2(α+β),a	VERB
ma-115	205	42	and	and	CCONJ
ma-115	205	43	b̂∗α−β,−2(α+β),a	b̂∗α−β,−2(α+β),a	PROPN
ma-115	205	44	arise	arise	NOUN
ma-115	205	45	from	from	ADP
ma-115	205	46	the	the	DET
ma-115	205	47	adjoint	adjoint	NOUN
ma-115	205	48	transformation	transformation	NOUN
ma-115	205	49	respectively	respectively	ADV
ma-115	205	50	of	of	ADP
ma-115	205	51	b̂α−β,−2(α+β),a	b̂α−β,−2(α+β),a	NOUN
ma-115	205	52	and	and	CCONJ
ma-115	205	53	b̂∗α−β,−2(α+β),a	b̂∗α−β,−2(α+β),a	NOUN
ma-115	205	54	through	through	ADP
ma-115	205	55	the	the	DET
ma-115	205	56	operator	operator	NOUN
ma-115	205	57	k̂(2)+	k̂(2)+	NOUN
ma-115	205	58	=	=	SYM
ma-115	205	59	k̂	k̂	X
ma-115	205	60	(	(	PUNCT
ma-115	205	61	1	1	X
ma-115	205	62	)	)	PUNCT
ma-115	205	63	+	+	NOUN
ma-115	205	64	=	=	SYM
ma-115	205	65	(	(	PUNCT
ma-115	205	66	x	x	SYM
ma-115	205	67	2	2	NUM
ma-115	205	68	2	2	NUM
ma-115	205	69	)	)	PUNCT
ma-115	205	70	.	.	PUNCT
ma-115	206	1	in	in	ADP
ma-115	206	2	other	other	ADJ
ma-115	206	3	words	word	NOUN
ma-115	206	4	:	:	PUNCT
ma-115	206	5	b̂α−β,−2(α+β),a	b̂α−β,−2(α+β),a	NOUN
ma-115	206	6	=	=	SYM
ma-115	206	7	e	e	PROPN
ma-115	206	8	−i	−i	PROPN
ma-115	206	9	cot	cot	NOUN
ma-115	206	10	(	(	PUNCT
ma-115	206	11	φ	φ	NOUN
ma-115	206	12	)	)	PUNCT
ma-115	206	13	(	(	PUNCT
ma-115	206	14	x2	x2	NOUN
ma-115	206	15	2	2	X
ma-115	206	16	)	)	PUNCT
ma-115	206	17	b̂α−β,−2(α+β)e	b̂α−β,−2(α+β)e	NOUN
ma-115	207	1	i	i	PRON
ma-115	207	2	cot	cot	VERB
ma-115	207	3	(	(	PUNCT
ma-115	207	4	φ	φ	NOUN
ma-115	207	5	)	)	PUNCT
ma-115	207	6	(	(	PUNCT
ma-115	207	7	x2	x2	NOUN
ma-115	207	8	2	2	X
ma-115	207	9	)	)	PUNCT
ma-115	207	10	b̂∗α−β,−2(α+β),a	b̂∗α−β,−2(α+β),a	NOUN
ma-115	207	11	=	=	SYM
ma-115	207	12	e	e	PROPN
ma-115	207	13	−i	−i	PROPN
ma-115	207	14	cot	cot	NOUN
ma-115	207	15	(	(	PUNCT
ma-115	207	16	φ	φ	NOUN
ma-115	207	17	)	)	PUNCT
ma-115	207	18	(	(	PUNCT
ma-115	207	19	x2	x2	NOUN
ma-115	207	20	2	2	X
ma-115	207	21	)	)	PUNCT
ma-115	207	22	b̂∗α−β,−2(α+β)e	b̂∗α−β,−2(α+β)e	PUNCT
ma-115	208	1	i	i	PRON
ma-115	208	2	cot	cot	VERB
ma-115	208	3	(	(	PUNCT
ma-115	208	4	φ	φ	NOUN
ma-115	208	5	)	)	PUNCT
ma-115	208	6	(	(	PUNCT
ma-115	208	7	x2	x2	NOUN
ma-115	208	8	2	2	X
ma-115	208	9	)	)	PUNCT
ma-115	208	10	(	(	PUNCT
ma-115	208	11	44	44	NUM
ma-115	208	12	)	)	PUNCT
ma-115	208	13	which	which	PRON
ma-115	208	14	can	can	AUX
ma-115	208	15	be	be	AUX
ma-115	208	16	recast	recast	VERB
ma-115	208	17	as	as	ADP
ma-115	208	18	b̂α−β,−2(α+β),a	b̂α−β,−2(α+β),a	NOUN
ma-115	208	19	=	=	PUNCT
ma-115	208	20	xα+3β−1d̂ax	xα+3β−1d̂ax	PROPN
ma-115	208	21	2(α−β)+1d̂ax	2(α−β)+1d̂ax	NUM
ma-115	208	22	−3α−β	−3α−β	NOUN
ma-115	208	23	b̂∗α−β,−2(α+β),a	b̂∗α−β,−2(α+β),a	NOUN
ma-115	208	24	=	=	PUNCT
ma-115	208	25	x−3α−βd̂ax	x−3α−βd̂ax	PROPN
ma-115	208	26	2(α+β)+1d̂ax	2(α+β)+1d̂ax	NUM
ma-115	208	27	α+3β−1	α+3β−1	NUM
ma-115	208	28	(	(	PUNCT
ma-115	208	29	45	45	NUM
ma-115	208	30	)	)	PUNCT
ma-115	208	31	https://doi.org/10.28924/ada/ma.3.6	https://doi.org/10.28924/ada/ma.3.6	PROPN
ma-115	208	32	eur	eur	NOUN
ma-115	208	33	.	.	PUNCT
ma-115	209	1	j.	j.	PROPN
ma-115	209	2	math	math	PROPN
ma-115	209	3	.	.	PUNCT
ma-115	210	1	anal	anal	PROPN
ma-115	210	2	.	.	PUNCT
ma-115	211	1	10.28924	10.28924	NUM
ma-115	211	2	/	/	SYM
ma-115	211	3	ada	ada	PROPN
ma-115	211	4	/	/	SYM
ma-115	211	5	ma.3.6	ma.3.6	PROPN
ma-115	211	6	9	9	NUM
ma-115	211	7	where	where	SCONJ
ma-115	211	8	d̂a	d̂a	PROPN
ma-115	211	9	being	be	AUX
ma-115	211	10	a	a	DET
ma-115	211	11	linear	linear	ADJ
ma-115	211	12	combination	combination	NOUN
ma-115	211	13	of	of	ADP
ma-115	211	14	the	the	DET
ma-115	211	15	heisenberg	heisenberg	PROPN
ma-115	211	16	operators	operator	NOUN
ma-115	211	17	x	x	PUNCT
ma-115	211	18	and	and	CCONJ
ma-115	211	19	−i	−i	PROPN
ma-115	211	20	∂∂x	∂∂x	PROPN
ma-115	211	21	as	as	ADP
ma-115	211	22	d̂a	d̂a	X
ma-115	211	23	=	=	SYM
ma-115	211	24	e	e	PROPN
ma-115	211	25	−i	−i	PROPN
ma-115	211	26	cot	cot	NOUN
ma-115	211	27	(	(	PUNCT
ma-115	211	28	φ	φ	NOUN
ma-115	211	29	)	)	PUNCT
ma-115	211	30	(	(	PUNCT
ma-115	211	31	x2	x2	NOUN
ma-115	211	32	2	2	X
ma-115	211	33	)	)	PUNCT
ma-115	211	34	∂	∂	NOUN
ma-115	212	1	∂x	∂x	PROPN
ma-115	212	2	e	e	NOUN
ma-115	212	3	i	i	PRON
ma-115	212	4	cot	cot	VERB
ma-115	212	5	(	(	PUNCT
ma-115	212	6	φ	φ	NOUN
ma-115	212	7	)	)	PUNCT
ma-115	212	8	(	(	PUNCT
ma-115	212	9	x2	x2	NOUN
ma-115	212	10	2	2	X
ma-115	212	11	)	)	PUNCT
ma-115	213	1	=	=	NOUN
ma-115	213	2	i	i	PRON
ma-115	213	3	sinφ	sinφ	VERB
ma-115	213	4	[	[	PUNCT
ma-115	213	5	cos(φ)x	cos(φ)x	ADJ
ma-115	213	6	−	−	NOUN
ma-115	213	7	i	i	PRON
ma-115	213	8	sin(φ	sin(φ	PROPN
ma-115	213	9	)	)	PUNCT
ma-115	213	10	∂	∂	PUNCT
ma-115	214	1	∂x	∂x	PROPN
ma-115	214	2	]	]	PUNCT
ma-115	214	3	(	(	PUNCT
ma-115	214	4	46	46	NUM
ma-115	214	5	)	)	PUNCT
ma-115	214	6	the	the	DET
ma-115	214	7	exponential	exponential	ADJ
ma-115	214	8	operators	operator	NOUN
ma-115	214	9	ebb̂α−β,−2(α+β),a	ebb̂α−β,−2(α+β),a	PROPN
ma-115	214	10	and	and	CCONJ
ma-115	214	11	ebb̂∗α−β,−2(α+β),a	ebb̂∗α−β,−2(α+β),a	PROPN
ma-115	214	12	arise	arise	VERB
ma-115	214	13	from	from	ADP
ma-115	214	14	the	the	DET
ma-115	214	15	same	same	ADJ
ma-115	214	16	adjoint	adjoint	NOUN
ma-115	214	17	transfor	transfor	NOUN
ma-115	214	18	-	-	PUNCT
ma-115	214	19	mations	mation	NOUN
ma-115	214	20	of	of	ADP
ma-115	214	21	ebb̂α−β,−2(α+β	ebb̂α−β,−2(α+β	NOUN
ma-115	214	22	)	)	PUNCT
ma-115	214	23	and	and	CCONJ
ma-115	214	24	ebb̂∗α−β,−2(α+β	ebb̂∗α−β,−2(α+β	NOUN
ma-115	214	25	)	)	PUNCT
ma-115	214	26	respectively	respectively	ADV
ma-115	214	27	;	;	PUNCT
ma-115	214	28	viz	viz	NUM
ma-115	214	29	ebb̂α−β,−2(α+β),a	ebb̂α−β,−2(α+β),a	PROPN
ma-115	214	30	=	=	PUNCT
ma-115	214	31	e	e	PROPN
ma-115	214	32	−i	−i	PROPN
ma-115	214	33	cot	cot	NOUN
ma-115	214	34	(	(	PUNCT
ma-115	214	35	φ	φ	NOUN
ma-115	214	36	)	)	PUNCT
ma-115	214	37	(	(	PUNCT
ma-115	214	38	x2	x2	NOUN
ma-115	214	39	2	2	X
ma-115	214	40	)	)	PUNCT
ma-115	214	41	ebb̂α−β,−2(α+β)e	ebb̂α−β,−2(α+β)e	PROPN
ma-115	215	1	i	i	PRON
ma-115	215	2	cot	cot	VERB
ma-115	215	3	(	(	PUNCT
ma-115	215	4	φ	φ	NOUN
ma-115	215	5	)	)	PUNCT
ma-115	215	6	(	(	PUNCT
ma-115	215	7	x2	x2	NOUN
ma-115	215	8	2	2	X
ma-115	215	9	)	)	PUNCT
ma-115	215	10	e	e	VERB
ma-115	215	11	bb̂∗	bb̂∗	NOUN
ma-115	215	12	α−β,−2(α+β),a	α−β,−2(α+β),a	X
ma-115	215	13	=	=	SYM
ma-115	215	14	e	e	PROPN
ma-115	215	15	−i	−i	PROPN
ma-115	215	16	cot	cot	NOUN
ma-115	215	17	(	(	PUNCT
ma-115	215	18	φ	φ	NOUN
ma-115	215	19	)	)	PUNCT
ma-115	215	20	(	(	PUNCT
ma-115	215	21	x2	x2	NOUN
ma-115	215	22	2	2	X
ma-115	215	23	)	)	PUNCT
ma-115	215	24	e	e	VERB
ma-115	215	25	bb̂∗	bb̂∗	NOUN
ma-115	215	26	α−β,−2(α+β)e	α−β,−2(α+β)e	NOUN
ma-115	215	27	i	i	PRON
ma-115	215	28	cot	cot	INTJ
ma-115	215	29	(	(	PUNCT
ma-115	215	30	φ	φ	NOUN
ma-115	215	31	)	)	PUNCT
ma-115	215	32	(	(	PUNCT
ma-115	215	33	x2	x2	NOUN
ma-115	215	34	2	2	X
ma-115	215	35	)	)	PUNCT
ma-115	215	36	(	(	PUNCT
ma-115	215	37	47	47	NUM
ma-115	215	38	)	)	PUNCT
ma-115	215	39	which	which	PRON
ma-115	215	40	on	on	ADP
ma-115	215	41	account	account	NOUN
ma-115	215	42	of	of	ADP
ma-115	215	43	(	(	PUNCT
ma-115	215	44	15	15	NUM
ma-115	215	45	)	)	PUNCT
ma-115	215	46	yields	yield	VERB
ma-115	215	47	an	an	DET
ma-115	215	48	explicit	explicit	ADJ
ma-115	215	49	functional	functional	ADJ
ma-115	215	50	expression	expression	NOUN
ma-115	215	51	for	for	ADP
ma-115	215	52	both	both	PRON
ma-115	215	53	operators.accordingly	operators.accordingly	ADV
ma-115	215	54	,	,	PUNCT
ma-115	215	55	thesolution	thesolution	NOUN
ma-115	215	56	of	of	ADP
ma-115	215	57	equation	equation	NOUN
ma-115	215	58	(	(	PUNCT
ma-115	215	59	41	41	NUM
ma-115	215	60	)	)	PUNCT
ma-115	215	61	can	can	AUX
ma-115	215	62	be	be	AUX
ma-115	215	63	written	write	VERB
ma-115	215	64	as	as	ADP
ma-115	215	65	h(x	h(x	PROPN
ma-115	215	66	,	,	PUNCT
ma-115	215	67	τ	τ	X
ma-115	215	68	)	)	PUNCT
ma-115	215	69	=	=	SYM
ma-115	216	1	k	k	PROPN
ma-115	216	2	2τ	2τ	PROPN
ma-115	216	3	x1−4(α+β	x1−4(α+β	PROPN
ma-115	216	4	)	)	PUNCT
ma-115	216	5	∫	∫	PROPN
ma-115	217	1	∞	∞	PROPN
ma-115	217	2	0	0	NUM
ma-115	217	3	(	(	PUNCT
ma-115	217	4	xy)2(α+β)e−	xy)2(α+β)e−	PROPN
ma-115	217	5	(	(	PUNCT
ma-115	217	6	k	k	NOUN
ma-115	217	7	4τ	4τ	NUM
ma-115	217	8	)	)	PUNCT
ma-115	217	9	(	(	PUNCT
ma-115	217	10	x2+y2)e−	x2+y2)e−	X
ma-115	217	11	(	(	PUNCT
ma-115	217	12	i	i	NOUN
ma-115	217	13	2	2	X
ma-115	217	14	)	)	PUNCT
ma-115	217	15	cot(φ)(x2−y2)iα−β	cot(φ)(x2−y2)iα−β	PROPN
ma-115	217	16	(	(	PUNCT
ma-115	217	17	k	k	PROPN
ma-115	217	18	2τ	2τ	NUM
ma-115	217	19	xy	xy	PROPN
ma-115	217	20	)	)	PUNCT
ma-115	218	1	f	f	PROPN
ma-115	218	2	(	(	PUNCT
ma-115	218	3	y)dy	y)dy	PROPN
ma-115	218	4	(	(	PUNCT
ma-115	218	5	48	48	NUM
ma-115	218	6	)	)	PUNCT
ma-115	218	7	under	under	ADP
ma-115	218	8	the	the	DET
ma-115	218	9	same	same	ADJ
ma-115	218	10	condition	condition	NOUN
ma-115	218	11	specified	specify	VERB
ma-115	218	12	in	in	ADP
ma-115	218	13	connection	connection	NOUN
ma-115	218	14	with	with	ADP
ma-115	218	15	equation	equation	NOUN
ma-115	218	16	(	(	PUNCT
ma-115	218	17	14	14	NUM
ma-115	218	18	)	)	PUNCT
ma-115	218	19	.	.	PUNCT
ma-115	219	1	one	one	PRON
ma-115	219	2	can	can	AUX
ma-115	219	3	also	also	ADV
ma-115	219	4	note	note	VERB
ma-115	219	5	thatthe	thatthe	NOUN
ma-115	219	6	similarity	similarity	NOUN
ma-115	219	7	transformation	transformation	NOUN
ma-115	219	8	like	like	ADP
ma-115	219	9	link	link	NOUN
ma-115	219	10	between	between	ADP
ma-115	219	11	the	the	DET
ma-115	219	12	operators	operator	NOUN
ma-115	219	13	b̂α−β,−2(α+β),a	b̂α−β,−2(α+β),a	PROPN
ma-115	219	14	and	and	CCONJ
ma-115	219	15	b̂α−β,−2(α+β)suggests	b̂α−β,−2(α+β)suggest	NOUN
ma-115	219	16	to	to	PART
ma-115	219	17	recover	recover	VERB
ma-115	219	18	equation(48	equation(48	NOUN
ma-115	219	19	)	)	PUNCT
ma-115	219	20	from(41	from(41	NOUN
ma-115	219	21	)	)	PUNCT
ma-115	219	22	transforming	transform	VERB
ma-115	219	23	h(x	h(x	PROPN
ma-115	219	24	,	,	PUNCT
ma-115	219	25	τ	τ	PROPN
ma-115	219	26	)	)	PUNCT
ma-115	219	27	to	to	ADP
ma-115	219	28	h(x	h(x	PROPN
ma-115	219	29	,	,	PUNCT
ma-115	219	30	τ	τ	PROPN
ma-115	219	31	)	)	PUNCT
ma-115	219	32	=	=	SYM
ma-115	219	33	h(x	h(x	PROPN
ma-115	219	34	,	,	PUNCT
ma-115	219	35	τ)e	τ)e	PUNCT
ma-115	219	36	i	i	PRON
ma-115	219	37	cot	cot	NOUN
ma-115	219	38	(	(	PUNCT
ma-115	219	39	φ	φ	NOUN
ma-115	219	40	)	)	PUNCT
ma-115	219	41	(	(	PUNCT
ma-115	219	42	x2	x2	NOUN
ma-115	219	43	2	2	NUM
ma-115	219	44	)	)	PUNCT
ma-115	219	45	.in	.in	PART
ma-115	220	1	fact	fact	NOUN
ma-115	220	2	the	the	DET
ma-115	220	3	fractional	fractional	ADJ
ma-115	220	4	transforms	transform	VERB
ma-115	220	5	ĥa1,α−β,−2(α+β	ĥa1,α−β,−2(α+β	NOUN
ma-115	220	6	)	)	PUNCT
ma-115	220	7	and	and	CCONJ
ma-115	220	8	ĥa2,α−β,−2(α+β	ĥa2,α−β,−2(α+β	NUM
ma-115	220	9	)	)	PUNCT
ma-115	220	10	are	be	AUX
ma-115	220	11	linked	link	VERB
ma-115	220	12	to	to	ADP
ma-115	220	13	ĥaα−β	ĥaα−β	PROPN
ma-115	220	14	through	through	ADP
ma-115	220	15	thesame	thesame	ADJ
ma-115	220	16	similarity	similarity	NOUN
ma-115	220	17	transformation	transformation	NOUN
ma-115	220	18	holding	holding	NOUN
ma-115	220	19	between	between	ADP
ma-115	220	20	the	the	DET
ma-115	220	21	ordinary	ordinary	ADJ
ma-115	220	22	transforms	transform	NOUN
ma-115	220	23	;	;	PUNCT
ma-115	220	24	viz	viz	NUM
ma-115	220	25	.	.	PUNCT
ma-115	220	26	ĥa1,α−β,−2(α+β	ĥa1,α−β,−2(α+β	NOUN
ma-115	220	27	)	)	PUNCT
ma-115	221	1	=	=	VERB
ma-115	221	2	x−2(α+β)+	x−2(α+β)+	VERB
ma-115	221	3	1	1	NUM
ma-115	221	4	2	2	NUM
ma-115	221	5	ĥaα−β	ĥaα−β	NOUN
ma-115	221	6	x2(α+β)−	x2(α+β)−	PROPN
ma-115	221	7	1	1	NUM
ma-115	221	8	2	2	NUM
ma-115	221	9	ĥa2,α−β,−2(α+β	ĥa2,α−β,−2(α+β	NUM
ma-115	221	10	)	)	PUNCT
ma-115	222	1	=	=	PUNCT
ma-115	222	2	x2(α+β)−	x2(α+β)−	PROPN
ma-115	222	3	1	1	NUM
ma-115	222	4	2	2	NUM
ma-115	222	5	ĥaα−β	ĥaα−β	NOUN
ma-115	222	6	x−2(α+β)+	x−2(α+β)+	VERB
ma-115	222	7	1	1	NUM
ma-115	222	8	2	2	NUM
ma-115	222	9	as	as	ADP
ma-115	222	10	a	a	DET
ma-115	222	11	straightforward	straightforward	ADJ
ma-115	222	12	consequence	consequence	NOUN
ma-115	222	13	of	of	ADP
ma-115	222	14	the	the	DET
ma-115	222	15	relations	relation	NOUN
ma-115	222	16	b̂α−β,−2(α+β),a	b̂α−β,−2(α+β),a	PROPN
ma-115	222	17	=	=	PUNCT
ma-115	222	18	x2(α+β)−	x2(α+β)−	PROPN
ma-115	222	19	1	1	NUM
ma-115	222	20	2	2	NUM
ma-115	222	21	b̂α−β	b̂α−β	NOUN
ma-115	222	22	,	,	PUNCT
ma-115	222	23	a	a	DET
ma-115	222	24	x	x	X
ma-115	222	25	−2(α+β)+	−2(α+β)+	SYM
ma-115	222	26	1	1	NUM
ma-115	222	27	2	2	NUM
ma-115	222	28	b̂∗α−β,−2(α+β),a	b̂∗α−β,−2(α+β),a	NOUN
ma-115	222	29	=	=	PUNCT
ma-115	222	30	x−2(α+β)+	x−2(α+β)+	VERB
ma-115	222	31	1	1	NUM
ma-115	222	32	2	2	NUM
ma-115	222	33	b̂α−β	b̂α−β	NOUN
ma-115	222	34	,	,	PUNCT
ma-115	222	35	a	a	DET
ma-115	222	36	x	x	SYM
ma-115	222	37	2(α+β)−	2(α+β)−	NUM
ma-115	222	38	1	1	NUM
ma-115	222	39	2	2	NUM
ma-115	222	40	.	.	PUNCT
ma-115	223	1	5	5	X
ma-115	223	2	.	.	X
ma-115	223	3	barut	barut	NOUN
ma-115	223	4	-	-	PUNCT
ma-115	223	5	girardello	girardello	NOUN
ma-115	223	6	-	-	PUNCT
ma-115	223	7	type	type	NOUN
ma-115	223	8	transformations	transformation	NOUN
ma-115	223	9	:	:	PUNCT
ma-115	223	10	the	the	DET
ma-115	223	11	functional	functional	ADJ
ma-115	223	12	expression	expression	NOUN
ma-115	223	13	(	(	PUNCT
ma-115	223	14	15	15	NUM
ma-115	223	15	)	)	PUNCT
ma-115	223	16	of	of	ADP
ma-115	223	17	ebb̂∗α−β,−2(α+β	ebb̂∗α−β,−2(α+β	NOUN
ma-115	223	18	)	)	PUNCT
ma-115	223	19	resembles	resemble	VERB
ma-115	223	20	the	the	DET
ma-115	223	21	barut	barut	NOUN
ma-115	223	22	-	-	PUNCT
ma-115	223	23	girardello	girardello	NOUN
ma-115	223	24	-	-	PUNCT
ma-115	223	25	type	type	NOUN
ma-115	223	26	transform.the	transform.the	PRON
ma-115	223	27	barut	barut	NOUN
ma-115	223	28	-	-	PUNCT
ma-115	223	29	girardello	girardello	NOUN
ma-115	223	30	-	-	PUNCT
ma-115	223	31	type	type	NOUN
ma-115	223	32	transform	transform	NOUN
ma-115	223	33	of	of	ADP
ma-115	223	34	bessel	bessel	ADJ
ma-115	223	35	order	order	NOUN
ma-115	223	36	α−	α−	ADP
ma-115	223	37	β	β	X
ma-115	223	38	is	be	AUX
ma-115	223	39	defined	define	VERB
ma-115	223	40	by	by	ADP
ma-115	223	41	[	[	X
ma-115	223	42	3	3	NUM
ma-115	223	43	]	]	PUNCT
ma-115	223	44	.	.	PUNCT
ma-115	224	1	[	[	PUNCT
ma-115	224	2	ĝα−βf	ĝα−βf	VERB
ma-115	224	3	]	]	PUNCT
ma-115	224	4	(	(	PUNCT
ma-115	224	5	y	y	NOUN
ma-115	224	6	)	)	PUNCT
ma-115	224	7	=	=	SYM
ma-115	225	1	√	√	NUM
ma-115	225	2	2	2	NUM
ma-115	225	3	∫	∫	NOUN
ma-115	225	4	∞	∞	NOUN
ma-115	225	5	0	0	PUNCT
ma-115	225	6	(	(	PUNCT
ma-115	225	7	xy)1/2e−(1/2)(x	xy)1/2e−(1/2)(x	PROPN
ma-115	225	8	2+y2)iα−β	2+y2)iα−β	NUM
ma-115	225	9	(	(	PUNCT
ma-115	225	10	√	√	PROPN
ma-115	225	11	2xy)f	2xy)f	PROPN
ma-115	225	12	(	(	PUNCT
ma-115	225	13	x)dx	x)dx	PROPN
ma-115	225	14	.	.	PUNCT
ma-115	226	1	(	(	PUNCT
ma-115	226	2	49	49	NUM
ma-115	226	3	)	)	PUNCT
ma-115	226	4	as	as	ADP
ma-115	226	5	a	a	DET
ma-115	226	6	straightforward	straightforward	ADJ
ma-115	226	7	generalization	generalization	NOUN
ma-115	226	8	of	of	ADP
ma-115	226	9	the	the	DET
ma-115	226	10	notion	notion	NOUN
ma-115	226	11	of	of	ADP
ma-115	226	12	coherent	coherent	ADJ
ma-115	226	13	stakes	stake	NOUN
ma-115	226	14	associated	associate	VERB
ma-115	226	15	with	with	ADP
ma-115	226	16	the	the	DET
ma-115	226	17	heisenbergalgebra	heisenbergalgebra	NOUN
ma-115	226	18	,	,	PUNCT
ma-115	226	19	such	such	ADJ
ma-115	226	20	generalized	generalized	ADJ
ma-115	226	21	coherent	coherent	ADJ
ma-115	226	22	stakes	stake	NOUN
ma-115	226	23	were	be	AUX
ma-115	226	24	introduced	introduce	VERB
ma-115	226	25	as	as	ADP
ma-115	226	26	eigenstates	eigenstate	NOUN
ma-115	226	27	of	of	ADP
ma-115	226	28	the	the	DET
ma-115	226	29	lowering	lower	VERB
ma-115	226	30	operator	operator	NOUN
ma-115	226	31	ofthe	ofthe	NOUN
ma-115	226	32	aforementioned	aforementione	VERB
ma-115	226	33	algebra	algebra	NOUN
ma-115	226	34	in	in	ADP
ma-115	226	35	the	the	DET
ma-115	226	36	relative	relative	ADJ
ma-115	226	37	discrete	discrete	ADJ
ma-115	226	38	representations	representation	NOUN
ma-115	226	39	d±(k	d±(k	NOUN
ma-115	226	40	)	)	PUNCT
ma-115	226	41	,	,	PUNCT
ma-115	226	42	k	k	X
ma-115	226	43	=	=	PUNCT
ma-115	226	44	−1/2,−1,−3/2	−1/2,−1,−3/2	PROPN
ma-115	226	45	,	,	PUNCT
ma-115	226	46	...	...	PUNCT
ma-115	227	1	https://doi.org/10.28924/ada/ma.3.6	https://doi.org/10.28924/ada/ma.3.6	PROPN
ma-115	227	2	eur	eur	PROPN
ma-115	227	3	.	.	PUNCT
ma-115	228	1	j.	j.	PROPN
ma-115	228	2	math	math	PROPN
ma-115	228	3	.	.	PUNCT
ma-115	229	1	anal	anal	PROPN
ma-115	229	2	.	.	PUNCT
ma-115	230	1	10.28924	10.28924	NUM
ma-115	230	2	/	/	SYM
ma-115	230	3	ada	ada	PROPN
ma-115	230	4	/	/	SYM
ma-115	230	5	ma.3.6	ma.3.6	PROPN
ma-115	230	6	10then	10then	ADV
ma-115	230	7	taking	take	VERB
ma-115	230	8	2b	2b	NOUN
ma-115	230	9	=	=	SYM
ma-115	230	10	1√	1√	NUM
ma-115	230	11	2	2	NUM
ma-115	230	12	in	in	ADP
ma-115	230	13	equation	equation	NOUN
ma-115	230	14	(	(	PUNCT
ma-115	230	15	15	15	NUM
ma-115	230	16	)	)	PUNCT
ma-115	230	17	and	and	CCONJ
ma-115	230	18	multiplying	multiply	VERB
ma-115	230	19	the	the	DET
ma-115	230	20	integrand	integrand	NOUN
ma-115	230	21	function	function	NOUN
ma-115	230	22	by	by	ADP
ma-115	230	23	e−(1/2)(x	e−(1/2)(x	PROPN
ma-115	230	24	2+y2)e(1/2)(x	2+y2)e(1/2)(x	NUM
ma-115	230	25	2+y2	2+y2	NOUN
ma-115	230	26	)	)	PUNCT
ma-115	230	27	,	,	PUNCT
ma-115	230	28	we	we	PRON
ma-115	230	29	end	end	VERB
ma-115	230	30	up	up	ADP
ma-115	230	31	expression	expression	NOUN
ma-115	230	32	[	[	PUNCT
ma-115	230	33	e−(1/	e−(1/	NOUN
ma-115	230	34	√	√	NUM
ma-115	230	35	2)k̂	2)k̂	NUM
ma-115	230	36	(	(	PUNCT
ma-115	230	37	1	1	NUM
ma-115	230	38	)	)	PUNCT
ma-115	230	39	−	−	PROPN
ma-115	231	1	f	f	X
ma-115	231	2	]	]	X
ma-115	231	3	(	(	PUNCT
ma-115	231	4	y	y	NOUN
ma-115	231	5	)	)	PUNCT
ma-115	231	6	=	=	NOUN
ma-115	232	1	e−(y	e−(y	PROPN
ma-115	232	2	2/2	2/2	NUM
ma-115	232	3	)	)	PUNCT
ma-115	232	4	(	(	PUNCT
ma-115	232	5	√	√	NUM
ma-115	232	6	2−1)√2	2−1)√2	NUM
ma-115	232	7	y1−4(α+β	y1−4(α+β	NOUN
ma-115	232	8	)	)	PUNCT
ma-115	232	9	∫	∫	PROPN
ma-115	232	10	∞	∞	PROPN
ma-115	232	11	0	0	NUM
ma-115	233	1	(	(	PUNCT
ma-115	233	2	xy)2(α+β	xy)2(α+β	NUM
ma-115	233	3	)	)	PUNCT
ma-115	233	4	e−(1/2)(x	e−(1/2)(x	PROPN
ma-115	233	5	2+y2	2+y2	NOUN
ma-115	233	6	)	)	PUNCT
ma-115	233	7	iα−β	iα−β	PROPN
ma-115	233	8	(	(	PUNCT
ma-115	233	9	√	√	NUM
ma-115	233	10	2xy	2xy	ADJ
ma-115	233	11	)	)	PUNCT
ma-115	233	12	e−(x	e−(x	NOUN
ma-115	233	13	2/2	2/2	NUM
ma-115	233	14	)	)	PUNCT
ma-115	233	15	(	(	PUNCT
ma-115	233	16	√	√	PROPN
ma-115	233	17	2−1)f	2−1)f	NUM
ma-115	233	18	(	(	PUNCT
ma-115	233	19	x)dx	x)dx	PROPN
ma-115	233	20	.	.	PUNCT
ma-115	234	1	this	this	PRON
ma-115	234	2	allows	allow	VERB
ma-115	234	3	us	we	PRON
ma-115	234	4	to	to	PART
ma-115	234	5	define	define	VERB
ma-115	234	6	the	the	DET
ma-115	234	7	first	first	ADJ
ma-115	234	8	barut	barut	NOUN
ma-115	234	9	-	-	PUNCT
ma-115	234	10	girardello	girardello	NOUN
ma-115	234	11	-	-	PUNCT
ma-115	234	12	type	type	NOUN
ma-115	234	13	transform	transform	NOUN
ma-115	234	14	of	of	ADP
ma-115	234	15	bessel	bessel	ADJ
ma-115	234	16	order	order	NOUN
ma-115	234	17	α−β	α−β	PROPN
ma-115	234	18	,	,	PUNCT
ma-115	234	19	dependingon	dependingon	VERB
ma-115	234	20	a	a	DET
ma-115	234	21	real	real	ADJ
ma-115	234	22	parameter	parameter	NOUN
ma-115	234	23	−2(α+	−2(α+	NUM
ma-115	234	24	β	β	NOUN
ma-115	234	25	)	)	PUNCT
ma-115	234	26	,	,	PUNCT
ma-115	234	27	through	through	ADP
ma-115	234	28	the	the	DET
ma-115	234	29	expression	expression	NOUN
ma-115	234	30	[	[	PUNCT
ma-115	234	31	ĝ1,α−β,−2(α+β)f	ĝ1,α−β,−2(α+β)f	NOUN
ma-115	234	32	]	]	X
ma-115	234	33	(	(	PUNCT
ma-115	234	34	y	y	NOUN
ma-115	234	35	)	)	PUNCT
ma-115	234	36	=	=	SYM
ma-115	234	37	√	√	NUM
ma-115	234	38	2	2	NUM
ma-115	234	39	y1−4(α+β	y1−4(α+β	NOUN
ma-115	234	40	)	)	PUNCT
ma-115	234	41	∫	∫	PROPN
ma-115	235	1	∞	∞	PROPN
ma-115	235	2	0	0	NUM
ma-115	235	3	(	(	PUNCT
ma-115	235	4	xy)2(α+β	xy)2(α+β	NUM
ma-115	235	5	)	)	PUNCT
ma-115	235	6	e−(1/2)(x	e−(1/2)(x	PROPN
ma-115	235	7	2+y2	2+y2	NOUN
ma-115	235	8	)	)	PUNCT
ma-115	235	9	iα−β	iα−β	PROPN
ma-115	235	10	(	(	PUNCT
ma-115	235	11	√	√	PROPN
ma-115	235	12	2xy)f	2xy)f	PROPN
ma-115	235	13	(	(	PUNCT
ma-115	235	14	x)dx	x)dx	PROPN
ma-115	235	15	.	.	PUNCT
ma-115	236	1	(	(	PUNCT
ma-115	236	2	50	50	NUM
ma-115	236	3	)	)	PUNCT
ma-115	236	4	thus	thus	ADV
ma-115	236	5	we	we	PRON
ma-115	236	6	may	may	AUX
ma-115	236	7	write	write	VERB
ma-115	236	8	ĝ1,α−β,−2(α+β	ĝ1,α−β,−2(α+β	NOUN
ma-115	236	9	)	)	PUNCT
ma-115	236	10	=	=	PUNCT
ma-115	237	1	e	e	X
ma-115	237	2	(	(	PUNCT
ma-115	237	3	√	√	PROPN
ma-115	237	4	2−1)k̂(1)+	2−1)k̂(1)+	NUM
ma-115	237	5	ek̂	ek̂	NUM
ma-115	237	6	(	(	PUNCT
ma-115	237	7	1	1	NUM
ma-115	237	8	)	)	PUNCT
ma-115	237	9	−	−	PROPN
ma-115	237	10	/	/	SYM
ma-115	237	11	√	√	NOUN
ma-115	237	12	2	2	NUM
ma-115	237	13	e	e	NOUN
ma-115	237	14	(	(	PUNCT
ma-115	237	15	√	√	PROPN
ma-115	237	16	2−1)k̂(1)+	2−1)k̂(1)+	NUM
ma-115	237	17	which	which	PRON
ma-115	237	18	can	can	AUX
ma-115	237	19	eventually	eventually	ADV
ma-115	237	20	be	be	AUX
ma-115	237	21	imposed	impose	VERB
ma-115	237	22	into	into	ADP
ma-115	237	23	the	the	DET
ma-115	237	24	single	single	ADJ
ma-115	237	25	exponential	exponential	ADJ
ma-115	237	26	form	form	NOUN
ma-115	237	27	:	:	PUNCT
ma-115	237	28	ĝ1,α−β,−2(α+β	ĝ1,α−β,−2(α+β	NOUN
ma-115	237	29	)	)	PUNCT
ma-115	237	30	=	=	SYM
ma-115	237	31	e	e	X
ma-115	237	32	(	(	PUNCT
ma-115	237	33	π/4	π/4	PROPN
ma-115	237	34	)	)	PUNCT
ma-115	237	35	[	[	PUNCT
ma-115	237	36	k̂	k̂	X
ma-115	237	37	(	(	PUNCT
ma-115	237	38	1	1	NUM
ma-115	237	39	)	)	PUNCT
ma-115	237	40	+	+	CCONJ
ma-115	237	41	−k̂	−k̂	PROPN
ma-115	237	42	(	(	PUNCT
ma-115	237	43	1	1	NUM
ma-115	237	44	)	)	PUNCT
ma-115	237	45	−	−	NOUN
ma-115	237	46	]	]	PUNCT
ma-115	237	47	.	.	PUNCT
ma-115	238	1	(	(	PUNCT
ma-115	238	2	51	51	NUM
ma-115	238	3	)	)	PUNCT
ma-115	238	4	it	it	PRON
ma-115	238	5	clearly	clearly	ADV
ma-115	238	6	states	state	VERB
ma-115	238	7	that	that	DET
ma-115	238	8	ĝ1,α−β,−2(α+β	ĝ1,α−β,−2(α+β	NOUN
ma-115	238	9	)	)	PUNCT
ma-115	238	10	can	can	AUX
ma-115	238	11	be	be	AUX
ma-115	238	12	regarded	regard	VERB
ma-115	238	13	as	as	ADP
ma-115	238	14	the	the	DET
ma-115	238	15	evolution	evolution	NOUN
ma-115	238	16	operator	operator	NOUN
ma-115	238	17	e−iτĥ	e−iτĥ	PROPN
ma-115	238	18	,	,	PUNCT
ma-115	238	19	associatedwith	associatedwith	ADP
ma-115	238	20	the	the	DET
ma-115	238	21	dynamical	dynamical	ADJ
ma-115	238	22	problem	problem	NOUN
ma-115	238	23	ruled	rule	VERB
ma-115	238	24	by	by	ADP
ma-115	238	25	the	the	DET
ma-115	238	26	hamiltonian	hamiltonian	ADJ
ma-115	238	27	operator	operator	NOUN
ma-115	238	28	ĥ	ĥ	PUNCT
ma-115	238	29	=	=	SYM
ma-115	238	30	k̂	k̂	X
ma-115	238	31	(	(	PUNCT
ma-115	238	32	1	1	X
ma-115	238	33	)	)	PUNCT
ma-115	239	1	+	+	CCONJ
ma-115	240	1	−	−	PROPN
ma-115	240	2	k̂	k̂	NOUN
ma-115	240	3	(	(	PUNCT
ma-115	240	4	1	1	X
ma-115	240	5	)	)	PUNCT
ma-115	240	6	−	−	NOUN
ma-115	241	1	=	=	SYM
ma-115	241	2	1	1	NUM
ma-115	241	3	2	2	NUM
ma-115	241	4	[	[	PUNCT
ma-115	241	5	x2	x2	NOUN
ma-115	241	6	+	+	NOUN
ma-115	241	7	b̂∗α−β,−2(α+β	b̂∗α−β,−2(α+β	NOUN
ma-115	241	8	)	)	PUNCT
ma-115	241	9	]	]	PUNCT
ma-115	241	10	and	and	CCONJ
ma-115	241	11	evaluated	evaluate	VERB
ma-115	241	12	at	at	ADP
ma-115	241	13	the	the	DET
ma-115	241	14	purely	purely	ADV
ma-115	241	15	imaginary	imaginary	ADJ
ma-115	241	16	value	value	NOUN
ma-115	241	17	τ	τ	PROPN
ma-115	241	18	=	=	SYM
ma-115	241	19	i(π/4	i(π/4	PROPN
ma-115	241	20	)	)	PUNCT
ma-115	241	21	of	of	ADP
ma-115	241	22	the	the	DET
ma-115	241	23	evolution	evolution	NOUN
ma-115	241	24	variable.now	variable.now	SCONJ
ma-115	241	25	we	we	PRON
ma-115	241	26	can	can	AUX
ma-115	241	27	define	define	VERB
ma-115	241	28	the	the	DET
ma-115	241	29	second	second	ADJ
ma-115	241	30	barut	barut	NOUN
ma-115	241	31	-	-	PUNCT
ma-115	241	32	girardello	girardello	NOUN
ma-115	241	33	-	-	PUNCT
ma-115	241	34	type	type	NOUN
ma-115	241	35	transform	transform	NOUN
ma-115	241	36	of	of	ADP
ma-115	241	37	bessel	bessel	ADJ
ma-115	241	38	order	order	NOUN
ma-115	241	39	α−	α−	ADP
ma-115	241	40	β	β	NOUN
ma-115	241	41	as	as	ADP
ma-115	241	42	[	[	PUNCT
ma-115	241	43	ĝ2,α−β,−2(α+β)f	ĝ2,α−β,−2(α+β)f	NOUN
ma-115	241	44	]	]	X
ma-115	241	45	(	(	PUNCT
ma-115	241	46	y	y	NOUN
ma-115	241	47	)	)	PUNCT
ma-115	241	48	=	=	SYM
ma-115	242	1	√	√	NUM
ma-115	242	2	2	2	NUM
ma-115	242	3	∫	∫	NOUN
ma-115	242	4	∞	∞	PROPN
ma-115	242	5	0	0	PROPN
ma-115	242	6	x1−4(α+β	x1−4(α+β	PROPN
ma-115	242	7	)	)	PUNCT
ma-115	242	8	(	(	PUNCT
ma-115	242	9	xy)2(α+β	xy)2(α+β	X
ma-115	242	10	)	)	PUNCT
ma-115	242	11	e−(1/2)(x	e−(1/2)(x	PROPN
ma-115	242	12	2+y2)iα−β	2+y2)iα−β	NUM
ma-115	242	13	(	(	PUNCT
ma-115	242	14	√	√	PROPN
ma-115	242	15	2xy)f	2xy)f	NOUN
ma-115	242	16	(	(	PUNCT
ma-115	242	17	x)dx	x)dx	PROPN
ma-115	242	18	(	(	PUNCT
ma-115	242	19	52	52	NUM
ma-115	242	20	)	)	PUNCT
ma-115	242	21	for	for	ADP
ma-115	242	22	which	which	PRON
ma-115	242	23	the	the	DET
ma-115	242	24	following	follow	VERB
ma-115	242	25	operational	operational	ADJ
ma-115	242	26	relatoins	relatoin	NOUN
ma-115	242	27	can	can	AUX
ma-115	242	28	be	be	AUX
ma-115	242	29	stated	state	VERB
ma-115	242	30	as	as	ADP
ma-115	242	31	:	:	PUNCT
ma-115	242	32	ĝ2,α−β,−2(α+β	ĝ2,α−β,−2(α+β	ADJ
ma-115	242	33	)	)	PUNCT
ma-115	242	34	=	=	PUNCT
ma-115	243	1	e	e	X
ma-115	243	2	(	(	PUNCT
ma-115	243	3	√	√	PROPN
ma-115	243	4	2−1)k̂(2)+	2−1)k̂(2)+	NUM
ma-115	243	5	ek̂	ek̂	NUM
ma-115	243	6	(	(	PUNCT
ma-115	243	7	2	2	NUM
ma-115	243	8	)	)	PUNCT
ma-115	243	9	−	−	PROPN
ma-115	243	10	/	/	SYM
ma-115	243	11	√	√	NOUN
ma-115	243	12	2	2	NUM
ma-115	243	13	e	e	NOUN
ma-115	243	14	(	(	PUNCT
ma-115	243	15	√	√	NUM
ma-115	243	16	2−1)k̂(2)+	2−1)k̂(2)+	NUM
ma-115	243	17	=	=	SYM
ma-115	243	18	e	e	X
ma-115	243	19	(	(	PUNCT
ma-115	243	20	π/4	π/4	PROPN
ma-115	243	21	)	)	PUNCT
ma-115	243	22	[	[	PUNCT
ma-115	243	23	k̂	k̂	X
ma-115	243	24	(	(	PUNCT
ma-115	243	25	2	2	NUM
ma-115	243	26	)	)	PUNCT
ma-115	243	27	+	+	CCONJ
ma-115	243	28	−k̂	−k̂	PROPN
ma-115	243	29	(	(	PUNCT
ma-115	243	30	2	2	NUM
ma-115	243	31	)	)	PUNCT
ma-115	243	32	−	−	NOUN
ma-115	243	33	]	]	PUNCT
ma-115	243	34	,	,	PUNCT
ma-115	243	35	(	(	PUNCT
ma-115	243	36	53	53	NUM
ma-115	243	37	)	)	PUNCT
ma-115	243	38	involving	involve	VERB
ma-115	243	39	of	of	ADP
ma-115	243	40	course	course	NOUN
ma-115	243	41	the	the	DET
ma-115	243	42	operators	operator	NOUN
ma-115	243	43	(	(	PUNCT
ma-115	243	44	23	23	NUM
ma-115	243	45	)	)	PUNCT
ma-115	243	46	.	.	PUNCT
ma-115	244	1	accordingly	accordingly	ADV
ma-115	244	2	,	,	PUNCT
ma-115	244	3	ĝ2,α−β,−2(α+β	ĝ2,α−β,−2(α+β	PROPN
ma-115	244	4	)	)	PUNCT
ma-115	244	5	can	can	AUX
ma-115	244	6	be	be	AUX
ma-115	244	7	interpreted	interpret	VERB
ma-115	244	8	as	as	ADP
ma-115	244	9	theevolution	theevolution	NOUN
ma-115	244	10	operator	operator	NOUN
ma-115	244	11	operator	operator	NOUN
ma-115	244	12	e−iτĥ	e−iτĥ	PROPN
ma-115	244	13	,	,	PUNCT
ma-115	244	14	associated	associate	VERB
ma-115	244	15	with	with	ADP
ma-115	244	16	the	the	DET
ma-115	244	17	dynamical	dynamical	ADJ
ma-115	244	18	problem	problem	NOUN
ma-115	244	19	ruled	rule	VERB
ma-115	244	20	by	by	ADP
ma-115	244	21	the	the	DET
ma-115	244	22	hamiltonianoperator	hamiltonianoperator	NOUN
ma-115	244	23	ĥ	ĥ	PUNCT
ma-115	244	24	=	=	SYM
ma-115	244	25	k̂	k̂	X
ma-115	244	26	(	(	PUNCT
ma-115	244	27	2	2	NUM
ma-115	244	28	)	)	PUNCT
ma-115	245	1	+	+	CCONJ
ma-115	246	1	−	−	PROPN
ma-115	246	2	k̂	k̂	NOUN
ma-115	246	3	(	(	PUNCT
ma-115	246	4	2	2	NUM
ma-115	246	5	)	)	PUNCT
ma-115	246	6	−	−	NOUN
ma-115	247	1	=	=	SYM
ma-115	247	2	1	1	NUM
ma-115	247	3	2	2	NUM
ma-115	247	4	[	[	PUNCT
ma-115	247	5	x2	x2	NOUN
ma-115	247	6	+	+	CCONJ
ma-115	247	7	b̂α−β,−2(α+β	b̂α−β,−2(α+β	NOUN
ma-115	247	8	)	)	PUNCT
ma-115	247	9	]	]	PUNCT
ma-115	247	10	and	and	CCONJ
ma-115	247	11	evaluated	evaluate	VERB
ma-115	247	12	at	at	ADP
ma-115	247	13	the	the	DET
ma-115	247	14	same	same	ADJ
ma-115	247	15	complex	complex	ADJ
ma-115	247	16	value	value	NOUN
ma-115	247	17	τ	τ	X
ma-115	247	18	=	=	SYM
ma-115	247	19	i(π/4	i(π/4	PROPN
ma-115	247	20	)	)	PUNCT
ma-115	247	21	of	of	ADP
ma-115	247	22	the	the	DET
ma-115	247	23	evolution	evolution	NOUN
ma-115	247	24	variable	variable	NOUN
ma-115	247	25	as	as	ADP
ma-115	247	26	ĝ1,α−β,−2(α+β	ĝ1,α−β,−2(α+β	NOUN
ma-115	247	27	)	)	PUNCT
ma-115	247	28	.both	.both	DET
ma-115	247	29	definitions	definition	NOUN
ma-115	247	30	(	(	PUNCT
ma-115	247	31	50	50	NUM
ma-115	247	32	)	)	PUNCT
ma-115	247	33	and(52	and(52	NUM
ma-115	247	34	)	)	PUNCT
ma-115	247	35	can	can	AUX
ma-115	247	36	be	be	AUX
ma-115	247	37	recast	recast	VERB
ma-115	247	38	into	into	ADP
ma-115	247	39	the	the	DET
ma-115	247	40	comprehensive	comprehensive	ADJ
ma-115	247	41	expression	expression	NOUN
ma-115	247	42	[	[	PUNCT
ma-115	247	43	ĝj	ĝj	PROPN
ma-115	247	44	,	,	PUNCT
ma-115	247	45	α−β,−2(α+β)f	α−β,−2(α+β)f	NOUN
ma-115	247	46	]	]	PUNCT
ma-115	247	47	(	(	PUNCT
ma-115	247	48	y	y	NOUN
ma-115	247	49	)	)	PUNCT
ma-115	247	50	=	=	SYM
ma-115	248	1	∫	∫	PROPN
ma-115	249	1	∞	∞	NUM
ma-115	249	2	0	0	PUNCT
ma-115	250	1	k	k	PROPN
ma-115	250	2	(	(	PUNCT
ma-115	250	3	bg	bg	PROPN
ma-115	250	4	)	)	PUNCT
ma-115	250	5	j	j	PROPN
ma-115	250	6	,	,	PUNCT
ma-115	250	7	α−β,−2(α+β)(x	α−β,−2(α+β)(x	NOUN
ma-115	250	8	,	,	PUNCT
ma-115	250	9	y)f	y)f	NOUN
ma-115	250	10	(	(	PUNCT
ma-115	250	11	x)dx	x)dx	PROPN
ma-115	250	12	,	,	PUNCT
ma-115	250	13	j	j	NOUN
ma-115	250	14	=	=	SYM
ma-115	250	15	1	1	NUM
ma-115	250	16	,	,	PUNCT
ma-115	250	17	2	2	NUM
ma-115	250	18	.	.	PUNCT
ma-115	250	19	(	(	PUNCT
ma-115	250	20	54	54	NUM
ma-115	250	21	)	)	PUNCT
ma-115	250	22	in	in	ADP
ma-115	250	23	terms	term	NOUN
ma-115	250	24	of	of	ADP
ma-115	250	25	the	the	DET
ma-115	250	26	kernels	kernel	NOUN
ma-115	250	27	k	k	PROPN
ma-115	250	28	(	(	PUNCT
ma-115	250	29	bg	bg	PROPN
ma-115	250	30	)	)	PUNCT
ma-115	250	31	1,α−β,−2(α+β)(x	1,α−β,−2(α+β)(x	PROPN
ma-115	250	32	,	,	PUNCT
ma-115	250	33	y	y	NOUN
ma-115	250	34	)	)	PUNCT
ma-115	250	35	=	=	SYM
ma-115	251	1	√	√	NUM
ma-115	251	2	2y1−2(α+β)(x)2(α+β)iα−β	2y1−2(α+β)(x)2(α+β)iα−β	NUM
ma-115	251	3	(	(	PUNCT
ma-115	251	4	√	√	PROPN
ma-115	251	5	2xy)e−(1/2)(x	2xy)e−(1/2)(x	NUM
ma-115	251	6	2+y2	2+y2	NOUN
ma-115	251	7	)	)	PUNCT
ma-115	252	1	=	=	SYM
ma-115	252	2	k	k	X
ma-115	252	3	(	(	PUNCT
ma-115	252	4	bg	bg	PROPN
ma-115	252	5	)	)	PUNCT
ma-115	252	6	2,α−β,−2(α+β)(y	2,α−β,−2(α+β)(y	NUM
ma-115	252	7	,	,	PUNCT
ma-115	252	8	x	x	NOUN
ma-115	252	9	)	)	PUNCT
ma-115	252	10	https://doi.org/10.28924/ada/ma.3.6	https://doi.org/10.28924/ada/ma.3.6	PROPN
ma-115	252	11	eur	eur	PROPN
ma-115	252	12	.	.	PUNCT
ma-115	253	1	j.	j.	PROPN
ma-115	253	2	math	math	PROPN
ma-115	253	3	.	.	PUNCT
ma-115	254	1	anal	anal	PROPN
ma-115	254	2	.	.	PUNCT
ma-115	255	1	10.28924	10.28924	NUM
ma-115	255	2	/	/	SYM
ma-115	255	3	ada	ada	PROPN
ma-115	255	4	/	/	SYM
ma-115	255	5	ma.3.6	ma.3.6	PROPN
ma-115	255	6	11	11	NUM
ma-115	255	7	which	which	PRON
ma-115	255	8	relate	relate	VERB
ma-115	255	9	to	to	ADP
ma-115	255	10	the	the	DET
ma-115	255	11	kernel	kernel	PROPN
ma-115	255	12	k	k	PROPN
ma-115	255	13	(	(	PUNCT
ma-115	255	14	bg	bg	PROPN
ma-115	255	15	)	)	PUNCT
ma-115	255	16	α−β	α−β	PROPN
ma-115	255	17	(	(	PUNCT
ma-115	255	18	x	x	X
ma-115	255	19	,	,	PUNCT
ma-115	255	20	y	y	NOUN
ma-115	255	21	)	)	PUNCT
ma-115	255	22	=	=	SYM
ma-115	256	1	√	√	NUM
ma-115	256	2	2iα−β	2iα−β	NUM
ma-115	256	3	(	(	PUNCT
ma-115	256	4	√	√	PROPN
ma-115	256	5	2xy)e−(1/2)(x	2xy)e−(1/2)(x	NUM
ma-115	256	6	2+y2	2+y2	NOUN
ma-115	256	7	)	)	PUNCT
ma-115	256	8	of	of	ADP
ma-115	256	9	the	the	DET
ma-115	256	10	conven	conven	VERB
ma-115	256	11	-	-	PUNCT
ma-115	256	12	tional	tional	ADJ
ma-115	256	13	transform	transform	NOUN
ma-115	256	14	(	(	PUNCT
ma-115	256	15	49	49	NUM
ma-115	256	16	)	)	PUNCT
ma-115	256	17	through	through	ADP
ma-115	256	18	the	the	DET
ma-115	256	19	same	same	ADJ
ma-115	256	20	similarity	similarity	NOUN
ma-115	256	21	transformation	transformation	NOUN
ma-115	256	22	like	like	ADP
ma-115	256	23	relation	relation	NOUN
ma-115	256	24	holding	holding	NOUN
ma-115	256	25	between	between	ADP
ma-115	256	26	k1,α−β,−2(α+β)(x	k1,α−β,−2(α+β)(x	PROPN
ma-115	256	27	,	,	PUNCT
ma-115	256	28	y	y	PROPN
ma-115	256	29	)	)	PUNCT
ma-115	256	30	,	,	PUNCT
ma-115	256	31	k2,α−β,−2(α+β)(y	k2,α−β,−2(α+β)(y	NOUN
ma-115	256	32	,	,	PUNCT
ma-115	256	33	x	x	NOUN
ma-115	256	34	)	)	PUNCT
ma-115	256	35	and	and	CCONJ
ma-115	256	36	kα−β(x	kα−β(x	PROPN
ma-115	256	37	,	,	PUNCT
ma-115	256	38	y	y	NOUN
ma-115	256	39	)	)	PUNCT
ma-115	256	40	.as	.as	PUNCT
ma-115	257	1	the	the	DET
ma-115	257	2	hankel	hankel	NOUN
ma-115	257	3	-	-	PUNCT
ma-115	257	4	type	type	NOUN
ma-115	257	5	transforms	transform	NOUN
ma-115	257	6	,	,	PUNCT
ma-115	257	7	the	the	PRON
ma-115	257	8	transforms	transform	VERB
ma-115	257	9	ĝ1,α−β,−2(α+β	ĝ1,α−β,−2(α+β	NOUN
ma-115	257	10	)	)	PUNCT
ma-115	257	11	and	and	CCONJ
ma-115	257	12	ĝ2,α−β,−2(α+β	ĝ2,α−β,−2(α+β	NOUN
ma-115	257	13	)	)	PUNCT
ma-115	257	14	are	be	AUX
ma-115	257	15	adjoint	adjoint	NOUN
ma-115	257	16	toeach	toeach	NOUN
ma-115	257	17	other	other	ADJ
ma-115	257	18	:	:	PUNCT
ma-115	257	19	ĝ∗1,α−β,−2(α+β	ĝ∗1,α−β,−2(α+β	NOUN
ma-115	257	20	)	)	PUNCT
ma-115	258	1	=	=	PUNCT
ma-115	258	2	ĝ2,α−β,−2(α+β	ĝ2,α−β,−2(α+β	NOUN
ma-115	258	3	)	)	PUNCT
ma-115	258	4	,	,	PUNCT
ma-115	258	5	ĝ∗2,α−β,−2(α+β	ĝ∗2,α−β,−2(α+β	NOUN
ma-115	258	6	)	)	PUNCT
ma-115	258	7	=	=	SYM
ma-115	258	8	ĝ1,α−β,−2(α+β	ĝ1,α−β,−2(α+β	NOUN
ma-115	258	9	)	)	PUNCT
ma-115	258	10	.	.	PUNCT
ma-115	259	1	(	(	PUNCT
ma-115	259	2	55	55	NUM
ma-115	259	3	)	)	PUNCT
ma-115	259	4	however	however	ADV
ma-115	259	5	,	,	PUNCT
ma-115	259	6	they	they	PRON
ma-115	259	7	are	be	AUX
ma-115	259	8	not	not	PART
ma-115	259	9	self	self	NOUN
ma-115	259	10	reciprocal	reciprocal	ADJ
ma-115	259	11	;	;	PUNCT
ma-115	259	12	the	the	DET
ma-115	259	13	respective	respective	ADJ
ma-115	259	14	inverse	inverse	NOUN
ma-115	259	15	transforms	transform	VERB
ma-115	259	16	can	can	AUX
ma-115	259	17	be	be	AUX
ma-115	259	18	easily	easily	ADV
ma-115	259	19	obtained	obtain	VERB
ma-115	259	20	fromthe	fromthe	ADJ
ma-115	259	21	corresponding	corresponding	ADJ
ma-115	259	22	factored	factor	VERB
ma-115	259	23	representation	representation	NOUN
ma-115	259	24	in	in	ADP
ma-115	259	25	equations	equation	NOUN
ma-115	259	26	(	(	PUNCT
ma-115	259	27	51	51	NUM
ma-115	259	28	)	)	PUNCT
ma-115	259	29	and	and	CCONJ
ma-115	259	30	(	(	PUNCT
ma-115	259	31	53	53	NUM
ma-115	259	32	)	)	PUNCT
ma-115	259	33	which	which	PRON
ma-115	259	34	yield	yield	VERB
ma-115	259	35	[	[	PUNCT
ma-115	259	36	ĝ−1	ĝ−1	VERB
ma-115	259	37	1,α−β,−2(α+β)f	1,α−β,−2(α+β)f	PROPN
ma-115	259	38	]	]	PUNCT
ma-115	259	39	(	(	PUNCT
ma-115	259	40	y	y	NOUN
ma-115	259	41	)	)	PUNCT
ma-115	259	42	=	=	SYM
ma-115	259	43	(	(	PUNCT
ma-115	259	44	−1)α−β+1	−1)α−β+1	ADJ
ma-115	259	45	√	√	NUM
ma-115	259	46	2	2	NUM
ma-115	259	47	y1−4(α+β	y1−4(α+β	NOUN
ma-115	259	48	)	)	PUNCT
ma-115	259	49	∫	∫	PROPN
ma-115	260	1	∞	∞	PROPN
ma-115	260	2	0	0	NUM
ma-115	260	3	(	(	PUNCT
ma-115	260	4	xy)2(α+β	xy)2(α+β	NUM
ma-115	260	5	)	)	PUNCT
ma-115	260	6	e(1/2)(x	e(1/2)(x	PROPN
ma-115	260	7	2+y2	2+y2	NOUN
ma-115	260	8	)	)	PUNCT
ma-115	260	9	iα−β	iα−β	PROPN
ma-115	260	10	(	(	PUNCT
ma-115	260	11	√	√	PROPN
ma-115	260	12	2xy)f	2xy)f	PROPN
ma-115	260	13	(	(	PUNCT
ma-115	260	14	x)dx	x)dx	PROPN
ma-115	260	15	=	=	SYM
ma-115	260	16	{	{	PUNCT
ma-115	260	17	[	[	PUNCT
ma-115	260	18	ĝ−1	ĝ−1	NOUN
ma-115	260	19	2,α−β,−2(α+β	2,α−β,−2(α+β	NUM
ma-115	260	20	)	)	PUNCT
ma-115	260	21	]	]	PUNCT
ma-115	260	22	∗	∗	X
ma-115	260	23	f	f	NOUN
ma-115	260	24	}	}	PUNCT
ma-115	260	25	(	(	PUNCT
ma-115	260	26	y	y	NOUN
ma-115	260	27	)	)	PUNCT
ma-115	260	28	.	.	PUNCT
ma-115	261	1	operational	operational	ADJ
ma-115	261	2	relations	relation	NOUN
ma-115	261	3	similar	similar	ADJ
ma-115	261	4	to	to	ADP
ma-115	261	5	(	(	PUNCT
ma-115	261	6	9	9	NUM
ma-115	261	7	)	)	PUNCT
ma-115	261	8	can	can	AUX
ma-115	261	9	be	be	AUX
ma-115	261	10	deduced	deduce	VERB
ma-115	261	11	for	for	ADP
ma-115	261	12	ĝ1,α−β,−2(α+β	ĝ1,α−β,−2(α+β	NOUN
ma-115	261	13	)	)	PUNCT
ma-115	261	14	and	and	CCONJ
ma-115	261	15	ĝ2,α−β,−2(α+β	ĝ2,α−β,−2(α+β	NOUN
ma-115	261	16	)	)	PUNCT
ma-115	261	17	.	.	PUNCT
ma-115	262	1	in	in	ADP
ma-115	262	2	fact	fact	NOUN
ma-115	262	3	:	:	PUNCT
ma-115	262	4	[	[	PUNCT
ma-115	262	5	ĝ1,α−β,−2(α+β	ĝ1,α−β,−2(α+β	NOUN
ma-115	262	6	)	)	PUNCT
ma-115	262	7	î∗α−β,−2(α+β)f	î∗α−β,−2(α+β)f	NOUN
ma-115	262	8	]	]	PUNCT
ma-115	262	9	(	(	PUNCT
ma-115	262	10	y	y	NOUN
ma-115	262	11	)	)	PUNCT
ma-115	262	12	=	=	SYM
ma-115	263	1	2y2	2y2	NUM
ma-115	263	2	[	[	PUNCT
ma-115	263	3	ĝ1,α−β,−2(α+β)f	ĝ1,α−β,−2(α+β)f	NOUN
ma-115	263	4	]	]	PUNCT
ma-115	263	5	(	(	PUNCT
ma-115	263	6	y	y	NOUN
ma-115	263	7	)	)	PUNCT
ma-115	263	8	,	,	PUNCT
ma-115	263	9	[	[	PUNCT
ma-115	263	10	ĝ2,α−β,−2(α+β	ĝ2,α−β,−2(α+β	NOUN
ma-115	263	11	)	)	PUNCT
ma-115	263	12	îα−β,−2(α+β)f	îα−β,−2(α+β)f	NOUN
ma-115	263	13	]	]	PUNCT
ma-115	263	14	(	(	PUNCT
ma-115	263	15	y	y	NOUN
ma-115	263	16	)	)	PUNCT
ma-115	263	17	=	=	SYM
ma-115	264	1	2y2	2y2	NUM
ma-115	264	2	[	[	PUNCT
ma-115	264	3	ĝ2,α−β,−2(α+β)f	ĝ2,α−β,−2(α+β)f	NOUN
ma-115	264	4	]	]	PUNCT
ma-115	264	5	(	(	PUNCT
ma-115	264	6	y	y	NOUN
ma-115	264	7	)	)	PUNCT
ma-115	264	8	,	,	PUNCT
ma-115	264	9	(	(	PUNCT
ma-115	264	10	56	56	NUM
ma-115	264	11	)	)	PUNCT
ma-115	264	12	with	with	ADP
ma-115	264	13	the	the	DET
ma-115	264	14	differential	differential	ADJ
ma-115	264	15	operator	operator	NOUN
ma-115	264	16	îα−β,−2(α+β	îα−β,−2(α+β	NOUN
ma-115	264	17	)	)	PUNCT
ma-115	264	18	being	be	AUX
ma-115	264	19	îα−β,−2(α+β	îα−β,−2(α+β	NOUN
ma-115	264	20	)	)	PUNCT
ma-115	264	21	=	=	SYM
ma-115	264	22	2	2	NUM
ma-115	264	23	[	[	PUNCT
ma-115	264	24	k̂	k̂	X
ma-115	264	25	(	(	PUNCT
ma-115	264	26	2	2	NUM
ma-115	264	27	)	)	PUNCT
ma-115	265	1	+	+	CCONJ
ma-115	265	2	−	−	PROPN
ma-115	265	3	k̂	k̂	NOUN
ma-115	265	4	(	(	PUNCT
ma-115	265	5	2	2	NUM
ma-115	265	6	)	)	PUNCT
ma-115	265	7	−	−	NOUN
ma-115	266	1	+	+	NUM
ma-115	266	2	2i	2i	NUM
ma-115	266	3	k̂	k̂	X
ma-115	266	4	(	(	PUNCT
ma-115	266	5	2	2	NUM
ma-115	266	6	)	)	PUNCT
ma-115	266	7	3	3	NUM
ma-115	266	8	]	]	PUNCT
ma-115	266	9	.	.	PUNCT
ma-115	267	1	(	(	PUNCT
ma-115	267	2	57	57	NUM
ma-115	267	3	)	)	PUNCT
ma-115	267	4	it	it	PRON
ma-115	267	5	can	can	AUX
ma-115	267	6	be	be	AUX
ma-115	267	7	easily	easily	ADV
ma-115	267	8	seen	see	VERB
ma-115	267	9	that	that	DET
ma-115	267	10	îα−β,−2(α+β	îα−β,−2(α+β	NOUN
ma-115	267	11	)	)	PUNCT
ma-115	267	12	=	=	SYM
ma-115	267	13	e−(x	e−(x	NOUN
ma-115	267	14	2/2	2/2	NUM
ma-115	267	15	)	)	PUNCT
ma-115	267	16	b̂α−β,−2(α+β	b̂α−β,−2(α+β	NOUN
ma-115	267	17	)	)	PUNCT
ma-115	267	18	e	e	NOUN
ma-115	267	19	−(x2/2	−(x2/2	PROPN
ma-115	267	20	)	)	PUNCT
ma-115	267	21	=	=	SYM
ma-115	268	1	x2(α+β)−(α−β)−1	x2(α+β)−(α−β)−1	NUM
ma-115	268	2	×	×	NOUN
ma-115	268	3	(	(	PUNCT
ma-115	268	4	x	x	SYM
ma-115	268	5	+	+	NUM
ma-115	268	6	∂	∂	NUM
ma-115	268	7	∂x	∂x	PROPN
ma-115	268	8	)	)	PUNCT
ma-115	268	9	x2(α−β)+1	x2(α−β)+1	PUNCT
ma-115	269	1	(	(	PUNCT
ma-115	269	2	x	x	SYM
ma-115	269	3	+	+	NUM
ma-115	269	4	∂	∂	NUM
ma-115	269	5	∂x	∂x	PROPN
ma-115	269	6	)	)	PUNCT
ma-115	269	7	x−(3α+β	x−(3α+β	NUM
ma-115	269	8	)	)	PUNCT
ma-115	269	9	(	(	PUNCT
ma-115	269	10	58	58	NUM
ma-115	269	11	)	)	PUNCT
ma-115	269	12	even	even	ADV
ma-115	269	13	though	though	SCONJ
ma-115	269	14	equation	equation	NOUN
ma-115	269	15	(	(	PUNCT
ma-115	269	16	56	56	NUM
ma-115	269	17	)	)	PUNCT
ma-115	269	18	correspond	correspond	VERB
ma-115	269	19	to	to	ADP
ma-115	269	20	equation	equation	NOUN
ma-115	269	21	(	(	PUNCT
ma-115	269	22	9	9	NUM
ma-115	269	23	)	)	PUNCT
ma-115	269	24	,	,	PUNCT
ma-115	269	25	pertaining	pertain	VERB
ma-115	269	26	to	to	ADP
ma-115	269	27	the	the	DET
ma-115	269	28	hankel	hankel	NOUN
ma-115	269	29	transform	transform	NOUN
ma-115	269	30	,	,	PUNCT
ma-115	269	31	in	in	ADP
ma-115	269	32	-	-	PUNCT
ma-115	269	33	volve	volve	NOUN
ma-115	269	34	operators	operator	NOUN
ma-115	269	35	îα−β,−2(α+β	îα−β,−2(α+β	VERB
ma-115	269	36	)	)	PUNCT
ma-115	269	37	and	and	CCONJ
ma-115	269	38	î∗α−β,−2(α+β	î∗α−β,−2(α+β	NOUN
ma-115	269	39	)	)	PUNCT
ma-115	269	40	comprise	comprise	VERB
ma-115	269	41	also	also	ADV
ma-115	269	42	the	the	DET
ma-115	269	43	operators	operator	NOUN
ma-115	270	1	k̂+	k̂+	PROPN
ma-115	270	2	and	and	CCONJ
ma-115	270	3	k̂3	k̂3	NOUN
ma-115	270	4	of	of	ADP
ma-115	270	5	thecorresponding	thecorresponding	NOUN
ma-115	270	6	algebras	algebra	NOUN
ma-115	270	7	.	.	PUNCT
ma-115	271	1	6	6	NUM
ma-115	271	2	.	.	X
ma-115	271	3	barut	barut	NOUN
ma-115	271	4	-	-	PUNCT
ma-115	271	5	girardello	girardello	NOUN
ma-115	271	6	-	-	PUNCT
ma-115	271	7	type	type	NOUN
ma-115	271	8	transforms	transform	NOUN
ma-115	271	9	of	of	ADP
ma-115	271	10	fractional	fractional	ADJ
ma-115	271	11	order	order	NOUN
ma-115	271	12	:	:	PUNCT
ma-115	271	13	we	we	PRON
ma-115	271	14	may	may	AUX
ma-115	271	15	introduce	introduce	VERB
ma-115	271	16	fractional	fractional	ADJ
ma-115	271	17	order	order	NOUN
ma-115	271	18	versions	version	NOUN
ma-115	271	19	of	of	ADP
ma-115	271	20	the	the	DET
ma-115	271	21	transforms	transform	NOUN
ma-115	271	22	ĝ1,α−β,−2(α+β	ĝ1,α−β,−2(α+β	NOUN
ma-115	271	23	)	)	PUNCT
ma-115	271	24	and	and	CCONJ
ma-115	271	25	ĝ2,α−β,−2(α+β	ĝ2,α−β,−2(α+β	NOUN
ma-115	271	26	)	)	PUNCT
ma-115	271	27	.	.	PUNCT
ma-115	272	1	let	let	VERB
ma-115	272	2	us	we	PRON
ma-115	272	3	consider	consider	VERB
ma-115	272	4	,	,	PUNCT
ma-115	272	5	the	the	DET
ma-115	272	6	disentanglement	disentanglement	NOUN
ma-115	272	7	relation	relation	NOUN
ma-115	272	8	for	for	ADP
ma-115	272	9	the	the	DET
ma-115	272	10	su(1	su(1	NOUN
ma-115	272	11	,	,	PUNCT
ma-115	272	12	1	1	X
ma-115	272	13	)	)	PUNCT
ma-115	272	14	algebra	algebra	NOUN
ma-115	272	15	generators	generator	NOUN
ma-115	272	16	eζ	eζ	ADP
ma-115	273	1	[	[	X
ma-115	273	2	k̂+−k̂−	k̂+−k̂−	X
ma-115	273	3	]	]	X
ma-115	273	4	=	=	SYM
ma-115	273	5	etan(ζ/2	etan(ζ/2	NOUN
ma-115	273	6	)	)	PUNCT
ma-115	274	1	k̂+	k̂+	PROPN
ma-115	274	2	e−	e−	PROPN
ma-115	274	3	sin(ζ	sin(ζ	PROPN
ma-115	274	4	)	)	PUNCT
ma-115	274	5	k̂−	k̂−	PROPN
ma-115	274	6	etan(ζ/2	etan(ζ/2	PROPN
ma-115	274	7	)	)	PUNCT
ma-115	275	1	k̂+	k̂+	NOUN
ma-115	275	2	,	,	PUNCT
ma-115	275	3	(	(	PUNCT
ma-115	275	4	59	59	NUM
ma-115	275	5	)	)	PUNCT
ma-115	275	6	holding	hold	VERB
ma-115	275	7	for	for	ADP
ma-115	275	8	−π	−π	NOUN
ma-115	275	9	<	<	X
ma-115	275	10	ζ	ζ	X
ma-115	275	11	<	<	X
ma-115	275	12	π	π	PROPN
ma-115	275	13	.	.	PUNCT
ma-115	276	1	the	the	DET
ma-115	276	2	expressions	expression	NOUN
ma-115	276	3	above	above	ADV
ma-115	276	4	obtained	obtain	VERB
ma-115	276	5	for	for	ADP
ma-115	276	6	ĝ1,α−β,−2(α+β	ĝ1,α−β,−2(α+β	NOUN
ma-115	276	7	)	)	PUNCT
ma-115	276	8	and	and	CCONJ
ma-115	276	9	ĝ2,α−β,−2(α+β)correspond	ĝ2,α−β,−2(α+β)correspond	VERB
ma-115	276	10	to	to	PART
ma-115	276	11	value	value	VERB
ma-115	276	12	ζ	ζ	NOUN
ma-115	276	13	=	=	SYM
ma-115	276	14	(	(	PUNCT
ma-115	276	15	π/4	π/4	PROPN
ma-115	276	16	)	)	PUNCT
ma-115	276	17	with	with	ADP
ma-115	276	18	appropriate	appropriate	ADJ
ma-115	276	19	set	set	NOUN
ma-115	276	20	of	of	ADP
ma-115	276	21	operations	operation	NOUN
ma-115	276	22	(	(	PUNCT
ma-115	276	23	21	21	NUM
ma-115	276	24	)	)	PUNCT
ma-115	276	25	and	and	CCONJ
ma-115	276	26	(	(	PUNCT
ma-115	276	27	23	23	X
ma-115	276	28	)	)	PUNCT
ma-115	276	29	being	be	AUX
ma-115	276	30	respectively	respectively	ADV
ma-115	276	31	https://doi.org/10.28924/ada/ma.3.6	https://doi.org/10.28924/ada/ma.3.6	PROPN
ma-115	276	32	eur	eur	NOUN
ma-115	276	33	.	.	PUNCT
ma-115	277	1	j.	j.	PROPN
ma-115	277	2	math	math	PROPN
ma-115	277	3	.	.	PUNCT
ma-115	278	1	anal	anal	PROPN
ma-115	278	2	.	.	PUNCT
ma-115	279	1	10.28924	10.28924	NUM
ma-115	279	2	/	/	SYM
ma-115	279	3	ada	ada	PROPN
ma-115	279	4	/	/	SYM
ma-115	279	5	ma.3.6	ma.3.6	PROPN
ma-115	279	6	12involved.let	12involved.let	NUM
ma-115	279	7	us	we	PRON
ma-115	279	8	refer	refer	VERB
ma-115	279	9	in	in	ADP
ma-115	279	10	particular	particular	ADJ
ma-115	279	11	to	to	ADP
ma-115	279	12	the	the	DET
ma-115	279	13	operators	operator	NOUN
ma-115	279	14	(	(	PUNCT
ma-115	279	15	17	17	NUM
ma-115	279	16	)	)	PUNCT
ma-115	279	17	so	so	SCONJ
ma-115	279	18	that	that	SCONJ
ma-115	279	19	on	on	ADP
ma-115	279	20	account	account	NOUN
ma-115	279	21	of	of	ADP
ma-115	279	22	(	(	PUNCT
ma-115	279	23	15	15	NUM
ma-115	279	24	)	)	PUNCT
ma-115	279	25	one	one	PRON
ma-115	279	26	ends	end	VERB
ma-115	279	27	up	up	ADP
ma-115	279	28	with	with	ADP
ma-115	279	29	[	[	PUNCT
ma-115	279	30	eζ	eζ	ADP
ma-115	279	31	[	[	X
ma-115	279	32	k̂	k̂	X
ma-115	279	33	(	(	PUNCT
ma-115	279	34	1	1	NUM
ma-115	279	35	)	)	PUNCT
ma-115	279	36	+	+	CCONJ
ma-115	279	37	−k̂	−k̂	PROPN
ma-115	279	38	(	(	PUNCT
ma-115	279	39	1	1	NUM
ma-115	279	40	)	)	PUNCT
ma-115	280	1	−	−	NOUN
ma-115	280	2	]	]	X
ma-115	280	3	f	f	X
ma-115	280	4	]	]	X
ma-115	280	5	=	=	SYM
ma-115	280	6	1	1	NUM
ma-115	280	7	sin	sin	VERB
ma-115	280	8	ζ	ζ	NOUN
ma-115	280	9	y1−4(α+β	y1−4(α+β	NOUN
ma-115	280	10	)	)	PUNCT
ma-115	280	11	∫	∫	PROPN
ma-115	280	12	∞	∞	PROPN
ma-115	280	13	0	0	NUM
ma-115	280	14	(	(	PUNCT
ma-115	280	15	xy)2(α+β	xy)2(α+β	NOUN
ma-115	280	16	)	)	PUNCT
ma-115	280	17	e−(1/2	e−(1/2	PROPN
ma-115	280	18	)	)	PUNCT
ma-115	280	19	cot(ζ)(x	cot(ζ)(x	NOUN
ma-115	280	20	2+y2	2+y2	NOUN
ma-115	280	21	)	)	PUNCT
ma-115	280	22	iα−β	iα−β	NOUN
ma-115	280	23	(	(	PUNCT
ma-115	280	24	xy	xy	PROPN
ma-115	280	25	sin	sin	VERB
ma-115	280	26	ζ	ζ	NOUN
ma-115	280	27	)	)	PUNCT
ma-115	280	28	f	f	NOUN
ma-115	281	1	(	(	PUNCT
ma-115	281	2	x)dx	x)dx	PROPN
ma-115	281	3	then	then	ADV
ma-115	281	4	,	,	PUNCT
ma-115	281	5	writing	write	VERB
ma-115	281	6	ζ	ζ	NOUN
ma-115	281	7	=	=	SYM
ma-115	281	8	(	(	PUNCT
ma-115	281	9	aπ/4	aπ/4	NOUN
ma-115	281	10	)	)	PUNCT
ma-115	281	11	,	,	PUNCT
ma-115	281	12	one	one	PRON
ma-115	281	13	can	can	AUX
ma-115	281	14	obtains	obtain	VERB
ma-115	281	15	the	the	DET
ma-115	281	16	ath	ath	NOUN
ma-115	281	17	power	power	NOUN
ma-115	281	18	of	of	ADP
ma-115	281	19	(	(	PUNCT
ma-115	281	20	51	51	NUM
ma-115	281	21	)	)	PUNCT
ma-115	281	22	,	,	PUNCT
ma-115	281	23	with	with	ADP
ma-115	281	24	the	the	DET
ma-115	281	25	first	first	ADJ
ma-115	281	26	barut	barut	NOUN
ma-115	281	27	-	-	PUNCT
ma-115	281	28	girardello	girardello	NOUN
ma-115	281	29	-	-	PUNCT
ma-115	281	30	typetransforms	typetransform	NOUN
ma-115	281	31	of	of	ADP
ma-115	281	32	fractional	fractional	ADJ
ma-115	281	33	order	order	NOUN
ma-115	281	34	a	a	PRON
ma-115	281	35	being	be	AUX
ma-115	281	36	accordingly	accordingly	ADV
ma-115	281	37	defined	define	VERB
ma-115	281	38	by	by	ADP
ma-115	281	39	the	the	DET
ma-115	281	40	functional	functional	ADJ
ma-115	281	41	expression	expression	NOUN
ma-115	281	42	:	:	PUNCT
ma-115	281	43	[	[	PUNCT
ma-115	281	44	ĝa1,α−β,−2(α+β)f	ĝa1,α−β,−2(α+β)f	NOUN
ma-115	281	45	]	]	PUNCT
ma-115	281	46	(	(	PUNCT
ma-115	281	47	y	y	NOUN
ma-115	281	48	)	)	PUNCT
ma-115	281	49	=	=	SYM
ma-115	281	50	1	1	NUM
ma-115	281	51	sin	sin	NOUN
ma-115	281	52	(	(	PUNCT
ma-115	281	53	φ/2	φ/2	NOUN
ma-115	281	54	)	)	PUNCT
ma-115	281	55	y1−4(α+β	y1−4(α+β	NOUN
ma-115	281	56	)	)	PUNCT
ma-115	281	57	∫	∫	PROPN
ma-115	281	58	∞	∞	PROPN
ma-115	281	59	0	0	NUM
ma-115	281	60	(	(	PUNCT
ma-115	281	61	xy)2(α+β	xy)2(α+β	NUM
ma-115	281	62	)	)	PUNCT
ma-115	281	63	e−	e−	PROPN
ma-115	281	64	cot(φ/2)(x	cot(φ/2)(x	ADJ
ma-115	281	65	2+y2	2+y2	NOUN
ma-115	281	66	)	)	PUNCT
ma-115	281	67	iα−β	iα−β	NOUN
ma-115	281	68	(	(	PUNCT
ma-115	281	69	xy	xy	PROPN
ma-115	281	70	sin	sin	NOUN
ma-115	281	71	(	(	PUNCT
ma-115	281	72	φ/2	φ/2	NUM
ma-115	281	73	)	)	PUNCT
ma-115	281	74	)	)	PUNCT
ma-115	282	1	f	f	PROPN
ma-115	282	2	(	(	PUNCT
ma-115	282	3	x)dx(60)with	x)dx(60)with	PROPN
ma-115	282	4	φ	φ	PROPN
ma-115	282	5	=	=	SYM
ma-115	282	6	(	(	PUNCT
ma-115	282	7	aπ/2	aπ/2	PROPN
ma-115	282	8	)	)	PUNCT
ma-115	282	9	,	,	PUNCT
ma-115	282	10	as	as	SCONJ
ma-115	282	11	beforethe	beforethe	DET
ma-115	282	12	second	second	ADJ
ma-115	282	13	barut	barut	NOUN
ma-115	282	14	-	-	PUNCT
ma-115	282	15	girardello	girardello	NOUN
ma-115	282	16	-	-	PUNCT
ma-115	282	17	type	type	NOUN
ma-115	282	18	transforms	transform	NOUN
ma-115	282	19	of	of	ADP
ma-115	282	20	fractional	fractional	ADJ
ma-115	282	21	order	order	NOUN
ma-115	282	22	a	a	PRON
ma-115	282	23	is	be	AUX
ma-115	282	24	similarly	similarly	ADV
ma-115	282	25	introduced	introduce	VERB
ma-115	282	26	through	through	ADP
ma-115	282	27	e	e	PROPN
ma-115	282	28	(	(	PUNCT
ma-115	282	29	aπ/4	aπ/4	NOUN
ma-115	282	30	)	)	PUNCT
ma-115	282	31	[	[	PUNCT
ma-115	282	32	k̂	k̂	X
ma-115	282	33	(	(	PUNCT
ma-115	282	34	2	2	NUM
ma-115	282	35	)	)	PUNCT
ma-115	282	36	+	+	CCONJ
ma-115	282	37	−k̂	−k̂	PROPN
ma-115	282	38	(	(	PUNCT
ma-115	282	39	2	2	NUM
ma-115	282	40	)	)	PUNCT
ma-115	282	41	−	−	NOUN
ma-115	282	42	]	]	PUNCT
ma-115	282	43	=	=	SYM
ma-115	282	44	ĝa2,α−β,−2(α+β	ĝa2,α−β,−2(α+β	NOUN
ma-115	282	45	)	)	PUNCT
ma-115	282	46	,	,	PUNCT
ma-115	282	47	(	(	PUNCT
ma-115	282	48	61	61	NUM
ma-115	282	49	)	)	PUNCT
ma-115	282	50	the	the	DET
ma-115	282	51	relevant	relevant	ADJ
ma-115	282	52	functional	functional	ADJ
ma-115	282	53	expression	expression	NOUN
ma-115	282	54	being	be	AUX
ma-115	282	55	then	then	ADV
ma-115	282	56	:	:	PUNCT
ma-115	282	57	[	[	PUNCT
ma-115	282	58	ĝa2,α−β,−2(α+β)f	ĝa2,α−β,−2(α+β)f	NOUN
ma-115	282	59	]	]	PUNCT
ma-115	282	60	(	(	PUNCT
ma-115	282	61	y	y	NOUN
ma-115	282	62	)	)	PUNCT
ma-115	282	63	=	=	SYM
ma-115	282	64	1	1	NUM
ma-115	282	65	sin	sin	NOUN
ma-115	282	66	(	(	PUNCT
ma-115	282	67	φ/2	φ/2	NUM
ma-115	282	68	)	)	PUNCT
ma-115	282	69	∫	∫	PROPN
ma-115	283	1	∞	∞	PROPN
ma-115	283	2	0	0	NUM
ma-115	283	3	x1−2(α+β)(xy)2(α+β	x1−2(α+β)(xy)2(α+β	NOUN
ma-115	283	4	)	)	PUNCT
ma-115	283	5	e−(1/2	e−(1/2	ADJ
ma-115	283	6	)	)	PUNCT
ma-115	283	7	cot(φ/2)(x	cot(φ/2)(x	ADJ
ma-115	283	8	2+y2	2+y2	NOUN
ma-115	283	9	)	)	PUNCT
ma-115	283	10	iα−β	iα−β	NOUN
ma-115	283	11	(	(	PUNCT
ma-115	283	12	xy	xy	PROPN
ma-115	283	13	sin	sin	NOUN
ma-115	283	14	(	(	PUNCT
ma-115	283	15	φ/2	φ/2	NUM
ma-115	283	16	)	)	PUNCT
ma-115	283	17	)	)	PUNCT
ma-115	284	1	f	f	PROPN
ma-115	284	2	(	(	PUNCT
ma-115	284	3	x)dx.(62)the	x)dx.(62)the	DET
ma-115	284	4	ordinary	ordinary	ADJ
ma-115	284	5	transforms	transform	NOUN
ma-115	284	6	are	be	AUX
ma-115	284	7	recovered	recover	VERB
ma-115	284	8	,	,	PUNCT
ma-115	284	9	of	of	ADP
ma-115	284	10	course	course	NOUN
ma-115	284	11	with	with	ADP
ma-115	284	12	a	a	DET
ma-115	284	13	=	=	ADJ
ma-115	284	14	1	1	NUM
ma-115	284	15	,	,	PUNCT
ma-115	284	16	while	while	SCONJ
ma-115	284	17	for	for	ADP
ma-115	284	18	α	α	PROPN
ma-115	284	19	+	+	X
ma-115	284	20	β	β	X
ma-115	284	21	=	=	SYM
ma-115	284	22	1	1	NUM
ma-115	284	23	4	4	NUM
ma-115	284	24	,	,	PUNCT
ma-115	284	25	we	we	PRON
ma-115	284	26	obtainthe	obtainthe	VERB
ma-115	284	27	conventional	conventional	ADJ
ma-115	284	28	barut	barut	NOUN
ma-115	284	29	-	-	PUNCT
ma-115	284	30	girardello	girardello	NOUN
ma-115	284	31	-	-	PUNCT
ma-115	284	32	type	type	NOUN
ma-115	284	33	transforms	transform	NOUN
ma-115	284	34	of	of	ADP
ma-115	284	35	fractional	fractional	ADJ
ma-115	284	36	order	order	NOUN
ma-115	284	37	a	a	PRON
ma-115	284	38	,	,	PUNCT
ma-115	284	39	ĝaα−β	ĝaα−β	PROPN
ma-115	284	40	,	,	PUNCT
ma-115	284	41	introduced	introduce	VERB
ma-115	284	42	in	in	ADP
ma-115	284	43	[	[	X
ma-115	284	44	16	16	NUM
ma-115	284	45	]	]	PUNCT
ma-115	284	46	.	.	PUNCT
ma-115	285	1	ĝa1,α−β,1/4	ĝa1,α−β,1/4	X
ma-115	286	1	=	=	PUNCT
ma-115	286	2	ĝa2,α−β,1/4	ĝa2,α−β,1/4	PROPN
ma-115	286	3	≡	≡	PROPN
ma-115	286	4	ĝ	ĝ	PROPN
ma-115	286	5	a	a	DET
ma-115	286	6	α−β	α−β	PROPN
ma-115	286	7	,	,	PUNCT
ma-115	286	8	with	with	ADP
ma-115	286	9	[	[	PUNCT
ma-115	286	10	ĝaα−βf	ĝaα−βf	NOUN
ma-115	286	11	]	]	PUNCT
ma-115	286	12	(	(	PUNCT
ma-115	286	13	y	y	NOUN
ma-115	286	14	)	)	PUNCT
ma-115	286	15	=	=	SYM
ma-115	286	16	1	1	NUM
ma-115	286	17	sin	sin	NOUN
ma-115	286	18	(	(	PUNCT
ma-115	286	19	φ/2	φ/2	NUM
ma-115	286	20	)	)	PUNCT
ma-115	286	21	∫	∫	PROPN
ma-115	286	22	∞	∞	NUM
ma-115	286	23	0	0	NUM
ma-115	287	1	√	√	PROPN
ma-115	287	2	xy	xy	PROPN
ma-115	287	3	e−(1/2	e−(1/2	PROPN
ma-115	287	4	)	)	PUNCT
ma-115	287	5	cot(φ/2)(x	cot(φ/2)(x	PROPN
ma-115	287	6	2+y2	2+y2	NOUN
ma-115	287	7	)	)	PUNCT
ma-115	288	1	iα−β	iα−β	NOUN
ma-115	288	2	(	(	PUNCT
ma-115	288	3	xy	xy	PROPN
ma-115	288	4	sin	sin	NOUN
ma-115	288	5	(	(	PUNCT
ma-115	288	6	φ/2	φ/2	NUM
ma-115	288	7	)	)	PUNCT
ma-115	288	8	)	)	PUNCT
ma-115	289	1	f	f	PROPN
ma-115	289	2	(	(	PUNCT
ma-115	289	3	x)dx	x)dx	PROPN
ma-115	289	4	.	.	PUNCT
ma-115	290	1	(	(	PUNCT
ma-115	290	2	63	63	NUM
ma-115	290	3	)	)	PUNCT
ma-115	290	4	the	the	DET
ma-115	290	5	fractional	fractional	NOUN
ma-115	290	6	transforms	transform	VERB
ma-115	290	7	ĝa1,α−β,−2(α+β	ĝa1,α−β,−2(α+β	NOUN
ma-115	290	8	)	)	PUNCT
ma-115	290	9	and	and	CCONJ
ma-115	290	10	ĝa2,α−β,−2(α+β	ĝa2,α−β,−2(α+β	NOUN
ma-115	290	11	)	)	PUNCT
ma-115	290	12	are	be	AUX
ma-115	290	13	cyclic	cyclic	ADJ
ma-115	290	14	with	with	ADP
ma-115	290	15	respect	respect	NOUN
ma-115	290	16	to	to	PART
ma-115	290	17	order	order	VERB
ma-115	290	18	a	a	PRON
ma-115	290	19	,	,	PUNCT
ma-115	290	20	being	be	AUX
ma-115	290	21	ĝa+8j	ĝa+8j	NOUN
ma-115	290	22	1,α−β,−2(α+β	1,α−β,−2(α+β	NUM
ma-115	290	23	)	)	PUNCT
ma-115	290	24	=	=	SYM
ma-115	290	25	ĝa1,α−β,−2(α+β	ĝa1,α−β,−2(α+β	NOUN
ma-115	290	26	)	)	PUNCT
ma-115	290	27	,	,	PUNCT
ma-115	290	28	ĝa+8j	ĝa+8j	VERB
ma-115	290	29	2,α−β,−2(α+β	2,α−β,−2(α+β	NUM
ma-115	290	30	)	)	PUNCT
ma-115	290	31	=	=	SYM
ma-115	290	32	ĝa2,α−β,−2(α+β	ĝa2,α−β,−2(α+β	NOUN
ma-115	290	33	)	)	PUNCT
ma-115	290	34	,	,	PUNCT
ma-115	290	35	(	(	PUNCT
ma-115	290	36	64	64	NUM
ma-115	290	37	)	)	PUNCT
ma-115	290	38	which	which	PRON
ma-115	290	39	allows	allow	VERB
ma-115	290	40	us	we	PRON
ma-115	290	41	to	to	PART
ma-115	290	42	limit	limit	VERB
ma-115	290	43	the	the	DET
ma-115	290	44	values	value	NOUN
ma-115	290	45	of	of	ADP
ma-115	290	46	a	a	PRON
ma-115	290	47	to	to	ADP
ma-115	290	48	the	the	DET
ma-115	290	49	interval	interval	NOUN
ma-115	290	50	a	a	DET
ma-115	290	51	∈	∈	PROPN
ma-115	291	1	[	[	X
ma-115	291	2	−4	−4	X
ma-115	291	3	,	,	PUNCT
ma-115	291	4	4].the	4].the	DET
ma-115	291	5	operational	operational	ADJ
ma-115	291	6	relations	relation	NOUN
ma-115	291	7	(	(	PUNCT
ma-115	291	8	55)can	55)can	NUM
ma-115	291	9	be	be	AUX
ma-115	291	10	generalized	generalize	VERB
ma-115	291	11	to	to	ADP
ma-115	291	12	ĝa1,α−β,−2(α+β	ĝa1,α−β,−2(α+β	NOUN
ma-115	291	13	)	)	PUNCT
ma-115	291	14	and	and	CCONJ
ma-115	291	15	ĝa2,α−β,−2(α+β	ĝa2,α−β,−2(α+β	NOUN
ma-115	291	16	)	)	PUNCT
ma-115	291	17	for	for	ADP
ma-115	291	18	which	which	PRON
ma-115	291	19	we	we	PRON
ma-115	291	20	obtain	obtain	VERB
ma-115	291	21	[	[	PUNCT
ma-115	291	22	ĝa1,α−β,−2(α+β	ĝa1,α−β,−2(α+β	NOUN
ma-115	291	23	)	)	PUNCT
ma-115	291	24	î	î	VERB
ma-115	291	25	∗	∗	NOUN
ma-115	291	26	α−β,−2(α+β),af	α−β,−2(α+β),af	PRON
ma-115	291	27	]	]	PUNCT
ma-115	291	28	(	(	PUNCT
ma-115	291	29	y	y	NOUN
ma-115	291	30	)	)	PUNCT
ma-115	291	31	=	=	PUNCT
ma-115	292	1	y2	y2	NOUN
ma-115	292	2	sin2	sin2	NOUN
ma-115	292	3	(	(	PUNCT
ma-115	292	4	φ/2	φ/2	NUM
ma-115	292	5	)	)	PUNCT
ma-115	292	6	[	[	PUNCT
ma-115	292	7	ĝ1,α−β,−2(α+β)f	ĝ1,α−β,−2(α+β)f	NOUN
ma-115	292	8	]	]	PUNCT
ma-115	292	9	(	(	PUNCT
ma-115	292	10	y	y	NOUN
ma-115	292	11	)	)	PUNCT
ma-115	292	12	,	,	PUNCT
ma-115	292	13	[	[	PUNCT
ma-115	292	14	ĝa2,α−β,−2(α+β	ĝa2,α−β,−2(α+β	NOUN
ma-115	292	15	)	)	PUNCT
ma-115	292	16	îα−β,−2(α+β),af	îα−β,−2(α+β),af	NOUN
ma-115	292	17	]	]	PUNCT
ma-115	292	18	(	(	PUNCT
ma-115	292	19	y	y	NOUN
ma-115	292	20	)	)	PUNCT
ma-115	292	21	=	=	PUNCT
ma-115	292	22	y2	y2	NOUN
ma-115	292	23	sin2	sin2	NOUN
ma-115	292	24	(	(	PUNCT
ma-115	292	25	φ/2	φ/2	NUM
ma-115	292	26	)	)	PUNCT
ma-115	292	27	[	[	PUNCT
ma-115	292	28	ĝ2,α−β,−2(α+β)f	ĝ2,α−β,−2(α+β)f	NOUN
ma-115	292	29	]	]	X
ma-115	292	30	(	(	PUNCT
ma-115	292	31	y	y	NOUN
ma-115	292	32	)	)	PUNCT
ma-115	292	33	.	.	PUNCT
ma-115	293	1	(	(	PUNCT
ma-115	293	2	65	65	NUM
ma-115	293	3	)	)	PUNCT
ma-115	293	4	the	the	DET
ma-115	293	5	differential	differential	ADJ
ma-115	293	6	operator	operator	NOUN
ma-115	293	7	îα−β,−2(α+β),a	îα−β,−2(α+β),a	NOUN
ma-115	293	8	is	be	AUX
ma-115	293	9	given	give	VERB
ma-115	293	10	by	by	ADP
ma-115	293	11	îα−β,−2(α+β),a	îα−β,−2(α+β),a	PROPN
ma-115	293	12	=	=	SYM
ma-115	293	13	2	2	NUM
ma-115	293	14	cot2(φ/2	cot2(φ/2	NOUN
ma-115	293	15	)	)	PUNCT
ma-115	293	16	k̂	k̂	NOUN
ma-115	293	17	(	(	PUNCT
ma-115	293	18	2	2	X
ma-115	293	19	)	)	PUNCT
ma-115	293	20	+	+	CCONJ
ma-115	294	1	−	−	PROPN
ma-115	294	2	k̂	k̂	NOUN
ma-115	294	3	(	(	PUNCT
ma-115	294	4	2	2	NUM
ma-115	294	5	)	)	PUNCT
ma-115	294	6	−	−	PROPN
ma-115	295	1	+	+	CCONJ
ma-115	295	2	4i	4i	NUM
ma-115	295	3	cot(φ/2	cot(φ/2	NOUN
ma-115	295	4	)	)	PUNCT
ma-115	295	5	k̂	k̂	PROPN
ma-115	295	6	(	(	PUNCT
ma-115	295	7	2	2	X
ma-115	295	8	)	)	SYM
ma-115	295	9	3	3	NUM
ma-115	295	10	=	=	NOUN
ma-115	295	11	e[1−cot(φ/2)](x	e[1−cot(φ/2)](x	VERB
ma-115	295	12	2/2	2/2	NUM
ma-115	295	13	)	)	PUNCT
ma-115	295	14	îα−β,−2(α+β	îα−β,−2(α+β	NOUN
ma-115	295	15	)	)	PUNCT
ma-115	295	16	e	e	NOUN
ma-115	295	17	−[1−cot(φ/2)](x2/2	−[1−cot(φ/2)](x2/2	PROPN
ma-115	295	18	)	)	PUNCT
ma-115	295	19	.	.	PUNCT
ma-115	296	1	(	(	PUNCT
ma-115	296	2	66	66	NUM
ma-115	296	3	)	)	PUNCT
ma-115	296	4	https://doi.org/10.28924/ada/ma.3.6	https://doi.org/10.28924/ada/ma.3.6	PROPN
ma-115	296	5	eur	eur	PROPN
ma-115	296	6	.	.	PUNCT
ma-115	297	1	j.	j.	PROPN
ma-115	297	2	math	math	PROPN
ma-115	297	3	.	.	PUNCT
ma-115	298	1	anal	anal	PROPN
ma-115	298	2	.	.	PUNCT
ma-115	299	1	10.28924	10.28924	NUM
ma-115	299	2	/	/	SYM
ma-115	299	3	ada	ada	PROPN
ma-115	299	4	/	/	PROPN
ma-115	299	5	ma.3.6	ma.3.6	PROPN
ma-115	299	6	13by	13by	NOUN
ma-115	299	7	using	use	VERB
ma-115	299	8	equation	equation	NOUN
ma-115	299	9	(	(	PUNCT
ma-115	299	10	57	57	NUM
ma-115	299	11	)	)	PUNCT
ma-115	299	12	we	we	PRON
ma-115	299	13	have	have	VERB
ma-115	299	14	îα−β,−2(α+β),a	îα−β,−2(α+β),a	NOUN
ma-115	299	15	=	=	PUNCT
ma-115	299	16	e−	e−	PROPN
ma-115	299	17	cot(φ/2)(x	cot(φ/2)(x	PROPN
ma-115	299	18	2/2	2/2	NUM
ma-115	299	19	)	)	PUNCT
ma-115	299	20	b̂α−β,−2(α+β	b̂α−β,−2(α+β	NOUN
ma-115	299	21	)	)	PUNCT
ma-115	299	22	e	e	NOUN
ma-115	299	23	cot(φ/2)(x2/2	cot(φ/2)(x2/2	PROPN
ma-115	299	24	)	)	PUNCT
ma-115	300	1	=	=	SYM
ma-115	300	2	e2(α+β)−(α−β)−1îax	e2(α+β)−(α−β)−1îax	NOUN
ma-115	300	3	2(α−β)+1îax	2(α−β)+1îax	NUM
ma-115	300	4	−2(α+β)−(α−β	−2(α+β)−(α−β	NOUN
ma-115	300	5	)	)	PUNCT
ma-115	300	6	(	(	PUNCT
ma-115	300	7	67	67	NUM
ma-115	300	8	)	)	PUNCT
ma-115	300	9	with	with	ADP
ma-115	300	10	îa	îa	X
ma-115	300	11	=	=	SYM
ma-115	300	12	e−	e−	PROPN
ma-115	300	13	cot(φ/2)(x	cot(φ/2)(x	PROPN
ma-115	300	14	2/2	2/2	NUM
ma-115	300	15	)	)	PUNCT
ma-115	300	16	∂	∂	NUM
ma-115	300	17	∂x	∂x	PROPN
ma-115	300	18	ecot(φ/2)(x	ecot(φ/2)(x	NOUN
ma-115	300	19	2/2	2/2	NUM
ma-115	300	20	)	)	PUNCT
ma-115	300	21	=	=	SYM
ma-115	300	22	1	1	NUM
ma-115	300	23	sin2	sin2	NOUN
ma-115	300	24	(	(	PUNCT
ma-115	300	25	φ/2	φ/2	NUM
ma-115	300	26	)	)	PUNCT
ma-115	300	27	[	[	PUNCT
ma-115	300	28	cos(φ/2)x	cos(φ/2)x	ADJ
ma-115	300	29	+	+	CCONJ
ma-115	300	30	sin(φ/2	sin(φ/2	PROPN
ma-115	300	31	)	)	PUNCT
ma-115	300	32	∂	∂	NUM
ma-115	301	1	∂x	∂x	PROPN
ma-115	301	2	]	]	PUNCT
ma-115	301	3	.	.	PUNCT
ma-115	302	1	(	(	PUNCT
ma-115	302	2	68	68	NUM
ma-115	302	3	)	)	PUNCT
ma-115	302	4	therefore	therefore	ADV
ma-115	302	5	,	,	PUNCT
ma-115	302	6	ĝa1,α−β,−2(α+β	ĝa1,α−β,−2(α+β	NOUN
ma-115	302	7	)	)	PUNCT
ma-115	302	8	and	and	CCONJ
ma-115	302	9	ĝa2,α−β,−2(α+β	ĝa2,α−β,−2(α+β	NOUN
ma-115	302	10	)	)	PUNCT
ma-115	302	11	are	be	AUX
ma-115	302	12	of	of	ADP
ma-115	302	13	relevance	relevance	NOUN
ma-115	302	14	in	in	ADP
ma-115	302	15	connection	connection	NOUN
ma-115	302	16	with	with	ADP
ma-115	302	17	evolution	evolution	NOUN
ma-115	302	18	equa	equa	NOUN
ma-115	302	19	-	-	PUNCT
ma-115	302	20	tions	tion	NOUN
ma-115	302	21	like	like	ADP
ma-115	302	22	k	k	PROPN
ma-115	302	23	∂	∂	NOUN
ma-115	302	24	∂τ	∂τ	PROPN
ma-115	302	25	h(x	h(x	PROPN
ma-115	302	26	,	,	PUNCT
ma-115	302	27	τ	τ	X
ma-115	302	28	)	)	PUNCT
ma-115	303	1	=	=	SYM
ma-115	303	2	p	p	X
ma-115	303	3	(	(	PUNCT
ma-115	303	4	î∗α−β,−2(α+β),a	î∗α−β,−2(α+β),a	PROPN
ma-115	303	5	)	)	PUNCT
ma-115	303	6	h(x	h(x	PROPN
ma-115	303	7	,	,	PUNCT
ma-115	303	8	τ	τ	PROPN
ma-115	303	9	)	)	PUNCT
ma-115	303	10	,	,	PUNCT
ma-115	303	11	or	or	CCONJ
ma-115	303	12	k	k	PROPN
ma-115	303	13	∂	∂	NOUN
ma-115	303	14	∂τ	∂τ	PROPN
ma-115	303	15	h(x	h(x	PROPN
ma-115	303	16	,	,	PUNCT
ma-115	303	17	τ	τ	X
ma-115	303	18	)	)	PUNCT
ma-115	303	19	=	=	SYM
ma-115	304	1	p	p	X
ma-115	304	2	(	(	PUNCT
ma-115	304	3	îα−β,−2(α+β),a	îα−β,−2(α+β),a	PROPN
ma-115	304	4	)	)	PUNCT
ma-115	304	5	h(x	h(x	PROPN
ma-115	304	6	,	,	PUNCT
ma-115	304	7	τ	τ	PROPN
ma-115	304	8	)	)	PUNCT
ma-115	304	9	involving	involve	VERB
ma-115	304	10	polynomial	polynomial	ADJ
ma-115	304	11	function	function	NOUN
ma-115	304	12	of	of	ADP
ma-115	304	13	îα−β,−2(α+β),a	îα−β,−2(α+β),a	PROPN
ma-115	304	14	and	and	CCONJ
ma-115	304	15	î∗α−β,−2(α+β),a	î∗α−β,−2(α+β),a	VERB
ma-115	304	16	respectively	respectively	ADV
ma-115	304	17	.	.	PUNCT
ma-115	305	1	7	7	X
ma-115	305	2	.	.	NUM
ma-115	305	3	generalized	generalize	VERB
ma-115	305	4	hankel	hankel	NOUN
ma-115	305	5	transforms	transform	VERB
ma-115	305	6	:	:	PUNCT
ma-115	305	7	the	the	DET
ma-115	305	8	h	h	NOUN
ma-115	305	9	and	and	CCONJ
ma-115	305	10	g	g	NOUN
ma-115	305	11	transform	transform	NOUN
ma-115	305	12	discussed	discuss	VERB
ma-115	305	13	above	above	ADV
ma-115	305	14	are	be	AUX
ma-115	305	15	associated	associate	VERB
ma-115	305	16	with	with	ADP
ma-115	305	17	hamiltonian	hamiltonian	ADJ
ma-115	305	18	operators	operator	NOUN
ma-115	305	19	involvinga	involvinga	VERB
ma-115	305	20	linear	linear	ADJ
ma-115	305	21	combination	combination	NOUN
ma-115	305	22	of	of	ADP
ma-115	305	23	the	the	DET
ma-115	305	24	generators	generator	NOUN
ma-115	305	25	k̂+	k̂+	PROPN
ma-115	305	26	and	and	CCONJ
ma-115	305	27	k̂−	k̂−	PROPN
ma-115	305	28	of	of	ADP
ma-115	305	29	the	the	DET
ma-115	305	30	relevant	relevant	ADJ
ma-115	305	31	su(1	su(1	NOUN
ma-115	305	32	,	,	PUNCT
ma-115	305	33	1	1	X
ma-115	305	34	)	)	PUNCT
ma-115	305	35	algebra	algebra	NOUN
ma-115	305	36	realizationsin	realizationsin	VERB
ma-115	305	37	a	a	DET
ma-115	305	38	form	form	NOUN
ma-115	305	39	that	that	PRON
ma-115	305	40	naturally	naturally	ADV
ma-115	305	41	suggests	suggest	VERB
ma-115	305	42	an	an	DET
ma-115	305	43	arbitrary	arbitrary	ADJ
ma-115	305	44	respectively	respectively	ADV
ma-115	305	45	with	with	ADP
ma-115	305	46	the	the	DET
ma-115	305	47	attractive	attractive	ADJ
ma-115	305	48	and	and	CCONJ
ma-115	305	49	repulsive	repulsive	ADJ
ma-115	305	50	radialquantum	radialquantum	NOUN
ma-115	305	51	mechanics	mechanic	NOUN
ma-115	305	52	oscillator.the	oscillator.the	DET
ma-115	305	53	dynamical	dynamical	ADJ
ma-115	305	54	symmetry	symmetry	NOUN
ma-115	305	55	of	of	ADP
ma-115	305	56	the	the	DET
ma-115	305	57	linear	linear	ADJ
ma-115	305	58	quantum	quantum	ADJ
ma-115	305	59	mechanical	mechanical	ADJ
ma-115	305	60	oscillator	oscillator	NOUN
ma-115	305	61	is	be	AUX
ma-115	305	62	that	that	PRON
ma-115	305	63	of	of	ADP
ma-115	305	64	the	the	DET
ma-115	305	65	su(1	su(1	NOUN
ma-115	305	66	,	,	PUNCT
ma-115	305	67	1	1	X
ma-115	305	68	)	)	PUNCT
ma-115	305	69	algebra	algebra	NOUN
ma-115	305	70	,	,	PUNCT
ma-115	305	71	whose	whose	DET
ma-115	305	72	generator	generator	NOUN
ma-115	305	73	are	be	AUX
ma-115	305	74	defined	define	VERB
ma-115	305	75	in	in	ADP
ma-115	305	76	terms	term	NOUN
ma-115	305	77	of	of	ADP
ma-115	305	78	the	the	DET
ma-115	305	79	position	position	NOUN
ma-115	305	80	and	and	CCONJ
ma-115	305	81	momentum	momentum	NOUN
ma-115	305	82	operators	operator	NOUN
ma-115	305	83	are	be	AUX
ma-115	305	84	defined	define	VERB
ma-115	305	85	in	in	ADP
ma-115	305	86	terms	term	NOUN
ma-115	305	87	ofthe	ofthe	ADJ
ma-115	305	88	position	position	NOUN
ma-115	305	89	and	and	CCONJ
ma-115	305	90	momentum	momentum	NOUN
ma-115	305	91	operators	operator	NOUN
ma-115	305	92	x̂	x̂	PUNCT
ma-115	305	93	and	and	CCONJ
ma-115	305	94	p̂	p̂	X
ma-115	306	1	=	=	PUNCT
ma-115	306	2	i	i	INTJ
ma-115	306	3	(	(	PUNCT
ma-115	306	4	d	d	X
ma-115	306	5	dx	dx	PROPN
ma-115	306	6	)	)	PUNCT
ma-115	306	7	(	(	PUNCT
ma-115	306	8	h	h	NOUN
ma-115	306	9	=	=	NOUN
ma-115	306	10	1	1	X
ma-115	306	11	)	)	PUNCT
ma-115	306	12	through	through	ADP
ma-115	306	13	the	the	DET
ma-115	306	14	self	self	NOUN
ma-115	306	15	-	-	PUNCT
ma-115	306	16	adjoint	adjoint	NOUN
ma-115	306	17	quadranticexpressions	quadranticexpression	NOUN
ma-115	306	18	k̂+	k̂+	NOUN
ma-115	306	19	=	=	NOUN
ma-115	306	20	1	1	NUM
ma-115	306	21	2	2	NUM
ma-115	306	22	x̂2	x̂2	NOUN
ma-115	306	23	=	=	SYM
ma-115	306	24	1	1	NUM
ma-115	306	25	2	2	NUM
ma-115	306	26	x2	x2	NOUN
ma-115	306	27	,	,	PUNCT
ma-115	306	28	k̂−	k̂−	PROPN
ma-115	306	29	=	=	PUNCT
ma-115	307	1	−	−	PROPN
ma-115	307	2	i	i	PRON
ma-115	307	3	2	2	NUM
ma-115	307	4	p̂2	p̂2	VERB
ma-115	307	5	=	=	PUNCT
ma-115	307	6	−	−	PROPN
ma-115	307	7	1	1	NUM
ma-115	307	8	2	2	NUM
ma-115	307	9	d2	d2	PROPN
ma-115	307	10	dx2	dx2	PROPN
ma-115	307	11	,	,	PUNCT
ma-115	307	12	k̂3	k̂3	NOUN
ma-115	307	13	=	=	SYM
ma-115	307	14	1	1	NUM
ma-115	307	15	4	4	NUM
ma-115	307	16	(	(	PUNCT
ma-115	307	17	x̂	x̂	NUM
ma-115	307	18	p̂	p̂	X
ma-115	307	19	+	+	CCONJ
ma-115	307	20	p̂x̂	p̂x̂	X
ma-115	307	21	)	)	PUNCT
ma-115	307	22	=	=	SYM
ma-115	308	1	−	−	NOUN
ma-115	309	1	i	i	PRON
ma-115	309	2	2	2	NUM
ma-115	309	3	(	(	PUNCT
ma-115	309	4	x	x	PROPN
ma-115	309	5	d	d	NOUN
ma-115	309	6	dx	dx	PROPN
ma-115	309	7	+	+	NOUN
ma-115	309	8	1	1	NUM
ma-115	309	9	2	2	NUM
ma-115	309	10	)	)	PUNCT
ma-115	309	11	.	.	PUNCT
ma-115	310	1	thus	thus	ADV
ma-115	310	2	the	the	DET
ma-115	310	3	conventional	conventional	ADJ
ma-115	310	4	hankel	hankel	NOUN
ma-115	310	5	transform	transform	NOUN
ma-115	310	6	of	of	ADP
ma-115	310	7	any	any	DET
ma-115	310	8	order	order	NOUN
ma-115	310	9	a	a	X
ma-115	310	10	,	,	PUNCT
ma-115	310	11	being	be	AUX
ma-115	310	12	associated	associate	VERB
ma-115	310	13	with	with	ADP
ma-115	310	14	the	the	DET
ma-115	310	15	sum	sum	NOUN
ma-115	310	16	operator	operator	NOUN
ma-115	310	17	k̂1	k̂1	NOUN
ma-115	310	18	=	=	PUNCT
ma-115	310	19	k̂+	k̂+	PROPN
ma-115	310	20	+	+	CCONJ
ma-115	310	21	k̂−	k̂−	PROPN
ma-115	310	22	,	,	PUNCT
ma-115	310	23	turns	turn	VERB
ma-115	310	24	out	out	ADP
ma-115	310	25	to	to	PART
ma-115	310	26	be	be	AUX
ma-115	310	27	linked	link	VERB
ma-115	310	28	to	to	ADP
ma-115	310	29	the	the	DET
ma-115	310	30	dynamics	dynamic	NOUN
ma-115	310	31	of	of	ADP
ma-115	310	32	the	the	DET
ma-115	310	33	alternative	alternative	ADJ
ma-115	310	34	radial	radial	ADJ
ma-115	310	35	oscillator	oscillator	NOUN
ma-115	310	36	,	,	PUNCT
ma-115	310	37	therelevant	therelevant	ADJ
ma-115	310	38	k̂−	k̂−	PROPN
ma-115	310	39	generator	generator	NOUN
ma-115	310	40	(	(	PUNCT
ma-115	310	41	12	12	NUM
ma-115	310	42	)	)	PUNCT
ma-115	310	43	being	be	AUX
ma-115	310	44	the	the	DET
ma-115	310	45	radical	radical	ADJ
ma-115	310	46	part	part	NOUN
ma-115	310	47	of	of	ADP
ma-115	310	48	the	the	DET
ma-115	310	49	2d	2d	NUM
ma-115	310	50	laplacian	laplacian	ADJ
ma-115	310	51	operator	operator	NOUN
ma-115	310	52	.	.	PUNCT
ma-115	311	1	in	in	ADP
ma-115	311	2	fact	fact	NOUN
ma-115	311	3	,	,	PUNCT
ma-115	311	4	as	as	ADP
ma-115	311	5	notedearlier	notedearlier	NOUN
ma-115	311	6	,	,	PUNCT
ma-115	311	7	the	the	DET
ma-115	311	8	hankel	hankel	NOUN
ma-115	311	9	transform	transform	NOUN
ma-115	311	10	of	of	ADP
ma-115	311	11	integer	integer	NOUN
ma-115	311	12	bessel	bessel	NOUN
ma-115	311	13	order	order	NOUN
ma-115	311	14	can	can	AUX
ma-115	311	15	be	be	AUX
ma-115	311	16	regarded	regard	VERB
ma-115	311	17	as	as	ADP
ma-115	311	18	the	the	DET
ma-115	311	19	radial	radial	ADJ
ma-115	311	20	part	part	NOUN
ma-115	311	21	of	of	ADP
ma-115	311	22	the	the	DET
ma-115	311	23	2dfourier	2dfourier	NUM
ma-115	311	24	transform	transform	NOUN
ma-115	311	25	of	of	ADP
ma-115	311	26	rotationally	rotationally	ADV
ma-115	311	27	symmetric	symmetric	ADJ
ma-115	311	28	function	function	NOUN
ma-115	311	29	,	,	PUNCT
ma-115	311	30	when	when	SCONJ
ma-115	311	31	polar	polar	ADJ
ma-115	311	32	co	co	NOUN
ma-115	311	33	-	-	NOUN
ma-115	311	34	ordinates	ordinate	NOUN
ma-115	311	35	are	be	AUX
ma-115	311	36	adopted.in	adopted.in	X
ma-115	311	37	otherwords	otherword	NOUN
ma-115	311	38	we	we	PRON
ma-115	311	39	have	have	VERB
ma-115	311	40	[	[	PUNCT
ma-115	311	41	f̂a	f̂a	PROPN
ma-115	311	42	f	f	PROPN
ma-115	311	43	(	(	PUNCT
ma-115	311	44	ζ	ζ	PROPN
ma-115	311	45	,	,	PUNCT
ma-115	311	46	η	η	NOUN
ma-115	311	47	)	)	PUNCT
ma-115	311	48	]	]	PUNCT
ma-115	312	1	(	(	PUNCT
ma-115	312	2	x	x	X
ma-115	312	3	,	,	PUNCT
ma-115	312	4	y	y	NOUN
ma-115	312	5	)	)	PUNCT
ma-115	312	6	=	=	PUNCT
ma-115	312	7	e−imφ	e−imφ	NOUN
ma-115	312	8	e−imθ	e−imθ	NOUN
ma-115	312	9	[	[	PUNCT
ma-115	312	10	ĥam	ĥam	X
ma-115	312	11	ρ1/2	ρ1/2	PRON
ma-115	312	12	g(ρ	g(ρ	PROPN
ma-115	312	13	)	)	PUNCT
ma-115	312	14	]	]	PUNCT
ma-115	312	15	(	(	PUNCT
ma-115	312	16	r	r	NOUN
ma-115	312	17	)	)	PUNCT
ma-115	312	18	,	,	PUNCT
ma-115	312	19	m	m	VERB
ma-115	312	20	=	=	NOUN
ma-115	312	21	0	0	NUM
ma-115	312	22	,	,	PUNCT
ma-115	312	23	1	1	NUM
ma-115	312	24	,	,	PUNCT
ma-115	312	25	2	2	NUM
ma-115	312	26	,	,	PUNCT
ma-115	312	27	...	...	PUNCT
ma-115	312	28	(	(	PUNCT
ma-115	312	29	69	69	NUM
ma-115	312	30	)	)	PUNCT
ma-115	312	31	where	where	SCONJ
ma-115	312	32	(	(	PUNCT
ma-115	312	33	ρ	ρ	PROPN
ma-115	312	34	,	,	PUNCT
ma-115	312	35	φ	φ	NUM
ma-115	312	36	)	)	PUNCT
ma-115	312	37	and	and	CCONJ
ma-115	312	38	(	(	PUNCT
ma-115	312	39	r	r	NOUN
ma-115	312	40	,	,	PUNCT
ma-115	312	41	θ	θ	NOUN
ma-115	312	42	)	)	PUNCT
ma-115	312	43	are	be	AUX
ma-115	312	44	polar	polar	ADJ
ma-115	312	45	co	co	NOUN
ma-115	312	46	-	-	NOUN
ma-115	312	47	ordinates	ordinate	NOUN
ma-115	312	48	respectively	respectively	ADV
ma-115	312	49	in	in	ADP
ma-115	312	50	the	the	DET
ma-115	312	51	function	function	NOUN
ma-115	312	52	and	and	CCONJ
ma-115	312	53	transform	transform	VERB
ma-115	312	54	domainand	domainand	NOUN
ma-115	312	55	f	f	PROPN
ma-115	312	56	is	be	AUX
ma-115	312	57	a	a	DET
ma-115	312	58	rotationally	rotationally	ADV
ma-115	312	59	symmetric	symmetric	ADJ
ma-115	312	60	function	function	NOUN
ma-115	312	61	:	:	PUNCT
ma-115	313	1	f	f	X
ma-115	313	2	(	(	PUNCT
ma-115	313	3	ζ	ζ	PROPN
ma-115	313	4	,	,	PUNCT
ma-115	313	5	η	η	NOUN
ma-115	313	6	)	)	PUNCT
ma-115	313	7	=	=	SYM
ma-115	313	8	g(ρ	g(ρ	PROPN
ma-115	313	9	)	)	PUNCT
ma-115	313	10	e	e	NOUN
ma-115	313	11	imφ	imφ	NOUN
ma-115	313	12	.	.	PUNCT
ma-115	314	1	https://doi.org/10.28924/ada/ma.3.6	https://doi.org/10.28924/ada/ma.3.6	PROPN
ma-115	314	2	eur	eur	PROPN
ma-115	314	3	.	.	PUNCT
ma-115	315	1	j.	j.	PROPN
ma-115	315	2	math	math	PROPN
ma-115	315	3	.	.	PUNCT
ma-115	316	1	anal	anal	PROPN
ma-115	316	2	.	.	PUNCT
ma-115	317	1	10.28924	10.28924	NUM
ma-115	317	2	/	/	SYM
ma-115	317	3	ada	ada	PROPN
ma-115	317	4	/	/	PROPN
ma-115	317	5	ma.3.6	ma.3.6	PROPN
ma-115	317	6	14evidently	14evidently	ADV
ma-115	317	7	(	(	PUNCT
ma-115	317	8	69	69	NUM
ma-115	317	9	)	)	PUNCT
ma-115	317	10	can	can	AUX
ma-115	317	11	be	be	AUX
ma-115	317	12	generalised	generalise	VERB
ma-115	317	13	to	to	ADP
ma-115	317	14	the	the	DET
ma-115	317	15	transform	transform	NOUN
ma-115	317	16	(	(	PUNCT
ma-115	317	17	21	21	NUM
ma-115	317	18	)	)	PUNCT
ma-115	317	19	and	and	CCONJ
ma-115	317	20	(	(	PUNCT
ma-115	317	21	24	24	NUM
ma-115	317	22	)	)	PUNCT
ma-115	317	23	as	as	ADP
ma-115	317	24	[	[	PUNCT
ma-115	317	25	f̂a	f̂a	PROPN
ma-115	317	26	f	f	PROPN
ma-115	317	27	(	(	PUNCT
ma-115	317	28	ζ	ζ	PROPN
ma-115	317	29	,	,	PUNCT
ma-115	317	30	η	η	NOUN
ma-115	317	31	)	)	PUNCT
ma-115	317	32	]	]	PUNCT
ma-115	318	1	(	(	PUNCT
ma-115	318	2	x	x	X
ma-115	318	3	,	,	PUNCT
ma-115	318	4	y	y	NOUN
ma-115	318	5	)	)	PUNCT
ma-115	318	6	=	=	PUNCT
ma-115	318	7	e−imφ	e−imφ	NOUN
ma-115	318	8	e−imθ	e−imθ	NOUN
ma-115	318	9	r−1	r−1	PROPN
ma-115	318	10	+	+	PROPN
ma-115	318	11	2(α+β	2(α+β	NUM
ma-115	318	12	)	)	PUNCT
ma-115	318	13	[	[	PUNCT
ma-115	318	14	ĥa1,m	ĥa1,m	NOUN
ma-115	318	15	ρ1−2(α+β	ρ1−2(α+β	NOUN
ma-115	318	16	)	)	PUNCT
ma-115	318	17	g(ρ	g(ρ	PROPN
ma-115	318	18	)	)	PUNCT
ma-115	318	19	]	]	PUNCT
ma-115	319	1	(	(	PUNCT
ma-115	319	2	r	r	NOUN
ma-115	319	3	)	)	PUNCT
ma-115	319	4	,	,	PUNCT
ma-115	319	5	[	[	PUNCT
ma-115	319	6	f̂a	f̂a	PROPN
ma-115	319	7	f	f	PROPN
ma-115	319	8	(	(	PUNCT
ma-115	319	9	ζ	ζ	PROPN
ma-115	319	10	,	,	PUNCT
ma-115	319	11	η	η	NOUN
ma-115	319	12	)	)	PUNCT
ma-115	319	13	]	]	PUNCT
ma-115	319	14	(	(	PUNCT
ma-115	319	15	x	x	X
ma-115	319	16	,	,	PUNCT
ma-115	319	17	y	y	NOUN
ma-115	319	18	)	)	PUNCT
ma-115	319	19	=	=	PUNCT
ma-115	319	20	e−imφ	e−imφ	NOUN
ma-115	319	21	e−imθ	e−imθ	NOUN
ma-115	319	22	r−2(α+β	r−2(α+β	PROPN
ma-115	319	23	)	)	PUNCT
ma-115	319	24	[	[	PUNCT
ma-115	319	25	ĥa2,m,−2(α+β	ĥa2,m,−2(α+β	NOUN
ma-115	319	26	)	)	PUNCT
ma-115	319	27	ρ	ρ	PROPN
ma-115	319	28	2(α+β	2(α+β	NUM
ma-115	319	29	)	)	PUNCT
ma-115	319	30	g(ρ	g(ρ	PROPN
ma-115	319	31	)	)	PUNCT
ma-115	319	32	]	]	PUNCT
ma-115	320	1	(	(	PUNCT
ma-115	320	2	r	r	NOUN
ma-115	320	3	)	)	PUNCT
ma-115	320	4	for	for	ADP
ma-115	320	5	non	non	ADJ
ma-115	320	6	-	-	ADJ
ma-115	320	7	negative	negative	ADJ
ma-115	320	8	integers	integer	NOUN
ma-115	320	9	m	m	VERB
ma-115	320	10	and	and	CCONJ
ma-115	320	11	rotationally	rotationally	ADV
ma-115	320	12	symmetric	symmetric	ADJ
ma-115	320	13	functions.likewise	functions.likewise	PROPN
ma-115	320	14	,	,	PUNCT
ma-115	320	15	the	the	DET
ma-115	320	16	barut	barut	NOUN
ma-115	320	17	-	-	PUNCT
ma-115	320	18	girardello	girardello	NOUN
ma-115	320	19	transform	transform	NOUN
ma-115	320	20	resorting	resort	VERB
ma-115	320	21	to	to	ADP
ma-115	320	22	the	the	DET
ma-115	320	23	difference	difference	NOUN
ma-115	320	24	operator	operator	NOUN
ma-115	320	25	k̂2	k̂2	PUNCT
ma-115	321	1	=	=	PUNCT
ma-115	322	1	k̂+	k̂+	NOUN
ma-115	322	2	+	+	CCONJ
ma-115	322	3	k̂−,can	k̂−,can	PROPN
ma-115	322	4	be	be	AUX
ma-115	322	5	associated	associate	VERB
ma-115	322	6	with	with	ADP
ma-115	322	7	dynamics	dynamic	NOUN
ma-115	322	8	of	of	ADP
ma-115	322	9	the	the	DET
ma-115	322	10	repulsive	repulsive	ADJ
ma-115	322	11	radical	radical	ADJ
ma-115	322	12	oscillator.therefore	oscillator.therefore	ADJ
ma-115	322	13	barut	barut	NOUN
ma-115	322	14	-	-	PUNCT
ma-115	322	15	girardellotransform	girardellotransform	NOUN
ma-115	322	16	of	of	ADP
ma-115	322	17	integer	integer	NOUN
ma-115	322	18	bessel	bessel	NOUN
ma-115	322	19	order	order	NOUN
ma-115	322	20	can	can	AUX
ma-115	322	21	be	be	AUX
ma-115	322	22	regarded	regard	VERB
ma-115	322	23	as	as	SCONJ
ma-115	322	24	the	the	DET
ma-115	322	25	radial	radial	ADJ
ma-115	322	26	part	part	NOUN
ma-115	322	27	of	of	ADP
ma-115	322	28	the	the	DET
ma-115	322	29	2d	2d	NOUN
ma-115	322	30	-	-	PUNCT
ma-115	322	31	bargman	bargman	NOUN
ma-115	322	32	transform	transform	VERB
ma-115	322	33	b̂a	b̂a	NOUN
ma-115	323	1	[	[	X
ma-115	323	2	2	2	NUM
ma-115	323	3	,	,	PUNCT
ma-115	323	4	16	16	NUM
ma-115	323	5	,	,	PUNCT
ma-115	323	6	20	20	NUM
ma-115	323	7	]	]	PUNCT
ma-115	323	8	,	,	PUNCT
ma-115	323	9	the	the	DET
ma-115	323	10	inherent	inherent	ADJ
ma-115	323	11	relation	relation	NOUN
ma-115	323	12	being	be	AUX
ma-115	323	13	similar	similar	ADJ
ma-115	323	14	to	to	ADP
ma-115	323	15	(	(	PUNCT
ma-115	323	16	69	69	NUM
ma-115	323	17	)	)	PUNCT
ma-115	323	18	i.e.	i.e.	X
ma-115	323	19	[	[	PUNCT
ma-115	323	20	b̂a	b̂a	X
ma-115	323	21	f	f	NOUN
ma-115	323	22	(	(	PUNCT
ma-115	323	23	ζ	ζ	PROPN
ma-115	323	24	,	,	PUNCT
ma-115	323	25	η	η	NOUN
ma-115	323	26	)	)	PUNCT
ma-115	323	27	]	]	PUNCT
ma-115	323	28	(	(	PUNCT
ma-115	323	29	x	x	X
ma-115	323	30	,	,	PUNCT
ma-115	323	31	y	y	NOUN
ma-115	323	32	)	)	PUNCT
ma-115	324	1	=	=	NOUN
ma-115	324	2	e−imθ	e−imθ	NOUN
ma-115	324	3	r−1/2	r−1/2	PROPN
ma-115	324	4	[	[	PUNCT
ma-115	324	5	ĝam	ĝam	NOUN
ma-115	324	6	ρ1/2	ρ1/2	NUM
ma-115	324	7	g(ρ	g(ρ	PROPN
ma-115	324	8	)	)	PUNCT
ma-115	324	9	]	]	PUNCT
ma-115	325	1	(	(	PUNCT
ma-115	325	2	r	r	NOUN
ma-115	325	3	)	)	PUNCT
ma-115	325	4	,	,	PUNCT
ma-115	325	5	m	m	VERB
ma-115	325	6	=	=	NOUN
ma-115	325	7	0	0	NUM
ma-115	325	8	,	,	PUNCT
ma-115	325	9	1	1	NUM
ma-115	325	10	,	,	PUNCT
ma-115	325	11	2	2	NUM
ma-115	325	12	,	,	PUNCT
ma-115	325	13	...	...	PUNCT
ma-115	326	1	(	(	PUNCT
ma-115	326	2	70)with	70)with	NUM
ma-115	326	3	the	the	DET
ma-115	326	4	same	same	ADJ
ma-115	326	5	meaning	meaning	NOUN
ma-115	326	6	of	of	ADP
ma-115	326	7	the	the	DET
ma-115	326	8	symbols	symbol	NOUN
ma-115	326	9	as	as	ADP
ma-115	326	10	in	in	ADP
ma-115	326	11	equation	equation	NOUN
ma-115	326	12	(	(	PUNCT
ma-115	326	13	69).the	69).the	DET
ma-115	326	14	generalization	generalization	NOUN
ma-115	326	15	of	of	ADP
ma-115	326	16	(	(	PUNCT
ma-115	326	17	70	70	NUM
ma-115	326	18	)	)	PUNCT
ma-115	326	19	to	to	ADP
ma-115	326	20	the	the	DET
ma-115	326	21	transforms	transform	NOUN
ma-115	326	22	of	of	ADP
ma-115	326	23	the	the	DET
ma-115	326	24	first	first	ADJ
ma-115	326	25	and	and	CCONJ
ma-115	326	26	second	second	ADJ
ma-115	326	27	type	type	NOUN
ma-115	326	28	is	be	AUX
ma-115	326	29	obvious.following	obvious.followe	VERB
ma-115	326	30	the	the	DET
ma-115	326	31	correspondence	correspondence	NOUN
ma-115	326	32	of	of	ADP
ma-115	326	33	the	the	DET
ma-115	326	34	hankel	hankel	NOUN
ma-115	326	35	to	to	ADP
ma-115	326	36	the	the	DET
ma-115	326	37	fourier	fourier	NOUN
ma-115	326	38	transform	transform	NOUN
ma-115	326	39	,	,	PUNCT
ma-115	326	40	we	we	PRON
ma-115	326	41	may	may	AUX
ma-115	326	42	introduce	introduce	VERB
ma-115	326	43	a	a	DET
ma-115	326	44	gener	gener	NOUN
ma-115	326	45	-	-	PUNCT
ma-115	326	46	alized	alize	VERB
ma-115	326	47	fractional	fractional	ADJ
ma-115	326	48	hankel	hankel	NOUN
ma-115	326	49	transforms	transform	VERB
ma-115	326	50	as	as	SCONJ
ma-115	326	51	the	the	DET
ma-115	326	52	operator	operator	NOUN
ma-115	326	53	associated	associate	VERB
ma-115	326	54	with	with	ADP
ma-115	326	55	evolution	evolution	NOUN
ma-115	326	56	equation	equation	NOUN
ma-115	326	57	driven	drive	VERB
ma-115	326	58	by	by	ADP
ma-115	326	59	ageneric	ageneric	ADJ
ma-115	326	60	operator	operator	NOUN
ma-115	326	61	belonging	belong	VERB
ma-115	326	62	to	to	ADP
ma-115	326	63	the	the	DET
ma-115	326	64	su(1	su(1	NOUN
ma-115	326	65	,	,	PUNCT
ma-115	326	66	1	1	X
ma-115	326	67	)	)	PUNCT
ma-115	326	68	algebra	algebra	NOUN
ma-115	326	69	namely	namely	ADV
ma-115	326	70	ĥ(1,2	ĥ(1,2	NOUN
ma-115	326	71	)	)	PUNCT
ma-115	327	1	=	=	SYM
ma-115	327	2	ak̂	ak̂	PROPN
ma-115	327	3	(	(	PUNCT
ma-115	327	4	1,2	1,2	NUM
ma-115	327	5	)	)	PUNCT
ma-115	327	6	+	+	PUNCT
ma-115	327	7	+	+	CCONJ
ma-115	327	8	bk̂	bk̂	PROPN
ma-115	327	9	(	(	PUNCT
ma-115	327	10	1,2	1,2	NUM
ma-115	327	11	)	)	PUNCT
ma-115	327	12	−	−	PROPN
ma-115	328	1	+	+	CCONJ
ma-115	328	2	ck̂	ck̂	PROPN
ma-115	328	3	(	(	PUNCT
ma-115	328	4	1,2	1,2	NUM
ma-115	328	5	)	)	PUNCT
ma-115	328	6	3	3	NUM
ma-115	328	7	+	+	CCONJ
ma-115	328	8	d(v	d(v	ADJ
ma-115	329	1	+	+	CCONJ
ma-115	329	2	1)1̂	1)1̂	NUM
ma-115	329	3	being	be	AUX
ma-115	329	4	its	its	PRON
ma-115	329	5	pertinent	pertinent	NOUN
ma-115	329	6	to	to	ADP
ma-115	329	7	the	the	DET
ma-115	329	8	algebra	algebra	NOUN
ma-115	329	9	realization	realization	NOUN
ma-115	329	10	(	(	PUNCT
ma-115	329	11	17	17	NUM
ma-115	329	12	)	)	PUNCT
ma-115	329	13	or	or	CCONJ
ma-115	329	14	(	(	PUNCT
ma-115	329	15	23).we	23).we	NOUN
ma-115	329	16	exploit	exploit	VERB
ma-115	329	17	the	the	DET
ma-115	329	18	disentanglement	disentanglement	NOUN
ma-115	329	19	scheme	scheme	NOUN
ma-115	329	20	e−iτ	e−iτ	PROPN
ma-115	330	1	[	[	X
ma-115	330	2	ak̂	ak̂	PROPN
ma-115	330	3	(	(	PUNCT
ma-115	330	4	1,2	1,2	NUM
ma-115	330	5	)	)	PUNCT
ma-115	330	6	+	+	CCONJ
ma-115	331	1	+	+	PUNCT
ma-115	331	2	bk̂	bk̂	PROPN
ma-115	331	3	(	(	PUNCT
ma-115	331	4	1,2	1,2	NUM
ma-115	331	5	)	)	PUNCT
ma-115	331	6	−	−	PROPN
ma-115	332	1	+	+	NOUN
ma-115	332	2	ck̂	ck̂	PROPN
ma-115	332	3	(	(	PUNCT
ma-115	332	4	1,2	1,2	NUM
ma-115	332	5	)	)	PUNCT
ma-115	332	6	3	3	NUM
ma-115	333	1	+	+	NOUN
ma-115	333	2	d(v+1)1̂	d(v+1)1̂	X
ma-115	333	3	]	]	X
ma-115	333	4	=	=	PUNCT
ma-115	333	5	e−idτ(α−β+1	e−idτ(α−β+1	ADJ
ma-115	333	6	)	)	PUNCT
ma-115	333	7	eak̂	eak̂	PROPN
ma-115	333	8	(	(	PUNCT
ma-115	333	9	1,2	1,2	NUM
ma-115	333	10	)	)	PUNCT
ma-115	333	11	+	+	CCONJ
ma-115	333	12	eck̂	eck̂	PROPN
ma-115	333	13	(	(	PUNCT
ma-115	333	14	1,2	1,2	NUM
ma-115	333	15	)	)	PUNCT
ma-115	333	16	3	3	NUM
ma-115	333	17	e−iφk̂	e−iφk̂	PROPN
ma-115	333	18	(	(	PUNCT
ma-115	333	19	1,2	1,2	NUM
ma-115	333	20	)	)	PUNCT
ma-115	333	21	1	1	NUM
ma-115	333	22	,	,	PUNCT
ma-115	333	23	giving	give	VERB
ma-115	333	24	the	the	DET
ma-115	333	25	operator	operator	NOUN
ma-115	333	26	e−iτĥ(1,2	e−iτĥ(1,2	NOUN
ma-115	333	27	)	)	PUNCT
ma-115	333	28	in	in	ADP
ma-115	333	29	three	three	NUM
ma-115	333	30	-	-	PUNCT
ma-115	333	31	term	term	NOUN
ma-115	333	32	factored	factored	ADJ
ma-115	333	33	form	form	NOUN
ma-115	333	34	,	,	PUNCT
ma-115	333	35	apart	apart	ADV
ma-115	333	36	from	from	ADP
ma-115	333	37	the	the	DET
ma-115	333	38	phase	phase	NOUN
ma-115	333	39	factor	factor	NOUN
ma-115	333	40	e−idτ(v+1).we	e−idτ(v+1).we	PRON
ma-115	333	41	may	may	AUX
ma-115	333	42	introduce	introduce	VERB
ma-115	333	43	the	the	DET
ma-115	333	44	generalized	generalized	ADJ
ma-115	333	45	hankel	hankel	NOUN
ma-115	333	46	-	-	PUNCT
ma-115	333	47	type	type	NOUN
ma-115	333	48	transforms	transform	NOUN
ma-115	333	49	of	of	ADP
ma-115	333	50	first	first	ADJ
ma-115	333	51	and	and	CCONJ
ma-115	333	52	second	second	ADJ
ma-115	333	53	type	type	NOUN
ma-115	333	54	,	,	PUNCT
ma-115	333	55	depending	depend	VERB
ma-115	333	56	onthe	onthe	NOUN
ma-115	333	57	parameter	parameter	NOUN
ma-115	333	58	p	p	X
ma-115	333	59	,	,	PUNCT
ma-115	333	60	m	m	PROPN
ma-115	333	61	and	and	CCONJ
ma-115	333	62	γ	γ	X
ma-115	333	63	,	,	PUNCT
ma-115	333	64	[	[	PUNCT
ma-115	333	65	ĥa	ĥa	NOUN
ma-115	333	66	,	,	PUNCT
ma-115	333	67	p	p	X
ma-115	333	68	,	,	PUNCT
ma-115	333	69	m	m	PROPN
ma-115	333	70	,	,	PUNCT
ma-115	333	71	γ	γ	PROPN
ma-115	333	72	1,α−β,−2(α+β)f	1,α−β,−2(α+β)f	NUM
ma-115	333	73	]	]	PUNCT
ma-115	333	74	(	(	PUNCT
ma-115	333	75	y	y	NOUN
ma-115	333	76	)	)	PUNCT
ma-115	333	77	=	=	SYM
ma-115	333	78	e	e	X
ma-115	333	79	i(α−β+1)(γ−π/2	i(α−β+1)(γ−π/2	PROPN
ma-115	333	80	)	)	PUNCT
ma-115	333	81	m	m	VERB
ma-115	333	82	sin(φ	sin(φ	ADV
ma-115	333	83	)	)	PUNCT
ma-115	333	84	e−ip(y	e−ip(y	VERB
ma-115	333	85	2/2	2/2	NUM
ma-115	333	86	)	)	PUNCT
ma-115	333	87	y1−4(α+β	y1−4(α+β	NOUN
ma-115	333	88	)	)	PUNCT
ma-115	333	89	∫	∫	PROPN
ma-115	334	1	∞	∞	PROPN
ma-115	334	2	0	0	NUM
ma-115	334	3	(	(	PUNCT
ma-115	334	4	xy)2(α+β	xy)2(α+β	NUM
ma-115	334	5	)	)	PUNCT
ma-115	334	6	×	×	PROPN
ma-115	334	7	e(i/2	e(i/2	PROPN
ma-115	334	8	)	)	PUNCT
ma-115	334	9	cot(φ)(x2+(y2	cot(φ)(x2+(y2	PROPN
ma-115	334	10	/	/	SYM
ma-115	334	11	m2	m2	PROPN
ma-115	334	12	)	)	PUNCT
ma-115	334	13	)	)	PUNCT
ma-115	335	1	jα−β	jα−β	PROPN
ma-115	335	2	(	(	PUNCT
ma-115	335	3	xy	xy	NOUN
ma-115	335	4	m	m	VERB
ma-115	335	5	sin	sin	NOUN
ma-115	335	6	(	(	PUNCT
ma-115	335	7	φ/2	φ/2	NUM
ma-115	335	8	)	)	PUNCT
ma-115	335	9	)	)	PUNCT
ma-115	336	1	f	f	PROPN
ma-115	336	2	(	(	PUNCT
ma-115	336	3	x)dx	x)dx	PROPN
ma-115	336	4	(	(	PUNCT
ma-115	336	5	71	71	NUM
ma-115	336	6	)	)	PUNCT
ma-115	336	7	[	[	PUNCT
ma-115	336	8	ĥa	ĥa	NOUN
ma-115	336	9	,	,	PUNCT
ma-115	336	10	p	p	X
ma-115	336	11	,	,	PUNCT
ma-115	336	12	m	m	PROPN
ma-115	336	13	,	,	PUNCT
ma-115	336	14	γ	γ	X
ma-115	336	15	2,α−β,−2(α+β)f	2,α−β,−2(α+β)f	NUM
ma-115	336	16	]	]	PUNCT
ma-115	336	17	(	(	PUNCT
ma-115	336	18	y	y	NOUN
ma-115	336	19	)	)	PUNCT
ma-115	336	20	=	=	SYM
ma-115	336	21	e	e	X
ma-115	336	22	i(α−β+1)(γ−π/2	i(α−β+1)(γ−π/2	PROPN
ma-115	336	23	)	)	PUNCT
ma-115	336	24	m	m	VERB
ma-115	336	25	sin(φ	sin(φ	ADV
ma-115	336	26	)	)	PUNCT
ma-115	336	27	e−ip(y	e−ip(y	VERB
ma-115	336	28	2/2	2/2	NUM
ma-115	336	29	)	)	PUNCT
ma-115	336	30	∫	∫	PROPN
ma-115	336	31	∞	∞	PROPN
ma-115	336	32	0	0	NUM
ma-115	336	33	x1−4(α+β	x1−4(α+β	PROPN
ma-115	336	34	)	)	PUNCT
ma-115	336	35	(	(	PUNCT
ma-115	336	36	xy)2(α+β	xy)2(α+β	NUM
ma-115	336	37	)	)	PUNCT
ma-115	336	38	×	×	PROPN
ma-115	336	39	e(i/2	e(i/2	PROPN
ma-115	336	40	)	)	PUNCT
ma-115	336	41	cot(φ)(x2+(y2	cot(φ)(x2+(y2	PROPN
ma-115	336	42	/	/	SYM
ma-115	336	43	m2	m2	PROPN
ma-115	336	44	)	)	PUNCT
ma-115	336	45	)	)	PUNCT
ma-115	337	1	jα−β	jα−β	PROPN
ma-115	337	2	(	(	PUNCT
ma-115	337	3	xy	xy	NOUN
ma-115	337	4	m	m	VERB
ma-115	337	5	sin	sin	NOUN
ma-115	337	6	(	(	PUNCT
ma-115	337	7	φ/2	φ/2	NUM
ma-115	337	8	)	)	PUNCT
ma-115	337	9	)	)	PUNCT
ma-115	338	1	f	f	PROPN
ma-115	338	2	(	(	PUNCT
ma-115	338	3	x)dx	x)dx	PROPN
ma-115	338	4	.	.	PUNCT
ma-115	339	1	the	the	DET
ma-115	339	2	above	above	ADJ
ma-115	339	3	relations	relation	NOUN
ma-115	339	4	reproduce	reproduce	NOUN
ma-115	339	5	(	(	PUNCT
ma-115	339	6	21	21	NUM
ma-115	339	7	)	)	PUNCT
ma-115	339	8	and	and	CCONJ
ma-115	339	9	(	(	PUNCT
ma-115	339	10	24	24	NUM
ma-115	339	11	)	)	PUNCT
ma-115	339	12	respectively	respectively	ADV
ma-115	339	13	,	,	PUNCT
ma-115	339	14	for	for	ADP
ma-115	339	15	b	b	NOUN
ma-115	339	16	=	=	SYM
ma-115	339	17	a	a	PROPN
ma-115	339	18	,	,	PUNCT
ma-115	339	19	d	d	X
ma-115	339	20	=	=	SYM
ma-115	339	21	−a	−a	NOUN
ma-115	339	22	,	,	PUNCT
ma-115	339	23	c	c	NOUN
ma-115	339	24	=	=	SYM
ma-115	339	25	0	0	PROPN
ma-115	339	26	and	and	CCONJ
ma-115	339	27	aτ	aτ	ADV
ma-115	339	28	=	=	PUNCT
ma-115	339	29	φ;also	φ;also	PROPN
ma-115	339	30	relations	relation	NOUN
ma-115	339	31	like	like	ADP
ma-115	339	32	(	(	PUNCT
ma-115	339	33	9	9	NUM
ma-115	339	34	)	)	PUNCT
ma-115	339	35	can	can	AUX
ma-115	339	36	be	be	AUX
ma-115	339	37	deduced	deduce	VERB
ma-115	339	38	for	for	ADP
ma-115	339	39	the	the	DET
ma-115	339	40	generalized	generalize	VERB
ma-115	339	41	transform.in	transform.in	NUM
ma-115	339	42	addition	addition	NOUN
ma-115	339	43	,	,	PUNCT
ma-115	339	44	generalized	generalized	ADJ
ma-115	339	45	borut	borut	PROPN
ma-115	339	46	-	-	PUNCT
ma-115	339	47	girardello	girardello	PROPN
ma-115	339	48	type	type	NOUN
ma-115	339	49	transforms	transform	VERB
ma-115	339	50	can	can	AUX
ma-115	339	51	be	be	AUX
ma-115	339	52	introduced	introduce	VERB
ma-115	339	53	on	on	ADP
ma-115	339	54	the	the	DET
ma-115	339	55	basis	basis	NOUN
ma-115	339	56	of	of	ADP
ma-115	339	57	a	a	DET
ma-115	339	58	https://doi.org/10.28924/ada/ma.3.6	https://doi.org/10.28924/ada/ma.3.6	PROPN
ma-115	339	59	eur	eur	NOUN
ma-115	339	60	.	.	PUNCT
ma-115	340	1	j.	j.	PROPN
ma-115	340	2	math	math	PROPN
ma-115	340	3	.	.	PUNCT
ma-115	341	1	anal	anal	PROPN
ma-115	341	2	.	.	PUNCT
ma-115	342	1	10.28924	10.28924	NUM
ma-115	342	2	/	/	SYM
ma-115	342	3	ada	ada	PROPN
ma-115	342	4	/	/	SYM
ma-115	342	5	ma.3.6	ma.3.6	PROPN
ma-115	342	6	15	15	NUM
ma-115	342	7	disentanglement	disentanglement	NOUN
ma-115	342	8	scheme	scheme	NOUN
ma-115	342	9	involving	involve	VERB
ma-115	342	10	the	the	DET
ma-115	342	11	operators	operator	NOUN
ma-115	342	12	k̂(1,2)2	k̂(1,2)2	VERB
ma-115	342	13	instead	instead	ADV
ma-115	342	14	of	of	ADP
ma-115	342	15	k̂(1,2)1	k̂(1,2)1	PROPN
ma-115	343	1	.as	.as	PUNCT
ma-115	344	1	a	a	DET
ma-115	344	2	conclusion	conclusion	NOUN
ma-115	344	3	,	,	PUNCT
ma-115	344	4	we	we	PRON
ma-115	344	5	note	note	VERB
ma-115	344	6	that	that	SCONJ
ma-115	344	7	from	from	ADP
ma-115	344	8	equation	equation	NOUN
ma-115	344	9	(	(	PUNCT
ma-115	344	10	71	71	NUM
ma-115	344	11	)	)	PUNCT
ma-115	344	12	we	we	PRON
ma-115	344	13	may	may	AUX
ma-115	344	14	recover	recover	VERB
ma-115	344	15	with	with	ADP
ma-115	344	16	p	p	NOUN
ma-115	344	17	=	=	PUNCT
ma-115	344	18	ib	ib	PROPN
ma-115	344	19	/	/	SYM
ma-115	344	20	m2	m2	PROPN
ma-115	344	21	,	,	PUNCT
ma-115	344	22	m2	m2	PROPN
ma-115	344	23	=	=	PROPN
ma-115	344	24	1	1	NUM
ma-115	345	1	−	−	PROPN
ma-115	345	2	b2	b2	NOUN
ma-115	345	3	,	,	PUNCT
ma-115	345	4	tan(φ	tan(φ	PROPN
ma-115	345	5	)	)	PUNCT
ma-115	345	6	=	=	SYM
ma-115	345	7	−ib	−ib	PROPN
ma-115	345	8	and	and	CCONJ
ma-115	345	9	γ	γ	X
ma-115	345	10	=	=	SYM
ma-115	345	11	0	0	PROPN
ma-115	345	12	,	,	PUNCT
ma-115	345	13	the	the	DET
ma-115	345	14	integral	integral	ADJ
ma-115	345	15	transformations	transformation	NOUN
ma-115	345	16	corresponding	correspond	VERB
ma-115	345	17	to	to	ADP
ma-115	345	18	the	the	DET
ma-115	345	19	exponential	exponential	ADJ
ma-115	345	20	forms	form	NOUN
ma-115	345	21	e	e	NOUN
ma-115	345	22	bb̂∗	bb̂∗	NOUN
ma-115	345	23	α−β,−2(α+β	α−β,−2(α+β	NOUN
ma-115	345	24	)	)	PUNCT
ma-115	345	25	and	and	CCONJ
ma-115	345	26	ebb̂α−β,−2(α+β	ebb̂α−β,−2(α+β	NOUN
ma-115	345	27	)	)	PUNCT
ma-115	345	28	(	(	PUNCT
ma-115	345	29	see	see	VERB
ma-115	345	30	(	(	PUNCT
ma-115	345	31	15	15	NUM
ma-115	345	32	)	)	PUNCT
ma-115	345	33	and	and	CCONJ
ma-115	345	34	the	the	DET
ma-115	345	35	relevant	relevant	ADJ
ma-115	345	36	adjoint	adjoint	NOUN
ma-115	345	37	expression	expression	NOUN
ma-115	345	38	,	,	PUNCT
ma-115	345	39	easily	easily	ADV
ma-115	345	40	deducible)which	deducible)which	PRON
ma-115	345	41	can	can	AUX
ma-115	345	42	respectively	respectively	ADV
ma-115	345	43	be	be	AUX
ma-115	345	44	regarded	regard	VERB
ma-115	345	45	as	as	ADP
ma-115	345	46	the	the	DET
ma-115	345	47	first	first	ADJ
ma-115	345	48	and	and	CCONJ
ma-115	345	49	second	second	ADJ
ma-115	345	50	weiestrass	weiestrass	NOUN
ma-115	345	51	-	-	PUNCT
ma-115	345	52	gauss	gauss	ADJ
ma-115	345	53	integral	integral	ADJ
ma-115	345	54	transformsof	transformsof	NOUN
ma-115	345	55	bessel	bessel	ADJ
ma-115	345	56	order	order	NOUN
ma-115	345	57	α−β	α−β	X
ma-115	345	58	depending	depend	VERB
ma-115	345	59	on	on	ADP
ma-115	345	60	the	the	DET
ma-115	345	61	real	real	ADJ
ma-115	345	62	parameter	parameter	NOUN
ma-115	345	63	−2(α+β	−2(α+β	ADP
ma-115	345	64	)	)	PUNCT
ma-115	345	65	.	.	PUNCT
ma-115	346	1	they	they	PRON
ma-115	346	2	generalize	generalize	VERB
ma-115	346	3	to	to	ADP
ma-115	346	4	α+β	α+β	PROPN
ma-115	346	5	=	=	SYM
ma-115	347	1	1/4the	1/4the	DET
ma-115	347	2	expression	expression	NOUN
ma-115	347	3	of	of	ADP
ma-115	347	4	the	the	DET
ma-115	347	5	radical	radical	ADJ
ma-115	347	6	weiestrass	weiestrass	NOUN
ma-115	347	7	-	-	PUNCT
ma-115	347	8	gauss	gauss	ADJ
ma-115	347	9	integral	integral	ADJ
ma-115	347	10	transform	transform	NOUN
ma-115	347	11	,	,	PUNCT
ma-115	347	12	for	for	ADP
ma-115	347	13	which	which	PRON
ma-115	347	14	we	we	PRON
ma-115	347	15	have	have	VERB
ma-115	347	16	[	[	X
ma-115	347	17	16	16	NUM
ma-115	347	18	]	]	X
ma-115	347	19	[	[	PUNCT
ma-115	347	20	ŵα−β	ŵα−β	X
ma-115	347	21	,	,	PUNCT
ma-115	347	22	bf	bf	NOUN
ma-115	347	23	]	]	PUNCT
ma-115	347	24	(	(	PUNCT
ma-115	347	25	y	y	NOUN
ma-115	347	26	)	)	PUNCT
ma-115	347	27	=	=	PUNCT
ma-115	348	1	[	[	PUNCT
ma-115	348	2	e−(b/2)b̂α−β	e−(b/2)b̂α−β	NOUN
ma-115	348	3	f	f	X
ma-115	348	4	]	]	X
ma-115	348	5	(	(	PUNCT
ma-115	348	6	y	y	NOUN
ma-115	348	7	)	)	PUNCT
ma-115	348	8	=	=	SYM
ma-115	348	9	1	1	NUM
ma-115	348	10	b	b	X
ma-115	348	11	∫	∫	PROPN
ma-115	348	12	∞	∞	NOUN
ma-115	348	13	0	0	NUM
ma-115	348	14	(	(	PUNCT
ma-115	348	15	xy)(1/2	xy)(1/2	PROPN
ma-115	348	16	)	)	PUNCT
ma-115	348	17	e−(1/2b)(x	e−(1/2b)(x	PROPN
ma-115	348	18	2+y2	2+y2	NOUN
ma-115	348	19	)	)	PUNCT
ma-115	348	20	iα−β	iα−β	NOUN
ma-115	348	21	(	(	PUNCT
ma-115	348	22	xy	xy	PROPN
ma-115	348	23	b	b	PROPN
ma-115	348	24	)	)	PUNCT
ma-115	348	25	f	f	PROPN
ma-115	349	1	(	(	PUNCT
ma-115	349	2	x)dx	x)dx	PROPN
ma-115	349	3	for	for	ADP
ma-115	349	4	any	any	DET
ma-115	349	5	real	real	ADJ
ma-115	349	6	parameter	parameter	NOUN
ma-115	349	7	β	β	X
ma-115	349	8	>	>	X
ma-115	349	9	0	0	NUM
ma-115	349	10	.	.	PUNCT
ma-115	349	11	ŵα−β	ŵα−β	PROPN
ma-115	349	12	,	,	PUNCT
ma-115	349	13	b	b	PROPN
ma-115	349	14	arises	arise	VERB
ma-115	349	15	as	as	SCONJ
ma-115	349	16	the	the	DET
ma-115	349	17	transfer	transfer	NOUN
ma-115	349	18	operator	operator	NOUN
ma-115	349	19	associated	associate	VERB
ma-115	349	20	with	with	ADP
ma-115	349	21	the	the	DET
ma-115	349	22	radial	radial	ADJ
ma-115	349	23	part	part	NOUN
ma-115	349	24	of	of	ADP
ma-115	349	25	heat	heat	NOUN
ma-115	349	26	conduction	conduction	NOUN
ma-115	349	27	likeequations.it	likeequations.it	NOUN
ma-115	349	28	can	can	AUX
ma-115	349	29	be	be	AUX
ma-115	349	30	in	in	ADP
ma-115	349	31	fact	fact	NOUN
ma-115	349	32	considered	consider	VERB
ma-115	349	33	as	as	ADP
ma-115	349	34	the	the	DET
ma-115	349	35	radial	radial	ADJ
ma-115	349	36	part	part	NOUN
ma-115	349	37	of	of	ADP
ma-115	349	38	2d	2d	NUM
ma-115	349	39	fresnel	fresnel	NOUN
ma-115	349	40	transform	transform	NOUN
ma-115	349	41	for	for	ADP
ma-115	349	42	real	real	ADJ
ma-115	349	43	parametersis	parametersis	NOUN
ma-115	349	44	the	the	DET
ma-115	349	45	optical	optical	ADJ
ma-115	349	46	operator	operator	NOUN
ma-115	349	47	for	for	ADP
ma-115	349	48	free	free	ADJ
ma-115	349	49	propagation	propagation	NOUN
ma-115	349	50	.	.	PUNCT
ma-115	350	1	a	a	DET
ma-115	350	2	linear	linear	ADJ
ma-115	350	3	weiestrass	weiestrass	NOUN
ma-115	350	4	-	-	PUNCT
ma-115	350	5	gauss	gauss	ADJ
ma-115	350	6	integral	integral	ADJ
ma-115	350	7	transform	transform	NOUN
ma-115	350	8	has	have	AUX
ma-115	350	9	alsobeen	alsobeen	VERB
ma-115	350	10	introduced	introduce	VERB
ma-115	350	11	[	[	X
ma-115	350	12	19	19	NUM
ma-115	350	13	]	]	PUNCT
ma-115	350	14	the	the	DET
ma-115	350	15	relation	relation	NOUN
ma-115	350	16	of	of	ADP
ma-115	350	17	ŵm	ŵm	PROPN
ma-115	350	18	,	,	PUNCT
ma-115	350	19	b	b	NOUN
ma-115	350	20	,	,	PUNCT
ma-115	350	21	m	m	VERB
ma-115	350	22	=	=	NOUN
ma-115	350	23	0	0	NUM
ma-115	350	24	,	,	PUNCT
ma-115	350	25	1	1	NUM
ma-115	350	26	,	,	PUNCT
ma-115	350	27	2	2	NUM
ma-115	350	28	,	,	PUNCT
ma-115	350	29	...	...	PUNCT
ma-115	350	30	to	to	ADP
ma-115	350	31	it	it	PRON
ma-115	350	32	is	be	AUX
ma-115	350	33	evidently	evidently	ADV
ma-115	350	34	similar	similar	ADJ
ma-115	350	35	to	to	ADP
ma-115	350	36	(	(	PUNCT
ma-115	350	37	69	69	NUM
ma-115	350	38	)	)	PUNCT
ma-115	350	39	,	,	PUNCT
ma-115	350	40	whenrationally	whenrationally	ADV
ma-115	350	41	symmetric	symmetric	ADJ
ma-115	350	42	function	function	NOUN
ma-115	350	43	are	be	AUX
ma-115	350	44	involved	involve	VERB
ma-115	350	45	.	.	PUNCT
ma-115	351	1	remark	remark	NOUN
ma-115	351	2	.	.	PUNCT
ma-115	352	1	[	[	X
ma-115	352	2	(	(	PUNCT
ma-115	352	3	i)](1	i)](1	PROPN
ma-115	352	4	)	)	PUNCT
ma-115	352	5	if	if	SCONJ
ma-115	352	6	we	we	PRON
ma-115	352	7	take	take	VERB
ma-115	352	8	α	α	NOUN
ma-115	352	9	=	=	PUNCT
ma-115	352	10	ν	ν	NOUN
ma-115	352	11	2	2	NUM
ma-115	352	12	−	−	PROPN
ma-115	352	13	µ	µ	X
ma-115	352	14	4	4	NUM
ma-115	352	15	,	,	PUNCT
ma-115	352	16	β	β	NOUN
ma-115	352	17	=	=	SYM
ma-115	352	18	−µ4	−µ4	ADJ
ma-115	353	1	−	−	PROPN
ma-115	353	2	ν	ν	NOUN
ma-115	353	3	2	2	NUM
ma-115	353	4	throught	throught	NOUN
ma-115	353	5	this	this	DET
ma-115	353	6	paper	paper	NOUN
ma-115	353	7	then	then	ADV
ma-115	353	8	all	all	DET
ma-115	353	9	the	the	DET
ma-115	353	10	results	result	NOUN
ma-115	353	11	studied	study	VERB
ma-115	353	12	in	in	ADP
ma-115	353	13	this	this	DET
ma-115	353	14	paper	paper	NOUN
ma-115	353	15	reduce	reduce	VERB
ma-115	353	16	to	to	ADP
ma-115	353	17	the	the	DET
ma-115	353	18	results	result	NOUN
ma-115	353	19	studied	study	VERB
ma-115	353	20	in	in	ADP
ma-115	353	21	torre	torre	PROPN
ma-115	353	22	[	[	X
ma-115	353	23	17].(2	17].(2	NUM
ma-115	353	24	)	)	PUNCT
ma-115	353	25	authors	author	NOUN
ma-115	353	26	claim	claim	VERB
ma-115	353	27	that	that	SCONJ
ma-115	353	28	results	result	NOUN
ma-115	353	29	of	of	ADP
ma-115	353	30	this	this	DET
ma-115	353	31	paper	paper	NOUN
ma-115	353	32	are	be	AUX
ma-115	353	33	stronger	strong	ADJ
ma-115	353	34	than	than	ADP
ma-115	353	35	that	that	PRON
ma-115	353	36	of	of	ADP
ma-115	353	37	torre	torre	PROPN
ma-115	354	1	[	[	X
ma-115	354	2	17	17	NUM
ma-115	354	3	]	]	SYM
ma-115	354	4	.	.	PUNCT
ma-115	355	1	8	8	X
ma-115	355	2	.	.	PUNCT
ma-115	355	3	conclusions	conclusion	NOUN
ma-115	355	4	:	:	PUNCT
ma-115	355	5	following	follow	VERB
ma-115	355	6	the	the	DET
ma-115	355	7	scheme	scheme	NOUN
ma-115	355	8	already	already	ADV
ma-115	355	9	applied	apply	VERB
ma-115	355	10	to	to	ADP
ma-115	355	11	other	other	ADJ
ma-115	355	12	type	type	NOUN
ma-115	355	13	of	of	ADP
ma-115	355	14	transforms	transform	NOUN
ma-115	355	15	,	,	PUNCT
ma-115	355	16	like	like	ADP
ma-115	355	17	for	for	ADP
ma-115	355	18	instance	instance	NOUN
ma-115	355	19	,	,	PUNCT
ma-115	355	20	the	the	DET
ma-115	355	21	fouriertransform	fouriertransform	NOUN
ma-115	355	22	,	,	PUNCT
ma-115	355	23	we	we	PRON
ma-115	355	24	have	have	AUX
ma-115	355	25	introduced	introduce	VERB
ma-115	355	26	the	the	DET
ma-115	355	27	fractional	fractional	ADJ
ma-115	355	28	forms	form	NOUN
ma-115	355	29	of	of	ADP
ma-115	355	30	two	two	NUM
ma-115	355	31	adjoint	adjoint	NOUN
ma-115	355	32	self	self	NOUN
ma-115	355	33	-	-	PUNCT
ma-115	355	34	reciprocal	reciprocal	ADJ
ma-115	355	35	variants	variant	NOUN
ma-115	355	36	of	of	ADP
ma-115	355	37	thehankel	thehankel	NOUN
ma-115	355	38	type	type	NOUN
ma-115	355	39	transform	transform	NOUN
ma-115	355	40	,	,	PUNCT
ma-115	355	41	which	which	PRON
ma-115	355	42	,	,	PUNCT
ma-115	355	43	as	as	SCONJ
ma-115	355	44	noted	note	VERB
ma-115	355	45	are	be	AUX
ma-115	355	46	of	of	ADP
ma-115	355	47	interest	interest	NOUN
ma-115	355	48	in	in	ADP
ma-115	355	49	connection	connection	NOUN
ma-115	355	50	with	with	ADP
ma-115	355	51	evolution	evolution	NOUN
ma-115	355	52	problems	problem	NOUN
ma-115	355	53	ruledby	ruledby	VERB
ma-115	355	54	the	the	DET
ma-115	355	55	bessel	bessel	NOUN
ma-115	355	56	-	-	PUNCT
ma-115	355	57	type	type	NOUN
ma-115	355	58	differential	differential	ADJ
ma-115	355	59	operators	operator	NOUN
ma-115	355	60	,	,	PUNCT
ma-115	355	61	b̂α−β,−2(α+β	b̂α−β,−2(α+β	NOUN
ma-115	355	62	)	)	PUNCT
ma-115	355	63	=	=	PUNCT
ma-115	356	1	xα+3β−1dxx	xα+3β−1dxx	PROPN
ma-115	356	2	2(α−β)+1	2(α−β)+1	NUM
ma-115	356	3	dxx	dxx	NOUN
ma-115	356	4	−3α−β	−3α−β	PROPN
ma-115	356	5	and	and	CCONJ
ma-115	356	6	b̂α−β,−2(α+β	b̂α−β,−2(α+β	ADJ
ma-115	356	7	)	)	PUNCT
ma-115	356	8	=	=	PUNCT
ma-115	357	1	x−3α−βdxx	x−3α−βdxx	ADP
ma-115	357	2	2(α−β)+1dxx	2(α−β)+1dxx	NUM
ma-115	357	3	α+3β−1	α+3β−1	NOUN
ma-115	357	4	.	.	PUNCT
ma-115	358	1	the	the	DET
ma-115	358	2	fractional	fractional	ADJ
ma-115	358	3	order	order	NOUN
ma-115	358	4	transform	transform	NOUN
ma-115	358	5	relate	relate	VERB
ma-115	358	6	to	to	ADP
ma-115	358	7	evolution	evolution	NOUN
ma-115	358	8	problems	problem	NOUN
ma-115	358	9	ruled	rule	VERB
ma-115	358	10	the	the	DET
ma-115	358	11	operators	operator	NOUN
ma-115	358	12	b̂α−β,−2(α+β),a	b̂α−β,−2(α+β),a	VERB
ma-115	358	13	=	=	PUNCT
ma-115	358	14	xα+3β−1	xα+3β−1	PUNCT
ma-115	358	15	la	la	PROPN
ma-115	358	16	(	(	PUNCT
ma-115	358	17	x	x	NOUN
ma-115	358	18	,	,	PUNCT
ma-115	358	19	(	(	PUNCT
ma-115	358	20	∂	∂	X
ma-115	358	21	∂x	∂x	PROPN
ma-115	358	22	)	)	PUNCT
ma-115	358	23	)	)	PUNCT
ma-115	358	24	x2(α−β)+1	x2(α−β)+1	X
ma-115	359	1	la	la	PROPN
ma-115	359	2	(	(	PUNCT
ma-115	359	3	x	x	X
ma-115	359	4	,	,	PUNCT
ma-115	359	5	(	(	PUNCT
ma-115	359	6	∂	∂	X
ma-115	359	7	∂x	∂x	PROPN
ma-115	359	8	)	)	PUNCT
ma-115	359	9	)	)	PUNCT
ma-115	360	1	x−3α−β	x−3α−β	PROPN
ma-115	360	2	and	and	CCONJ
ma-115	360	3	b̂∗α−β,−2(α+β),a	b̂∗α−β,−2(α+β),a	PROPN
ma-115	360	4	=	=	PUNCT
ma-115	361	1	x−3α−β	x−3α−β	PROPN
ma-115	361	2	la	la	PROPN
ma-115	361	3	(	(	PUNCT
ma-115	361	4	x	x	X
ma-115	361	5	,	,	PUNCT
ma-115	361	6	(	(	PUNCT
ma-115	361	7	∂	∂	X
ma-115	361	8	∂x	∂x	PROPN
ma-115	361	9	)	)	PUNCT
ma-115	361	10	)	)	PUNCT
ma-115	361	11	x2(α−β)+1	x2(α−β)+1	X
ma-115	362	1	la	la	PROPN
ma-115	362	2	(	(	PUNCT
ma-115	362	3	x	x	X
ma-115	362	4	,	,	PUNCT
ma-115	362	5	(	(	PUNCT
ma-115	362	6	∂	∂	X
ma-115	362	7	∂x	∂x	PROPN
ma-115	362	8	)	)	PUNCT
ma-115	362	9	)	)	PUNCT
ma-115	362	10	xα+3β−1	xα+3β−1	PUNCT
ma-115	363	1	https://doi.org/10.28924/ada/ma.3.6	https://doi.org/10.28924/ada/ma.3.6	PROPN
ma-115	363	2	eur	eur	PROPN
ma-115	363	3	.	.	PUNCT
ma-115	364	1	j.	j.	PROPN
ma-115	364	2	math	math	PROPN
ma-115	364	3	.	.	PUNCT
ma-115	365	1	anal	anal	PROPN
ma-115	365	2	.	.	PUNCT
ma-115	366	1	10.28924	10.28924	NUM
ma-115	366	2	/	/	SYM
ma-115	366	3	ada	ada	PROPN
ma-115	366	4	/	/	SYM
ma-115	366	5	ma.3.6	ma.3.6	PROPN
ma-115	366	6	16where	16where	NUM
ma-115	367	1	la	la	PROPN
ma-115	367	2	(	(	PUNCT
ma-115	367	3	x	x	X
ma-115	367	4	,	,	PUNCT
ma-115	367	5	(	(	PUNCT
ma-115	367	6	∂∂x	∂∂x	PROPN
ma-115	367	7	)	)	PUNCT
ma-115	367	8	)	)	PUNCT
ma-115	367	9	is	be	AUX
ma-115	367	10	linear	linear	ADJ
ma-115	367	11	a	a	PRON
ma-115	367	12	-	-	PUNCT
ma-115	367	13	depending	depend	VERB
ma-115	367	14	combination	combination	NOUN
ma-115	367	15	of	of	ADP
ma-115	367	16	x	x	PUNCT
ma-115	367	17	and	and	CCONJ
ma-115	367	18	(	(	PUNCT
ma-115	367	19	∂∂x	∂∂x	PROPN
ma-115	367	20	)	)	PUNCT
ma-115	367	21	.	.	PUNCT
ma-115	368	1	since	since	SCONJ
ma-115	368	2	a	a	DET
ma-115	368	3	ranges	range	NOUN
ma-115	368	4	from	from	ADP
ma-115	368	5	-1	-1	PUNCT
ma-115	368	6	to	to	ADP
ma-115	368	7	1,it	1,it	NUM
ma-115	368	8	is	be	AUX
ma-115	368	9	evident	evident	ADJ
ma-115	368	10	that	that	SCONJ
ma-115	368	11	the	the	DET
ma-115	368	12	set	set	NOUN
ma-115	368	13	of	of	ADP
ma-115	368	14	evolution	evolution	NOUN
ma-115	368	15	problems	problem	NOUN
ma-115	368	16	inherent	inherent	ADJ
ma-115	368	17	in	in	ADP
ma-115	368	18	the	the	DET
ma-115	368	19	transforms	transform	NOUN
ma-115	368	20	has	have	AUX
ma-115	368	21	been	be	AUX
ma-115	368	22	greatly	greatly	ADV
ma-115	368	23	enlargeby	enlargeby	ADV
ma-115	368	24	the	the	DET
ma-115	368	25	fractionalization.in	fractionalization.in	PROPN
ma-115	368	26	general	general	NOUN
ma-115	368	27	we	we	PRON
ma-115	368	28	have	have	AUX
ma-115	368	29	shown	show	VERB
ma-115	368	30	that	that	SCONJ
ma-115	368	31	introduced	introduce	VERB
ma-115	368	32	transforms	transform	NOUN
ma-115	368	33	can	can	AUX
ma-115	368	34	be	be	AUX
ma-115	368	35	regarded	regard	VERB
ma-115	368	36	as	as	ADP
ma-115	368	37	the	the	DET
ma-115	368	38	evolution	evolution	NOUN
ma-115	368	39	operatorsassociated	operatorsassociate	VERB
ma-115	368	40	with	with	ADP
ma-115	368	41	evolution	evolution	NOUN
ma-115	368	42	problems	problem	NOUN
ma-115	368	43	having	have	VERB
ma-115	368	44	an	an	DET
ma-115	368	45	underlying	underlying	ADJ
ma-115	368	46	su(1	su(1	NOUN
ma-115	368	47	,	,	PUNCT
ma-115	368	48	1	1	NUM
ma-115	368	49	)	)	PUNCT
ma-115	368	50	symmetry	symmetry	NOUN
ma-115	368	51	,	,	PUNCT
ma-115	368	52	the	the	DET
ma-115	368	53	specific	specific	ADJ
ma-115	368	54	realizationof	realizationof	NOUN
ma-115	368	55	the	the	DET
ma-115	368	56	algebra	algebra	NOUN
ma-115	368	57	resorting	resort	VERB
ma-115	368	58	to	to	PART
ma-115	368	59	b̂α−β,−2(α+β	b̂α−β,−2(α+β	VERB
ma-115	368	60	)	)	PUNCT
ma-115	368	61	and	and	CCONJ
ma-115	368	62	b̂∗α−β,−2(α+β	b̂∗α−β,−2(α+β	NOUN
ma-115	368	63	)	)	PUNCT
ma-115	368	64	as	as	ADP
ma-115	368	65	the	the	DET
ma-115	368	66	relative	relative	ADJ
ma-115	368	67	ladder	ladder	NOUN
ma-115	368	68	operators.evidently	operators.evidently	ADV
ma-115	368	69	,	,	PUNCT
ma-115	368	70	transforms	transform	VERB
ma-115	368	71	of	of	ADP
ma-115	368	72	complex	complex	ADJ
ma-115	368	73	fractional	fractional	ADJ
ma-115	368	74	order	order	NOUN
ma-115	368	75	can	can	AUX
ma-115	368	76	be	be	AUX
ma-115	368	77	considered	consider	VERB
ma-115	368	78	although	although	SCONJ
ma-115	368	79	of	of	ADP
ma-115	368	80	course	course	NOUN
ma-115	368	81	the	the	DET
ma-115	368	82	space	space	NOUN
ma-115	368	83	offunctions	offunction	NOUN
ma-115	368	84	on	on	ADP
ma-115	368	85	which	which	PRON
ma-115	368	86	they	they	PRON
ma-115	368	87	can	can	AUX
ma-115	368	88	meaningfully	meaningfully	ADV
ma-115	368	89	be	be	AUX
ma-115	368	90	applied	apply	VERB
ma-115	368	91	must	must	AUX
ma-115	368	92	be	be	AUX
ma-115	368	93	carefully	carefully	ADV
ma-115	368	94	investigated	investigate	VERB
ma-115	368	95	.	.	PUNCT
ma-115	369	1	disregardinghere	disregardinghere	VERB
ma-115	369	2	this	this	DET
ma-115	369	3	aspect	aspect	NOUN
ma-115	369	4	of	of	ADP
ma-115	369	5	the	the	DET
ma-115	369	6	question	question	NOUN
ma-115	369	7	,	,	PUNCT
ma-115	369	8	we	we	PRON
ma-115	369	9	simply	simply	ADV
ma-115	369	10	note	note	VERB
ma-115	369	11	that	that	SCONJ
ma-115	369	12	due	due	ADP
ma-115	369	13	to	to	ADP
ma-115	369	14	the	the	DET
ma-115	369	15	additivity	additivity	NOUN
ma-115	369	16	with	with	ADP
ma-115	369	17	respect	respect	NOUN
ma-115	369	18	to	to	ADP
ma-115	369	19	the	the	DET
ma-115	369	20	order	order	NOUN
ma-115	369	21	,	,	PUNCT
ma-115	369	22	we	we	PRON
ma-115	369	23	may	may	AUX
ma-115	369	24	write	write	VERB
ma-115	369	25	ĥar+ial	ĥar+ial	PROPN
ma-115	369	26	j	j	PROPN
ma-115	369	27	,	,	PUNCT
ma-115	369	28	α−β,−2(α+β	α−β,−2(α+β	NOUN
ma-115	369	29	)	)	PUNCT
ma-115	369	30	=	=	SYM
ma-115	370	1	ĥar	ĥar	X
ma-115	370	2	j	j	NOUN
ma-115	370	3	,	,	PUNCT
ma-115	370	4	α−β,−2(α+β	α−β,−2(α+β	NOUN
ma-115	370	5	)	)	PUNCT
ma-115	371	1	+	+	CCONJ
ma-115	371	2	ĥial	ĥial	PROPN
ma-115	371	3	j	j	NOUN
ma-115	371	4	,	,	PUNCT
ma-115	371	5	α−β,−2(α+β	α−β,−2(α+β	NOUN
ma-115	371	6	)	)	PUNCT
ma-115	371	7	,	,	PUNCT
ma-115	371	8	j	j	PROPN
ma-115	371	9	=	=	SYM
ma-115	371	10	1	1	NUM
ma-115	371	11	,	,	PUNCT
ma-115	371	12	2	2	NUM
ma-115	371	13	.	.	X
ma-115	371	14	where	where	SCONJ
ma-115	371	15	ar	ar	PROPN
ma-115	371	16	and	and	CCONJ
ma-115	371	17	al	al	PROPN
ma-115	371	18	respectively	respectively	ADV
ma-115	371	19	denote	denote	VERB
ma-115	371	20	the	the	DET
ma-115	371	21	real	real	ADJ
ma-115	371	22	and	and	CCONJ
ma-115	371	23	imaginary	imaginary	ADJ
ma-115	371	24	part	part	NOUN
ma-115	371	25	of	of	ADP
ma-115	371	26	the	the	DET
ma-115	371	27	order	order	NOUN
ma-115	371	28	a	a	DET
ma-115	371	29	=	=	PUNCT
ma-115	371	30	ar	ar	PROPN
ma-115	371	31	+	+	CCONJ
ma-115	371	32	ial	ial	PROPN
ma-115	371	33	.thus	.thus	ADP
ma-115	371	34	ĥar	ĥar	PROPN
ma-115	371	35	j	j	PROPN
ma-115	371	36	,	,	PUNCT
ma-115	371	37	α−β,−2(α+β	α−β,−2(α+β	NOUN
ma-115	371	38	)	)	PUNCT
ma-115	371	39	,	,	PUNCT
ma-115	371	40	j	j	PROPN
ma-115	371	41	=	=	SYM
ma-115	371	42	1	1	NUM
ma-115	371	43	,	,	PUNCT
ma-115	371	44	2	2	NUM
ma-115	371	45	have	have	VERB
ma-115	371	46	just	just	ADV
ma-115	371	47	the	the	DET
ma-115	371	48	expression	expression	NOUN
ma-115	371	49	considered	consider	VERB
ma-115	371	50	in	in	ADP
ma-115	371	51	this	this	DET
ma-115	371	52	paper	paper	NOUN
ma-115	371	53	,	,	PUNCT
ma-115	371	54	while	while	SCONJ
ma-115	371	55	ĥial	ĥial	PROPN
ma-115	371	56	j	j	PROPN
ma-115	371	57	,	,	PUNCT
ma-115	371	58	α−β,−2(α+β	α−β,−2(α+β	NOUN
ma-115	371	59	)	)	PUNCT
ma-115	371	60	,	,	PUNCT
ma-115	371	61	j	j	PROPN
ma-115	371	62	=	=	SYM
ma-115	371	63	1	1	NUM
ma-115	371	64	,	,	PUNCT
ma-115	371	65	2	2	NUM
ma-115	371	66	are	be	AUX
ma-115	371	67	from	from	ADP
ma-115	371	68	then	then	ADV
ma-115	371	69	easily	easily	ADV
ma-115	371	70	deducible	deducible	ADJ
ma-115	371	71	replacing	replace	VERB
ma-115	371	72	φ	φ	NOUN
ma-115	371	73	with	with	ADP
ma-115	371	74	iφ.as	iφ.as	PROPN
ma-115	371	75	earlier	early	ADV
ma-115	371	76	mentioned	mention	VERB
ma-115	371	77	,	,	PUNCT
ma-115	371	78	the	the	DET
ma-115	371	79	hankel	hankel	NOUN
ma-115	371	80	transform	transform	NOUN
ma-115	371	81	is	be	AUX
ma-115	371	82	of	of	ADP
ma-115	371	83	interest	interest	NOUN
ma-115	371	84	within	within	ADP
ma-115	371	85	the	the	DET
ma-115	371	86	context	context	NOUN
ma-115	371	87	of	of	ADP
ma-115	371	88	the	the	DET
ma-115	371	89	fractional	fractional	ADJ
ma-115	371	90	calculus[17	calculus[17	PROPN
ma-115	371	91	]	]	PUNCT
ma-115	371	92	.	.	PUNCT
ma-115	372	1	following	follow	VERB
ma-115	372	2	the	the	DET
ma-115	372	3	arguments	argument	NOUN
ma-115	372	4	in	in	ADP
ma-115	372	5	[	[	X
ma-115	372	6	18	18	NUM
ma-115	372	7	]	]	PUNCT
ma-115	372	8	,	,	PUNCT
ma-115	372	9	for	for	ADP
ma-115	372	10	the	the	DET
ma-115	372	11	transforms	transform	NOUN
ma-115	372	12	of	of	ADP
ma-115	372	13	our	our	PRON
ma-115	372	14	concern	concern	NOUN
ma-115	372	15	we	we	PRON
ma-115	372	16	find	find	VERB
ma-115	372	17	that	that	SCONJ
ma-115	372	18	[	[	PUNCT
ma-115	372	19	ĥ1,α−β,−2(α+β)f	ĥ1,α−β,−2(α+β)f	NOUN
ma-115	372	20	]	]	PUNCT
ma-115	372	21	(	(	PUNCT
ma-115	372	22	y	y	NOUN
ma-115	372	23	)	)	PUNCT
ma-115	372	24	=	=	SYM
ma-115	373	1	21−(α−β	21−(α−β	X
ma-115	373	2	)	)	PUNCT
ma-115	373	3	x−α−3β+1√	x−α−3β+1√	PROPN
ma-115	374	1	π	π	X
ma-115	374	2	∫	∫	PROPN
ma-115	374	3	∞	∞	PROPN
ma-115	374	4	0	0	PROPN
ma-115	374	5	cos(yτ	cos(yτ	PROPN
ma-115	374	6	)	)	PUNCT
ma-115	374	7	[	[	PUNCT
ma-115	374	8	k̂α−β+1/2	k̂α−β+1/2	PROPN
ma-115	374	9	g1	g1	PROPN
ma-115	374	10	]	]	PUNCT
ma-115	374	11	(	(	PUNCT
ma-115	374	12	τ)dτ	τ)dτ	PROPN
ma-115	374	13	,	,	PUNCT
ma-115	374	14	[	[	PUNCT
ma-115	374	15	ĥ2,α−β,−2(α+β)f	ĥ2,α−β,−2(α+β)f	NOUN
ma-115	374	16	]	]	X
ma-115	374	17	(	(	PUNCT
ma-115	374	18	y	y	NOUN
ma-115	374	19	)	)	PUNCT
ma-115	375	1	=	=	SYM
ma-115	375	2	21−(α−β	21−(α−β	X
ma-115	375	3	)	)	PUNCT
ma-115	375	4	x−α−3β+1√	x−α−3β+1√	PROPN
ma-115	376	1	π	π	X
ma-115	376	2	∫	∫	PROPN
ma-115	376	3	∞	∞	PROPN
ma-115	376	4	0	0	PROPN
ma-115	376	5	cos(yτ	cos(yτ	PROPN
ma-115	376	6	)	)	PUNCT
ma-115	376	7	[	[	PUNCT
ma-115	376	8	k̂α−β+1/2	k̂α−β+1/2	PROPN
ma-115	376	9	g2	g2	PROPN
ma-115	376	10	]	]	PUNCT
ma-115	376	11	(	(	PUNCT
ma-115	376	12	τ)dτ	τ)dτ	NOUN
ma-115	376	13	(	(	PUNCT
ma-115	376	14	72	72	NUM
ma-115	376	15	)	)	PUNCT
ma-115	376	16	where	where	SCONJ
ma-115	376	17	k̂α−β+1/2	k̂α−β+1/2	PROPN
ma-115	376	18	is	be	AUX
ma-115	376	19	the	the	DET
ma-115	376	20	left	left	ADJ
ma-115	376	21	hand	hand	NOUN
ma-115	376	22	sided	side	VERB
ma-115	376	23	erdelyi	erdelyi	PROPN
ma-115	376	24	-	-	PUNCT
ma-115	376	25	kober	kober	NOUN
ma-115	376	26	fractional	fractional	ADJ
ma-115	376	27	integral	integral	ADJ
ma-115	376	28	operator	operator	NOUN
ma-115	376	29	,	,	PUNCT
ma-115	376	30	represented	represent	VERB
ma-115	376	31	by	by	ADP
ma-115	376	32	[	[	PUNCT
ma-115	376	33	k̂bg	k̂bg	X
ma-115	376	34	]	]	X
ma-115	376	35	(	(	PUNCT
ma-115	376	36	y	y	NOUN
ma-115	376	37	)	)	PUNCT
ma-115	376	38	=	=	SYM
ma-115	376	39	1	1	NUM
ma-115	376	40	γ(b	γ(b	NOUN
ma-115	376	41	)	)	PUNCT
ma-115	376	42	∫	∫	PROPN
ma-115	377	1	∞	∞	PROPN
ma-115	377	2	y	y	PROPN
ma-115	377	3	(	(	PUNCT
ma-115	377	4	y2	y2	INTJ
ma-115	377	5	−	−	PROPN
ma-115	377	6	x2)b−1	x2)b−1	PROPN
ma-115	377	7	x	x	SYM
ma-115	377	8	g(x	g(x	PROPN
ma-115	377	9	)	)	PUNCT
ma-115	377	10	dx	dx	PROPN
ma-115	377	11	,	,	PUNCT
ma-115	377	12	r(b	r(b	PROPN
ma-115	377	13	)	)	PUNCT
ma-115	377	14	>	>	X
ma-115	377	15	0	0	NUM
ma-115	377	16	,	,	PUNCT
ma-115	377	17	y	y	PROPN
ma-115	377	18	∈	∈	PROPN
ma-115	377	19	r	r	NOUN
ma-115	377	20	,	,	PUNCT
ma-115	377	21	and	and	CCONJ
ma-115	377	22	the	the	DET
ma-115	377	23	functions	function	NOUN
ma-115	377	24	g1(x	g1(x	NOUN
ma-115	377	25	)	)	PUNCT
ma-115	377	26	and	and	CCONJ
ma-115	377	27	g2(x	g2(x	PROPN
ma-115	377	28	)	)	PUNCT
ma-115	377	29	on	on	ADP
ma-115	377	30	which	which	PRON
ma-115	377	31	it	it	PRON
ma-115	377	32	acts	act	VERB
ma-115	377	33	in	in	ADP
ma-115	377	34	(	(	PUNCT
ma-115	377	35	72	72	NUM
ma-115	377	36	)	)	PUNCT
ma-115	377	37	involve	involve	VERB
ma-115	377	38	f	f	PROPN
ma-115	377	39	as	as	ADP
ma-115	377	40	g1(x	g1(x	NOUN
ma-115	377	41	)	)	PUNCT
ma-115	377	42	=	=	SYM
ma-115	378	1	xα+3β−1f	xα+3β−1f	PROPN
ma-115	378	2	(	(	PUNCT
ma-115	378	3	x	x	NOUN
ma-115	378	4	)	)	PUNCT
ma-115	378	5	,	,	PUNCT
ma-115	378	6	g2(x	g2(x	X
ma-115	378	7	)	)	PUNCT
ma-115	378	8	=	=	SYM
ma-115	378	9	x−3α−βf	x−3α−βf	PROPN
ma-115	378	10	(	(	PUNCT
ma-115	378	11	x).relations	x).relation	NOUN
ma-115	378	12	(	(	PUNCT
ma-115	378	13	72	72	NUM
ma-115	378	14	)	)	PUNCT
ma-115	378	15	holds	hold	VERB
ma-115	378	16	under	under	ADP
ma-115	378	17	the	the	DET
ma-115	378	18	assumption	assumption	NOUN
ma-115	378	19	that	that	SCONJ
ma-115	378	20	both	both	DET
ma-115	378	21	xg1(x	xg1(x	NOUN
ma-115	378	22	)	)	PUNCT
ma-115	378	23	and	and	CCONJ
ma-115	378	24	xg2(x	xg2(x	PROPN
ma-115	378	25	)	)	PUNCT
ma-115	378	26	are	be	AUX
ma-115	378	27	inegrable	inegrable	ADJ
ma-115	378	28	.	.	PUNCT
ma-115	379	1	note	note	NOUN
ma-115	379	2	thataccording	thataccorde	VERB
ma-115	379	3	to	to	PART
ma-115	379	4	sonine	sonine	VERB
ma-115	379	5	’s	’s	PART
ma-115	379	6	first	first	ADJ
ma-115	379	7	integral	integral	ADJ
ma-115	379	8	for	for	ADP
ma-115	379	9	bessel	bessel	ADJ
ma-115	379	10	functions	function	NOUN
ma-115	379	11	,	,	PUNCT
ma-115	379	12	we	we	PRON
ma-115	379	13	may	may	AUX
ma-115	379	14	say	say	VERB
ma-115	379	15	that	that	SCONJ
ma-115	379	16	the	the	DET
ma-115	379	17	right	right	ADJ
ma-115	379	18	hand	hand	NOUN
ma-115	379	19	sidederdelyi	sidederdelyi	PROPN
ma-115	379	20	-	-	PUNCT
ma-115	379	21	kober	kober	PROPN
ma-115	379	22	operator	operator	NOUN
ma-115	379	23	of	of	ADP
ma-115	379	24	order	order	NOUN
ma-115	379	25	b	b	NOUN
ma-115	379	26	acts	act	VERB
ma-115	379	27	on	on	ADP
ma-115	379	28	the	the	DET
ma-115	379	29	function	function	NOUN
ma-115	379	30	xα−β	xα−β	PROPN
ma-115	379	31	jα−β(x	jα−β(x	PROPN
ma-115	379	32	)	)	PUNCT
ma-115	379	33	as	as	ADP
ma-115	379	34	a	a	DET
ma-115	379	35	rising	rise	VERB
ma-115	379	36	operator	operator	NOUN
ma-115	379	37	turningit	turningit	NOUN
ma-115	379	38	into	into	ADP
ma-115	379	39	xα−β+b	xα−β+b	PROPN
ma-115	379	40	jα−β+b(x).expressions	jα−β+b(x).expression	NOUN
ma-115	379	41	similar	similar	ADJ
ma-115	379	42	to	to	ADP
ma-115	379	43	(	(	PUNCT
ma-115	379	44	72	72	NUM
ma-115	379	45	)	)	PUNCT
ma-115	379	46	can	can	AUX
ma-115	379	47	be	be	AUX
ma-115	379	48	deduced	deduce	VERB
ma-115	379	49	for	for	ADP
ma-115	379	50	the	the	DET
ma-115	379	51	fractional	fractional	ADJ
ma-115	379	52	order	order	NOUN
ma-115	379	53	transforms	transform	VERB
ma-115	379	54	,	,	PUNCT
ma-115	379	55	of	of	ADP
ma-115	379	56	course.in	course.in	NUM
ma-115	379	57	addition	addition	NOUN
ma-115	379	58	(	(	PUNCT
ma-115	379	59	72	72	NUM
ma-115	379	60	)	)	PUNCT
ma-115	379	61	as	as	SCONJ
ma-115	379	62	paralleled	parallel	VERB
ma-115	379	63	by	by	ADP
ma-115	379	64	similar	similar	ADJ
ma-115	379	65	expressions	expression	NOUN
ma-115	379	66	involving	involve	VERB
ma-115	379	67	the	the	DET
ma-115	379	68	barut	barut	NOUN
ma-115	379	69	-	-	PUNCT
ma-115	379	70	girardello	girardello	NOUN
ma-115	379	71	transform	transform	VERB
ma-115	379	72	ofthe	ofthe	NOUN
ma-115	379	73	first	first	ADJ
ma-115	379	74	and	and	CCONJ
ma-115	379	75	second	second	ADJ
ma-115	379	76	type	type	NOUN
ma-115	379	77	.	.	PUNCT
ma-115	380	1	as	as	ADP
ma-115	380	2	an	an	DET
ma-115	380	3	example	example	NOUN
ma-115	380	4	,	,	PUNCT
ma-115	380	5	we	we	PRON
ma-115	380	6	deduce	deduce	VERB
ma-115	380	7	here	here	ADV
ma-115	380	8	the	the	DET
ma-115	380	9	relation	relation	NOUN
ma-115	380	10	involving	involve	VERB
ma-115	380	11	the	the	DET
ma-115	380	12	conventionaltransform	conventionaltransform	NOUN
ma-115	380	13	(	(	PUNCT
ma-115	380	14	49	49	NUM
ma-115	380	15	)	)	PUNCT
ma-115	380	16	.	.	PUNCT
ma-115	381	1	on	on	ADP
ma-115	381	2	account	account	NOUN
ma-115	381	3	of	of	ADP
ma-115	381	4	the	the	DET
ma-115	381	5	integral	integral	ADJ
ma-115	381	6	representation	representation	NOUN
ma-115	381	7	of	of	ADP
ma-115	381	8	the	the	DET
ma-115	381	9	modified	modify	VERB
ma-115	381	10	bessel	bessel	NOUN
ma-115	381	11	function	function	NOUN
ma-115	381	12	of	of	ADP
ma-115	381	13	thefirst	thefirst	ADJ
ma-115	381	14	kind	kind	NOUN
ma-115	381	15	,	,	PUNCT
ma-115	381	16	iα−β	iα−β	NOUN
ma-115	381	17	,	,	PUNCT
ma-115	381	18	i.e.	i.e.	X
ma-115	381	19	iα−β(xy	iα−β(xy	NOUN
ma-115	381	20	)	)	PUNCT
ma-115	381	21	=	=	SYM
ma-115	381	22	21−(α−β	21−(α−β	X
ma-115	381	23	)	)	PUNCT
ma-115	381	24	yα−β	yα−β	PROPN
ma-115	381	25	x−(α−β)√	x−(α−β)√	PROPN
ma-115	382	1	π	π	PROPN
ma-115	382	2	γ(α−	γ(α−	X
ma-115	382	3	β	β	X
ma-115	382	4	+	+	NOUN
ma-115	382	5	1/2	1/2	NUM
ma-115	382	6	)	)	PUNCT
ma-115	382	7	∫	∫	NOUN
ma-115	382	8	x	x	X
ma-115	382	9	0	0	PUNCT
ma-115	383	1	(	(	PUNCT
ma-115	383	2	x2	x2	INTJ
ma-115	383	3	−	−	PROPN
ma-115	383	4	τ2)α−β−1/2	τ2)α−β−1/2	PROPN
ma-115	384	1	cosh(yτ)dτ	cosh(yτ)dτ	PROPN
ma-115	384	2	,	,	PUNCT
ma-115	384	3	r(α−	r(α−	NOUN
ma-115	384	4	β	β	X
ma-115	384	5	+	+	NOUN
ma-115	384	6	1/2	1/2	NUM
ma-115	384	7	)	)	PUNCT
ma-115	384	8	>	>	X
ma-115	384	9	0	0	NUM
ma-115	384	10	,	,	PUNCT
ma-115	384	11	https://doi.org/10.28924/ada/ma.3.6	https://doi.org/10.28924/ada/ma.3.6	PROPN
ma-115	384	12	eur	eur	PROPN
ma-115	384	13	.	.	PUNCT
ma-115	385	1	j.	j.	PROPN
ma-115	385	2	math	math	PROPN
ma-115	385	3	.	.	PUNCT
ma-115	386	1	anal	anal	PROPN
ma-115	386	2	.	.	PUNCT
ma-115	387	1	10.28924	10.28924	NUM
ma-115	387	2	/	/	SYM
ma-115	387	3	ada	ada	PROPN
ma-115	387	4	/	/	SYM
ma-115	387	5	ma.3.6	ma.3.6	PROPN
ma-115	387	6	17it	17it	PROPN
ma-115	387	7	is	be	AUX
ma-115	387	8	easy	easy	ADJ
ma-115	387	9	to	to	PART
ma-115	387	10	rewrite	rewrite	VERB
ma-115	387	11	(	(	PUNCT
ma-115	387	12	49	49	NUM
ma-115	387	13	)	)	PUNCT
ma-115	387	14	in	in	ADP
ma-115	387	15	the	the	DET
ma-115	387	16	form	form	NOUN
ma-115	387	17	[	[	PUNCT
ma-115	387	18	ĝα−βf	ĝα−βf	NOUN
ma-115	387	19	]	]	PUNCT
ma-115	387	20	(	(	PUNCT
ma-115	387	21	y	y	NOUN
ma-115	387	22	)	)	PUNCT
ma-115	387	23	=	=	SYM
ma-115	388	1	√	√	ADV
ma-115	388	2	2	2	NUM
ma-115	388	3	π	π	PROPN
ma-115	388	4	21+(α−β2	21+(α−β2	NUM
ma-115	388	5	)	)	PUNCT
ma-115	388	6	e−(1/2)y	e−(1/2)y	X
ma-115	388	7	2	2	NUM
ma-115	388	8	∫	∫	NOUN
ma-115	388	9	∞	∞	PROPN
ma-115	388	10	0	0	NUM
ma-115	388	11	cosh	cosh	PROPN
ma-115	388	12	(	(	PUNCT
ma-115	388	13	√	√	NOUN
ma-115	388	14	2yτ	2yτ	NOUN
ma-115	388	15	)	)	PUNCT
ma-115	389	1	[	[	X
ma-115	389	2	k̂α−β+1/2	k̂α−β+1/2	PROPN
ma-115	389	3	h](τ)dτ	h](τ)dτ	PROPN
ma-115	389	4	,	,	PUNCT
ma-115	389	5	with	with	ADP
ma-115	389	6	the	the	DET
ma-115	389	7	function	function	NOUN
ma-115	389	8	h(x	h(x	PROPN
ma-115	389	9	)	)	PUNCT
ma-115	389	10	being	be	AUX
ma-115	389	11	h(x	h(x	PROPN
ma-115	389	12	)	)	PUNCT
ma-115	389	13	=	=	SYM
ma-115	389	14	x−1−(α−β2	x−1−(α−β2	PROPN
ma-115	389	15	)	)	PUNCT
ma-115	389	16	e−(1/2)y	e−(1/2)y	X
ma-115	389	17	2	2	NUM
ma-115	389	18	f	f	X
ma-115	389	19	(	(	PUNCT
ma-115	389	20	x	x	NOUN
ma-115	389	21	)	)	PUNCT
ma-115	389	22	.	.	PUNCT
ma-115	390	1	the	the	DET
ma-115	390	2	above	above	ADJ
ma-115	390	3	relation	relation	NOUN
ma-115	390	4	holds	hold	VERB
ma-115	390	5	under	under	ADP
ma-115	390	6	the	the	DET
ma-115	390	7	assumption	assumption	NOUN
ma-115	390	8	that	that	SCONJ
ma-115	390	9	xh(x	xh(x	PUNCT
ma-115	390	10	)	)	PUNCT
ma-115	390	11	is	be	AUX
ma-115	390	12	integrable.we	integrable.we	PRON
ma-115	390	13	finally	finally	ADV
ma-115	390	14	note	note	VERB
ma-115	390	15	that	that	SCONJ
ma-115	390	16	,	,	PUNCT
ma-115	390	17	since	since	SCONJ
ma-115	390	18	several	several	ADJ
ma-115	390	19	forms	form	NOUN
ma-115	390	20	of	of	ADP
ma-115	390	21	the	the	DET
ma-115	390	22	erdelyi	erdelyi	NOUN
ma-115	390	23	-	-	PUNCT
ma-115	390	24	kober	kober	PROPN
ma-115	390	25	operator	operator	NOUN
ma-115	390	26	exist	exist	VERB
ma-115	390	27	in	in	ADP
ma-115	390	28	the	the	DET
ma-115	390	29	literature	literature	NOUN
ma-115	390	30	,	,	PUNCT
ma-115	390	31	arather	arather	ADV
ma-115	390	32	wide	wide	ADJ
ma-115	390	33	set	set	NOUN
ma-115	390	34	of	of	ADP
ma-115	390	35	relation	relation	NOUN
ma-115	390	36	linking	link	VERB
ma-115	390	37	the	the	DET
ma-115	390	38	hankel	hankel	NOUN
ma-115	390	39	transform	transform	NOUN
ma-115	390	40	to	to	ADP
ma-115	390	41	such	such	ADJ
ma-115	390	42	forms	form	NOUN
ma-115	390	43	can	can	AUX
ma-115	390	44	be	be	AUX
ma-115	390	45	deduced	deduce	VERB
ma-115	390	46	.	.	PUNCT
ma-115	391	1	references	reference	NOUN
ma-115	391	2	[	[	X
ma-115	391	3	1	1	NUM
ma-115	391	4	]	]	X
ma-115	391	5	p.p	p.p	PROPN
ma-115	391	6	.	.	PROPN
ma-115	391	7	banerjee	banerjee	PROPN
ma-115	391	8	,	,	PUNCT
ma-115	391	9	g.	g.	PROPN
ma-115	391	10	nehmetallah	nehmetallah	PROPN
ma-115	391	11	,	,	PUNCT
ma-115	391	12	m.r	m.r	PROPN
ma-115	391	13	.	.	PROPN
ma-115	391	14	chatterjee	chatterjee	PROPN
ma-115	391	15	,	,	PUNCT
ma-115	391	16	numerical	numerical	ADJ
ma-115	391	17	modeling	modeling	NOUN
ma-115	391	18	of	of	ADP
ma-115	391	19	cylindrically	cylindrically	ADV
ma-115	391	20	symmetric	symmetric	ADJ
ma-115	391	21	nonlinear	nonlinear	ADJ
ma-115	391	22	self	self	NOUN
ma-115	391	23	-	-	PUNCT
ma-115	391	24	focusing	focus	VERB
ma-115	391	25	using	use	VERB
ma-115	391	26	an	an	DET
ma-115	391	27	adaptive	adaptive	ADJ
ma-115	391	28	fast	fast	ADJ
ma-115	391	29	hankel	hankel	NOUN
ma-115	391	30	split	split	NOUN
ma-115	391	31	-	-	PUNCT
ma-115	391	32	step	step	NOUN
ma-115	391	33	method	method	NOUN
ma-115	391	34	,	,	PUNCT
ma-115	391	35	optics	optic	NOUN
ma-115	391	36	commun	commun	X
ma-115	391	37	.	.	PUNCT
ma-115	392	1	249	249	NUM
ma-115	392	2	(	(	PUNCT
ma-115	392	3	2005	2005	NUM
ma-115	392	4	)	)	PUNCT
ma-115	392	5	,	,	PUNCT
ma-115	392	6	293–300	293–300	NUM
ma-115	392	7	.	.	PUNCT
ma-115	393	1	https://doi	https://doi	X
ma-115	393	2	.	.	PUNCT
ma-115	394	1	org/10.1016	org/10.1016	PROPN
ma-115	394	2	/	/	SYM
ma-115	394	3	j.optcom.2004.12.048.[2	j.optcom.2004.12.048.[2	PROPN
ma-115	394	4	]	]	X
ma-115	394	5	v.	v.	PROPN
ma-115	394	6	bargmann	bargmann	PROPN
ma-115	394	7	,	,	PUNCT
ma-115	394	8	on	on	ADP
ma-115	394	9	a	a	DET
ma-115	394	10	hilbert	hilbert	NOUN
ma-115	394	11	space	space	NOUN
ma-115	394	12	of	of	ADP
ma-115	394	13	analytie	analytie	NOUN
ma-115	394	14	functions	function	NOUN
ma-115	394	15	and	and	CCONJ
ma-115	394	16	an	an	DET
ma-115	394	17	associated	associated	ADJ
ma-115	394	18	integral	integral	ADJ
ma-115	394	19	transform	transform	NOUN
ma-115	394	20	.	.	PUNCT
ma-115	395	1	part	part	PROPN
ma-115	395	2	ii	ii	PROPN
ma-115	395	3	.	.	PUNCT
ma-115	396	1	a	a	DET
ma-115	396	2	family	family	NOUN
ma-115	396	3	ofrelated	ofrelate	VERB
ma-115	396	4	function	function	NOUN
ma-115	396	5	spaces	space	VERB
ma-115	396	6	application	application	NOUN
ma-115	396	7	to	to	ADP
ma-115	396	8	distribution	distribution	NOUN
ma-115	396	9	theory	theory	NOUN
ma-115	396	10	,	,	PUNCT
ma-115	396	11	commun	commun	PROPN
ma-115	396	12	.	.	PUNCT
ma-115	397	1	pure	pure	ADJ
ma-115	397	2	appl	appl	PROPN
ma-115	397	3	.	.	PUNCT
ma-115	397	4	math	math	NOUN
ma-115	397	5	.	.	PUNCT
ma-115	398	1	20	20	NUM
ma-115	398	2	(	(	PUNCT
ma-115	398	3	1967	1967	NUM
ma-115	398	4	)	)	PUNCT
ma-115	398	5	,	,	PUNCT
ma-115	398	6	1–101	1–101	NUM
ma-115	398	7	.	.	PUNCT
ma-115	398	8	https	https	NOUN
ma-115	398	9	:	:	PUNCT
ma-115	398	10	//doi.org/10.1002	//doi.org/10.1002	NOUN
ma-115	398	11	/	/	SYM
ma-115	398	12	cpa.3160200102.[3	cpa.3160200102.[3	PROPN
ma-115	398	13	]	]	X
ma-115	398	14	a.o	a.o	PROPN
ma-115	398	15	.	.	PROPN
ma-115	398	16	barut	barut	PROPN
ma-115	398	17	,	,	PUNCT
ma-115	398	18	l.	l.	PROPN
ma-115	398	19	girardello	girardello	PROPN
ma-115	398	20	,	,	PUNCT
ma-115	398	21	new	new	ADJ
ma-115	398	22	"	"	PUNCT
ma-115	398	23	coherent	coherent	ADJ
ma-115	398	24	"	"	PUNCT
ma-115	398	25	states	state	NOUN
ma-115	398	26	associated	associate	VERB
ma-115	398	27	with	with	ADP
ma-115	398	28	non	non	ADJ
ma-115	398	29	-	-	ADJ
ma-115	398	30	compact	compact	ADJ
ma-115	398	31	groups	group	NOUN
ma-115	398	32	,	,	PUNCT
ma-115	398	33	commun.math	commun.math	PROPN
ma-115	398	34	.	.	PUNCT
ma-115	399	1	phys	phys	PROPN
ma-115	399	2	.	.	PUNCT
ma-115	400	1	21(1971	21(1971	NUM
ma-115	400	2	)	)	PUNCT
ma-115	400	3	,	,	PUNCT
ma-115	401	1	41–55	41–55	NOUN
ma-115	401	2	.	.	PUNCT
ma-115	402	1	https://doi.org/10.1007/bf01646483.[4	https://doi.org/10.1007/bf01646483.[4	PUNCT
ma-115	402	2	]	]	X
ma-115	402	3	m.j	m.j	PROPN
ma-115	402	4	.	.	PROPN
ma-115	402	5	buckingham	buckingham	PROPN
ma-115	402	6	,	,	PUNCT
ma-115	402	7	causality	causality	NOUN
ma-115	402	8	,	,	PUNCT
ma-115	402	9	stokes	stokes	PROPN
ma-115	402	10	’	'	PUNCT
ma-115	402	11	wave	wave	NOUN
ma-115	402	12	equation	equation	NOUN
ma-115	402	13	,	,	PUNCT
ma-115	402	14	and	and	CCONJ
ma-115	402	15	acoustic	acoustic	ADJ
ma-115	402	16	pulse	pulse	NOUN
ma-115	402	17	propagation	propagation	NOUN
ma-115	402	18	in	in	ADP
ma-115	402	19	a	a	DET
ma-115	402	20	viscous	viscous	ADJ
ma-115	402	21	fluid	fluid	NOUN
ma-115	402	22	,	,	PUNCT
ma-115	402	23	phys	phy	NOUN
ma-115	402	24	.	.	PUNCT
ma-115	403	1	rev.e	rev.e	PROPN
ma-115	403	2	.	.	PROPN
ma-115	403	3	72	72	NUM
ma-115	403	4	(	(	PUNCT
ma-115	403	5	2005	2005	NUM
ma-115	403	6	)	)	PUNCT
ma-115	403	7	,	,	PUNCT
ma-115	403	8	026610	026610	NUM
ma-115	403	9	.	.	PUNCT
ma-115	404	1	https://doi.org/10.1103/physreve.72.026610.[5	https://doi.org/10.1103/physreve.72.026610.[5	PROPN
ma-115	404	2	]	]	X
ma-115	404	3	e.	e.	PROPN
ma-115	404	4	hansen	hansen	PROPN
ma-115	404	5	,	,	PUNCT
ma-115	404	6	fast	fast	ADJ
ma-115	404	7	hankel	hankel	NOUN
ma-115	404	8	transform	transform	NOUN
ma-115	404	9	algorithm	algorithm	NOUN
ma-115	404	10	,	,	PUNCT
ma-115	404	11	ieee	ieee	NOUN
ma-115	404	12	trans	trans	PROPN
ma-115	404	13	.	.	PUNCT
ma-115	405	1	acoust	acoust	PROPN
ma-115	405	2	.	.	PUNCT
ma-115	405	3	,	,	PUNCT
ma-115	405	4	speech	speech	NOUN
ma-115	405	5	,	,	PUNCT
ma-115	405	6	signal	signal	NOUN
ma-115	405	7	process	process	NOUN
ma-115	405	8	.	.	PUNCT
ma-115	406	1	33	33	NUM
ma-115	406	2	(	(	PUNCT
ma-115	406	3	1985	1985	NUM
ma-115	406	4	)	)	PUNCT
ma-115	406	5	,	,	PUNCT
ma-115	406	6	666–671	666–671	NUM
ma-115	406	7	.	.	PUNCT
ma-115	407	1	https://doi.org/10.1109/tassp.1985.1164579.[6	https://doi.org/10.1109/tassp.1985.1164579.[6	ADP
ma-115	407	2	]	]	X
ma-115	407	3	m.	m.	NOUN
ma-115	407	4	linares	linare	NOUN
ma-115	407	5	,	,	PUNCT
ma-115	407	6	j.m.r	j.m.r	NOUN
ma-115	407	7	.	.	PROPN
ma-115	407	8	mendez	mendez	PROPN
ma-115	407	9	,	,	PUNCT
ma-115	407	10	a	a	DET
ma-115	407	11	hankel	hankel	NOUN
ma-115	407	12	type	type	NOUN
ma-115	407	13	integral	integral	ADJ
ma-115	407	14	transformation	transformation	NOUN
ma-115	407	15	on	on	ADP
ma-115	407	16	certain	certain	ADJ
ma-115	407	17	space	space	NOUN
ma-115	407	18	of	of	ADP
ma-115	407	19	distributions	distribution	NOUN
ma-115	407	20	,	,	PUNCT
ma-115	407	21	bull	bull	NOUN
ma-115	407	22	.	.	PUNCT
ma-115	408	1	cal	cal	PROPN
ma-115	408	2	.	.	PUNCT
ma-115	409	1	math.soc	math.soc	X
ma-115	409	2	.	.	PROPN
ma-115	409	3	83	83	NUM
ma-115	409	4	(	(	PUNCT
ma-115	409	5	1991	1991	NUM
ma-115	409	6	)	)	PUNCT
ma-115	409	7	,	,	PUNCT
ma-115	409	8	447	447	NUM
ma-115	409	9	-	-	SYM
ma-115	409	10	546.[7	546.[7	NUM
ma-115	409	11	]	]	X
ma-115	409	12	m.l	m.l	PROPN
ma-115	409	13	.	.	PUNCT
ma-115	409	14	linares	linare	NOUN
ma-115	409	15	,	,	PUNCT
ma-115	409	16	j.m.r.m	j.m.r.m	PROPN
ma-115	409	17	.	.	PROPN
ma-115	409	18	perez	perez	PROPN
ma-115	409	19	,	,	PUNCT
ma-115	409	20	hankel	hankel	NOUN
ma-115	409	21	complementary	complementary	ADJ
ma-115	409	22	integral	integral	ADJ
ma-115	409	23	transformations	transformation	NOUN
ma-115	409	24	of	of	ADP
ma-115	409	25	arbitrary	arbitrary	ADJ
ma-115	409	26	order	order	NOUN
ma-115	409	27	,	,	PUNCT
ma-115	409	28	int	int	NOUN
ma-115	409	29	.	.	PUNCT
ma-115	410	1	j.	j.	PROPN
ma-115	410	2	math	math	PROPN
ma-115	410	3	.	.	PUNCT
ma-115	411	1	math.sci	math.sci	X
ma-115	411	2	.	.	NOUN
ma-115	411	3	15	15	NUM
ma-115	411	4	(	(	PUNCT
ma-115	411	5	1992	1992	NUM
ma-115	411	6	)	)	PUNCT
ma-115	411	7	,	,	PUNCT
ma-115	411	8	323–332	323–332	NUM
ma-115	411	9	.	.	PUNCT
ma-115	412	1	https://doi.org/10.1155/s0161171292000401.[8	https://doi.org/10.1155/s0161171292000401.[8	PROPN
ma-115	412	2	]	]	PUNCT
ma-115	412	3	a.	a.	PROPN
ma-115	412	4	w.	w.	PROPN
ma-115	412	5	lohmann	lohmann	PROPN
ma-115	412	6	,	,	PUNCT
ma-115	412	7	image	image	NOUN
ma-115	412	8	rotation	rotation	NOUN
ma-115	412	9	,	,	PUNCT
ma-115	412	10	wigner	wigner	ADJ
ma-115	412	11	rotation	rotation	NOUN
ma-115	412	12	,	,	PUNCT
ma-115	412	13	and	and	CCONJ
ma-115	412	14	the	the	DET
ma-115	412	15	fractional	fractional	ADJ
ma-115	412	16	fourier	fourier	NOUN
ma-115	412	17	transform	transform	NOUN
ma-115	412	18	,	,	PUNCT
ma-115	412	19	j.	j.	PROPN
ma-115	412	20	opt	opt	PROPN
ma-115	412	21	.	.	PUNCT
ma-115	413	1	soc	soc	PROPN
ma-115	413	2	.	.	PUNCT
ma-115	414	1	am	be	AUX
ma-115	414	2	.	.	PUNCT
ma-115	415	1	a	a	DET
ma-115	415	2	10	10	NUM
ma-115	415	3	(	(	PUNCT
ma-115	415	4	1993),pp	1993),pp	NUM
ma-115	415	5	.	.	PUNCT
ma-115	416	1	2181	2181	NUM
ma-115	416	2	-	-	PUNCT
ma-115	416	3	2186	2186	NUM
ma-115	416	4	.	.	PUNCT
ma-115	417	1	https://doi.org/10.1364/josaa.10.002181.[9	https://doi.org/10.1364/josaa.10.002181.[9	NOUN
ma-115	417	2	]	]	X
ma-115	417	3	v.	v.	CCONJ
ma-115	417	4	namias	namias	PROPN
ma-115	417	5	,	,	PUNCT
ma-115	417	6	fractionalization	fractionalization	NOUN
ma-115	417	7	of	of	ADP
ma-115	417	8	hankel	hankel	NOUN
ma-115	417	9	transforms	transform	VERB
ma-115	417	10	,	,	PUNCT
ma-115	417	11	i	i	PRON
ma-115	417	12	m	m	VERB
ma-115	417	13	a	a	PROPN
ma-115	417	14	j.	j.	PROPN
ma-115	417	15	appl	appl	PROPN
ma-115	417	16	.	.	PROPN
ma-115	417	17	math	math	PROPN
ma-115	417	18	.	.	PUNCT
ma-115	418	1	26	26	NUM
ma-115	418	2	(	(	PUNCT
ma-115	418	3	1980	1980	NUM
ma-115	418	4	)	)	PUNCT
ma-115	418	5	,	,	PUNCT
ma-115	418	6	187–197	187–197	NUM
ma-115	418	7	.	.	PUNCT
ma-115	419	1	https://doi.org/10	https://doi.org/10	PROPN
ma-115	419	2	.	.	PROPN
ma-115	420	1	1093	1093	NUM
ma-115	420	2	/	/	SYM
ma-115	420	3	imamat/26.2.187.[10	imamat/26.2.187.[10	PROPN
ma-115	420	4	]	]	PUNCT
ma-115	420	5	s.p	s.p	PROPN
ma-115	420	6	.	.	PROPN
ma-115	420	7	malgonde	malgonde	PROPN
ma-115	420	8	,	,	PUNCT
ma-115	420	9	s.r	s.r	PROPN
ma-115	420	10	.	.	PROPN
ma-115	420	11	bandewar	bandewar	PROPN
ma-115	420	12	,	,	PUNCT
ma-115	420	13	on	on	ADP
ma-115	420	14	the	the	DET
ma-115	420	15	generalized	generalize	VERB
ma-115	420	16	hankel	hankel	NOUN
ma-115	420	17	-	-	PUNCT
ma-115	420	18	clifford	clifford	PROPN
ma-115	420	19	transformation	transformation	NOUN
ma-115	420	20	of	of	ADP
ma-115	420	21	arbitrary	arbitrary	ADJ
ma-115	420	22	order	order	NOUN
ma-115	420	23	,	,	PUNCT
ma-115	420	24	proc	proc	NOUN
ma-115	420	25	.	.	PUNCT
ma-115	421	1	in	in	ADP
ma-115	421	2	-	-	PUNCT
ma-115	421	3	dian	dian	ADJ
ma-115	421	4	acad	acad	NOUN
ma-115	421	5	.	.	PUNCT
ma-115	422	1	sci	sci	PROPN
ma-115	422	2	.	.	PUNCT
ma-115	423	1	(	(	PUNCT
ma-115	423	2	math	math	NOUN
ma-115	423	3	.	.	PUNCT
ma-115	424	1	sci	sci	PROPN
ma-115	424	2	.	.	PUNCT
ma-115	424	3	)	)	PUNCT
ma-115	425	1	110	110	NUM
ma-115	425	2	(	(	PUNCT
ma-115	425	3	2000	2000	NUM
ma-115	425	4	)	)	PUNCT
ma-115	425	5	,	,	PUNCT
ma-115	425	6	293	293	NUM
ma-115	425	7	-	-	SYM
ma-115	425	8	304	304	NUM
ma-115	425	9	.	.	PUNCT
ma-115	426	1	https://www.ias.ac.in/article/fulltext/pmsc/110/03/	https://www.ias.ac.in/article/fulltext/pmsc/110/03/	NOUN
ma-115	426	2	0293	0293	NUM
ma-115	426	3	-	-	SYM
ma-115	426	4	0304.[11	0304.[11	NUM
ma-115	426	5	]	]	X
ma-115	426	6	s.p	s.p	PROPN
ma-115	426	7	.	.	PROPN
ma-115	426	8	malgonde	malgonde	PROPN
ma-115	426	9	,	,	PUNCT
ma-115	426	10	l.	l.	PROPN
ma-115	426	11	debnath	debnath	PROPN
ma-115	426	12	,	,	PUNCT
ma-115	426	13	on	on	ADP
ma-115	426	14	hankel	hankel	NOUN
ma-115	426	15	type	type	NOUN
ma-115	426	16	integral	integral	ADJ
ma-115	426	17	transformations	transformation	NOUN
ma-115	426	18	of	of	ADP
ma-115	426	19	generalized	generalized	ADJ
ma-115	426	20	functions	function	NOUN
ma-115	426	21	,	,	PUNCT
ma-115	426	22	integr	integr	NOUN
ma-115	426	23	.	.	PUNCT
ma-115	427	1	transformsspec	transformsspec	PROPN
ma-115	427	2	.	.	PUNCT
ma-115	428	1	funct	funct	PROPN
ma-115	428	2	.	.	PUNCT
ma-115	429	1	15	15	NUM
ma-115	429	2	(	(	PUNCT
ma-115	429	3	2004	2004	NUM
ma-115	429	4	)	)	PUNCT
ma-115	429	5	,	,	PUNCT
ma-115	429	6	421–430	421–430	NUM
ma-115	429	7	.	.	PUNCT
ma-115	430	1	https://doi.org/10.1080/10652460410001686055.[12	https://doi.org/10.1080/10652460410001686055.[12	PROPN
ma-115	430	2	]	]	X
ma-115	430	3	s.p	s.p	PROPN
ma-115	430	4	.	.	PROPN
ma-115	430	5	malgonde	malgonde	PROPN
ma-115	430	6	,	,	PUNCT
ma-115	430	7	s.r	s.r	PROPN
ma-115	430	8	.	.	PROPN
ma-115	430	9	bandewar	bandewar	PROPN
ma-115	430	10	,	,	PUNCT
ma-115	430	11	l.	l.	PROPN
ma-115	430	12	debnath	debnath	PROPN
ma-115	430	13	,	,	PUNCT
ma-115	430	14	mixed	mixed	ADJ
ma-115	430	15	parseval	parseval	NOUN
ma-115	430	16	equation	equation	NOUN
ma-115	430	17	and	and	CCONJ
ma-115	430	18	generalized	generalized	ADJ
ma-115	430	19	hankel	hankel	NOUN
ma-115	430	20	-	-	PUNCT
ma-115	430	21	type	type	NOUN
ma-115	430	22	integraltransformation	integraltransformation	NOUN
ma-115	430	23	of	of	ADP
ma-115	430	24	distributions	distribution	NOUN
ma-115	430	25	,	,	PUNCT
ma-115	430	26	integr	integr	NOUN
ma-115	430	27	.	.	PROPN
ma-115	430	28	transforms	transform	VERB
ma-115	430	29	spec	spec	PROPN
ma-115	430	30	.	.	PUNCT
ma-115	431	1	funct	funct	PROPN
ma-115	431	2	.	.	PUNCT
ma-115	432	1	15	15	NUM
ma-115	432	2	(	(	PUNCT
ma-115	432	3	2004	2004	NUM
ma-115	432	4	)	)	PUNCT
ma-115	432	5	,	,	PUNCT
ma-115	433	1	431–443	431–443	NUM
ma-115	433	2	.	.	PUNCT
ma-115	434	1	https://doi.org/10.1080/	https://doi.org/10.1080/	NOUN
ma-115	434	2	10652460410001686046.[13	10652460410001686046.[13	NUM
ma-115	434	3	]	]	X
ma-115	434	4	a.v	a.v	PROPN
ma-115	434	5	.	.	PROPN
ma-115	434	6	oppenheim	oppenheim	PROPN
ma-115	434	7	,	,	PUNCT
ma-115	434	8	g.v	g.v	PROPN
ma-115	434	9	.	.	PROPN
ma-115	434	10	frisk	frisk	PROPN
ma-115	434	11	,	,	PUNCT
ma-115	434	12	d.r	d.r	PROPN
ma-115	434	13	.	.	PROPN
ma-115	434	14	martinez	martinez	PROPN
ma-115	434	15	,	,	PUNCT
ma-115	434	16	computation	computation	NOUN
ma-115	434	17	of	of	ADP
ma-115	434	18	the	the	DET
ma-115	434	19	hankel	hankel	NOUN
ma-115	434	20	transform	transform	VERB
ma-115	434	21	using	use	VERB
ma-115	434	22	projections	projection	NOUN
ma-115	434	23	,	,	PUNCT
ma-115	434	24	j.	j.	PROPN
ma-115	434	25	acoust	acoust	PROPN
ma-115	434	26	.	.	PUNCT
ma-115	435	1	soc.amer	soc.amer	X
ma-115	435	2	.	.	PUNCT
ma-115	436	1	68	68	NUM
ma-115	436	2	(	(	PUNCT
ma-115	436	3	1980	1980	NUM
ma-115	436	4	)	)	PUNCT
ma-115	436	5	,	,	PUNCT
ma-115	436	6	523–529	523–529	NUM
ma-115	436	7	.	.	PUNCT
ma-115	437	1	https://doi.org/10.1121/1.384765	https://doi.org/10.1121/1.384765	PROPN
ma-115	437	2	.	.	PUNCT
ma-115	438	1	https://doi.org/10.28924/ada/ma.3.6	https://doi.org/10.28924/ada/ma.3.6	PROPN
ma-115	438	2	https://doi.org/10.1016/j.optcom.2004.12.048	https://doi.org/10.1016/j.optcom.2004.12.048	PROPN
ma-115	438	3	https://doi.org/10.1016/j.optcom.2004.12.048	https://doi.org/10.1016/j.optcom.2004.12.048	NOUN
ma-115	438	4	https://doi.org/10.1002/cpa.3160200102	https://doi.org/10.1002/cpa.3160200102	PROPN
ma-115	438	5	https://doi.org/10.1002/cpa.3160200102	https://doi.org/10.1002/cpa.3160200102	PROPN
ma-115	438	6	https://doi.org/10.1007/bf01646483	https://doi.org/10.1007/bf01646483	PROPN
ma-115	438	7	https://doi.org/10.1103/physreve.72.026610	https://doi.org/10.1103/physreve.72.026610	NOUN
ma-115	438	8	https://doi.org/10.1109/tassp.1985.1164579	https://doi.org/10.1109/tassp.1985.1164579	PROPN
ma-115	438	9	https://doi.org/10.1155/s0161171292000401	https://doi.org/10.1155/s0161171292000401	PROPN
ma-115	438	10	https://doi.org/10.1364/josaa.10.002181	https://doi.org/10.1364/josaa.10.002181	VERB
ma-115	438	11	https://doi.org/10.1093/imamat/26.2.187	https://doi.org/10.1093/imamat/26.2.187	X
ma-115	438	12	https://doi.org/10.1093/imamat/26.2.187	https://doi.org/10.1093/imamat/26.2.187	PROPN
ma-115	438	13	https://www.ias.ac.in/article/fulltext/pmsc/110/03/0293-0304	https://www.ias.ac.in/article/fulltext/pmsc/110/03/0293-0304	NOUN
ma-115	438	14	https://www.ias.ac.in/article/fulltext/pmsc/110/03/0293-0304	https://www.ias.ac.in/article/fulltext/pmsc/110/03/0293-0304	VERB
ma-115	438	15	https://doi.org/10.1080/10652460410001686055	https://doi.org/10.1080/10652460410001686055	VERB
ma-115	438	16	https://doi.org/10.1080/10652460410001686046	https://doi.org/10.1080/10652460410001686046	VERB
ma-115	438	17	https://doi.org/10.1080/10652460410001686046	https://doi.org/10.1080/10652460410001686046	NOUN
ma-115	438	18	https://doi.org/10.1121/1.384765	https://doi.org/10.1121/1.384765	PROPN
ma-115	438	19	eur	eur	PROPN
ma-115	438	20	.	.	PUNCT
ma-115	439	1	j.	j.	PROPN
ma-115	439	2	math	math	PROPN
ma-115	439	3	.	.	PUNCT
ma-115	440	1	anal	anal	PROPN
ma-115	440	2	.	.	PUNCT
ma-115	441	1	10.28924	10.28924	NUM
ma-115	441	2	/	/	SYM
ma-115	441	3	ada	ada	PROPN
ma-115	441	4	/	/	SYM
ma-115	441	5	ma.3.6	ma.3.6	PROPN
ma-115	441	6	18	18	NUM
ma-115	442	1	[	[	X
ma-115	442	2	14	14	NUM
ma-115	442	3	]	]	X
ma-115	442	4	r.	r.	PROPN
ma-115	442	5	rabenstein	rabenstein	PROPN
ma-115	442	6	,	,	PUNCT
ma-115	442	7	p.	p.	PROPN
ma-115	442	8	steffen	steffen	PROPN
ma-115	442	9	,	,	PUNCT
ma-115	442	10	s.	s.	PROPN
ma-115	442	11	spors	spor	NOUN
ma-115	442	12	,	,	PUNCT
ma-115	442	13	representation	representation	NOUN
ma-115	442	14	of	of	ADP
ma-115	442	15	two	two	NUM
ma-115	442	16	-	-	PUNCT
ma-115	442	17	dimensional	dimensional	ADJ
ma-115	442	18	wave	wave	NOUN
ma-115	442	19	fields	field	NOUN
ma-115	442	20	by	by	ADP
ma-115	442	21	multidimensional	multidimensional	ADJ
ma-115	442	22	signals	signal	NOUN
ma-115	442	23	,	,	PUNCT
ma-115	442	24	signal	signal	NOUN
ma-115	442	25	process	process	NOUN
ma-115	442	26	.	.	PUNCT
ma-115	443	1	86	86	NUM
ma-115	443	2	(	(	PUNCT
ma-115	443	3	2006	2006	NUM
ma-115	443	4	)	)	PUNCT
ma-115	443	5	,	,	PUNCT
ma-115	443	6	1341–1351	1341–1351	NUM
ma-115	443	7	.	.	PUNCT
ma-115	444	1	https://doi.org/10.1016/j.sigpro.2005.10.001.[15	https://doi.org/10.1016/j.sigpro.2005.10.001.[15	X
ma-115	444	2	]	]	X
ma-115	444	3	a.l	a.l	PROPN
ma-115	444	4	.	.	PROPN
ma-115	444	5	schwartz	schwartz	PROPN
ma-115	444	6	,	,	PUNCT
ma-115	444	7	an	an	DET
ma-115	444	8	inversion	inversion	NOUN
ma-115	444	9	theorem	theorem	NOUN
ma-115	444	10	for	for	ADP
ma-115	444	11	hankel	hankel	NOUN
ma-115	444	12	transforms	transform	VERB
ma-115	444	13	,	,	PUNCT
ma-115	444	14	proc	proc	NOUN
ma-115	444	15	.	.	PUNCT
ma-115	445	1	amer	amer	PROPN
ma-115	445	2	.	.	PUNCT
ma-115	445	3	math	math	PROPN
ma-115	445	4	.	.	PUNCT
ma-115	446	1	soc	soc	PROPN
ma-115	446	2	.	.	PUNCT
ma-115	447	1	22	22	NUM
ma-115	447	2	(	(	PUNCT
ma-115	447	3	1969	1969	NUM
ma-115	447	4	)	)	PUNCT
ma-115	447	5	,	,	PUNCT
ma-115	448	1	713–717	713–717	NUM
ma-115	448	2	.	.	PUNCT
ma-115	449	1	https	https	NOUN
ma-115	449	2	:	:	PUNCT
ma-115	449	3	//doi.org/10.1090	//doi.org/10.1090	ADJ
ma-115	449	4	/	/	SYM
ma-115	449	5	s0002	s0002	NOUN
ma-115	449	6	-	-	PUNCT
ma-115	449	7	9939	9939	NUM
ma-115	449	8	-	-	PUNCT
ma-115	449	9	1969	1969	NUM
ma-115	449	10	-	-	PUNCT
ma-115	449	11	0243294	0243294	NUM
ma-115	449	12	-	-	SYM
ma-115	449	13	0.[16	0.[16	NOUN
ma-115	449	14	]	]	PUNCT
ma-115	449	15	a.	a.	NOUN
ma-115	449	16	torre	torre	PROPN
ma-115	449	17	,	,	PUNCT
ma-115	449	18	linear	linear	ADJ
ma-115	449	19	and	and	CCONJ
ma-115	449	20	radial	radial	ADJ
ma-115	449	21	canonical	canonical	ADJ
ma-115	449	22	transforms	transform	NOUN
ma-115	449	23	of	of	ADP
ma-115	449	24	fractional	fractional	ADJ
ma-115	449	25	order	order	NOUN
ma-115	449	26	,	,	PUNCT
ma-115	449	27	j.	j.	PROPN
ma-115	449	28	comput	comput	PROPN
ma-115	449	29	.	.	PUNCT
ma-115	450	1	appl	appl	PROPN
ma-115	450	2	.	.	PROPN
ma-115	450	3	math	math	NOUN
ma-115	450	4	.	.	PUNCT
ma-115	451	1	153	153	NUM
ma-115	451	2	(	(	PUNCT
ma-115	451	3	2003	2003	NUM
ma-115	451	4	)	)	PUNCT
ma-115	451	5	,	,	PUNCT
ma-115	451	6	477–486	477–486	NUM
ma-115	451	7	.	.	PUNCT
ma-115	452	1	https://doi.org/10.1016/s0377-0427(02)00637-4.[17	https://doi.org/10.1016/s0377-0427(02)00637-4.[17	PROPN
ma-115	452	2	]	]	PUNCT
ma-115	452	3	a.	a.	NOUN
ma-115	452	4	torre	torre	PROPN
ma-115	452	5	,	,	PUNCT
ma-115	452	6	hankel	hankel	NOUN
ma-115	452	7	-	-	PUNCT
ma-115	452	8	type	type	NOUN
ma-115	452	9	integral	integral	ADJ
ma-115	452	10	transforms	transform	NOUN
ma-115	452	11	and	and	CCONJ
ma-115	452	12	their	their	PRON
ma-115	452	13	fractionalization	fractionalization	NOUN
ma-115	452	14	:	:	PUNCT
ma-115	452	15	a	a	DET
ma-115	452	16	note	note	NOUN
ma-115	452	17	,	,	PUNCT
ma-115	452	18	integr	integr	PROPN
ma-115	452	19	.	.	PROPN
ma-115	452	20	transforms	transform	VERB
ma-115	452	21	spec	spec	PROPN
ma-115	452	22	.	.	PUNCT
ma-115	453	1	funct	funct	PROPN
ma-115	453	2	.	.	PUNCT
ma-115	454	1	19(2008	19(2008	NUM
ma-115	454	2	)	)	PUNCT
ma-115	454	3	,	,	PUNCT
ma-115	454	4	277–292	277–292	NUM
ma-115	454	5	.	.	PUNCT
ma-115	455	1	https://doi.org/10.1080/10652460701827848.[18	https://doi.org/10.1080/10652460701827848.[18	PROPN
ma-115	455	2	]	]	X
ma-115	455	3	v.k	v.k	PROPN
ma-115	455	4	.	.	PROPN
ma-115	455	5	tuan	tuan	PROPN
ma-115	455	6	,	,	PUNCT
ma-115	455	7	on	on	ADP
ma-115	455	8	the	the	DET
ma-115	455	9	range	range	NOUN
ma-115	455	10	of	of	ADP
ma-115	455	11	the	the	DET
ma-115	455	12	hankel	hankel	NOUN
ma-115	455	13	and	and	CCONJ
ma-115	455	14	extended	extend	VERB
ma-115	455	15	hankel	hankel	NOUN
ma-115	455	16	transforms	transform	VERB
ma-115	455	17	,	,	PUNCT
ma-115	455	18	j.	j.	PROPN
ma-115	455	19	math	math	PROPN
ma-115	455	20	.	.	PUNCT
ma-115	456	1	anal	anal	PROPN
ma-115	456	2	.	.	PUNCT
ma-115	456	3	appl	appl	PROPN
ma-115	456	4	.	.	PUNCT
ma-115	457	1	209	209	NUM
ma-115	457	2	(	(	PUNCT
ma-115	457	3	1997	1997	NUM
ma-115	457	4	)	)	PUNCT
ma-115	457	5	,	,	PUNCT
ma-115	457	6	460–478	460–478	NUM
ma-115	457	7	.	.	PUNCT
ma-115	457	8	https://doi.org/10.1006/jmaa.1997.5351.[19	https://doi.org/10.1006/jmaa.1997.5351.[19	PROPN
ma-115	457	9	]	]	X
ma-115	458	1	c.r	c.r	PROPN
ma-115	458	2	.	.	PROPN
ma-115	458	3	wilson	wilson	PROPN
ma-115	458	4	,	,	PUNCT
ma-115	458	5	the	the	DET
ma-115	458	6	abel	abel	NOUN
ma-115	458	7	-	-	PUNCT
ma-115	458	8	fourier	fourier	NOUN
ma-115	458	9	method	method	NOUN
ma-115	458	10	of	of	ADP
ma-115	458	11	hankel	hankel	NOUN
ma-115	458	12	transformation	transformation	NOUN
ma-115	458	13	:	:	PUNCT
ma-115	458	14	applications	application	NOUN
ma-115	458	15	to	to	ADP
ma-115	458	16	seismic	seismic	ADJ
ma-115	458	17	data	datum	NOUN
ma-115	458	18	,	,	PUNCT
ma-115	458	19	geophys	geophy	NOUN
ma-115	458	20	.	.	PUNCT
ma-115	459	1	prospect.34	prospect.34	NOUN
ma-115	459	2	(	(	PUNCT
ma-115	459	3	1986	1986	NUM
ma-115	459	4	)	)	PUNCT
ma-115	459	5	,	,	PUNCT
ma-115	459	6	545–568	545–568	NUM
ma-115	459	7	.	.	PUNCT
ma-115	460	1	https://doi.org/10.1111/j.1365-2478.1986.tb00481.x.[20	https://doi.org/10.1111/j.1365-2478.1986.tb00481.x.[20	PROPN
ma-115	460	2	]	]	PUNCT
ma-115	461	1	k.b	k.b	PROPN
ma-115	461	2	.	.	PROPN
ma-115	461	3	wolf	wolf	PROPN
ma-115	461	4	,	,	PUNCT
ma-115	461	5	canonical	canonical	ADJ
ma-115	461	6	transforms	transform	NOUN
ma-115	461	7	.	.	PUNCT
ma-115	462	1	i.	i.	PROPN
ma-115	462	2	complex	complex	PROPN
ma-115	462	3	linear	linear	PROPN
ma-115	462	4	transforms	transform	VERB
ma-115	462	5	,	,	PUNCT
ma-115	462	6	j.	j.	PROPN
ma-115	462	7	math	math	PROPN
ma-115	462	8	.	.	PUNCT
ma-115	463	1	phys	phy	NOUN
ma-115	463	2	.	.	PUNCT
ma-115	464	1	15	15	NUM
ma-115	464	2	(	(	PUNCT
ma-115	464	3	1974	1974	NUM
ma-115	464	4	)	)	PUNCT
ma-115	464	5	,	,	PUNCT
ma-115	464	6	1295–1301	1295–1301	NUM
ma-115	464	7	.	.	PUNCT
ma-115	465	1	https://doi	https://doi	PROPN
ma-115	465	2	.	.	PUNCT
ma-115	466	1	org/10.1063/1.1666811.[21	org/10.1063/1.1666811.[21	PROPN
ma-115	466	2	]	]	X
ma-115	467	1	k.b	k.b	PROPN
ma-115	467	2	.	.	PROPN
ma-115	467	3	wolf	wolf	PROPN
ma-115	467	4	,	,	PUNCT
ma-115	467	5	canonical	canonical	ADJ
ma-115	467	6	transforms	transform	NOUN
ma-115	467	7	.	.	PUNCT
ma-115	468	1	ii	ii	X
ma-115	468	2	.	.	PUNCT
ma-115	469	1	complex	complex	ADJ
ma-115	469	2	radial	radial	ADJ
ma-115	469	3	transforms	transform	VERB
ma-115	469	4	,	,	PUNCT
ma-115	469	5	j.	j.	PROPN
ma-115	469	6	math	math	PROPN
ma-115	469	7	.	.	PUNCT
ma-115	470	1	phys	phy	NOUN
ma-115	470	2	.	.	PUNCT
ma-115	471	1	15	15	NUM
ma-115	471	2	(	(	PUNCT
ma-115	471	3	1974	1974	NUM
ma-115	471	4	)	)	PUNCT
ma-115	471	5	,	,	PUNCT
ma-115	471	6	2102–2111	2102–2111	NUM
ma-115	471	7	.	.	PUNCT
ma-115	472	1	https://doi	https://doi	PROPN
ma-115	472	2	.	.	PUNCT
ma-115	473	1	org/10.1063/1.1666590.[22	org/10.1063/1.1666590.[22	PROPN
ma-115	473	2	]	]	X
ma-115	473	3	a.h	a.h	PROPN
ma-115	473	4	.	.	PROPN
ma-115	473	5	zemanian	zemanian	PROPN
ma-115	473	6	,	,	PUNCT
ma-115	473	7	generalized	generalize	VERB
ma-115	473	8	integral	integral	ADJ
ma-115	473	9	transformations	transformation	NOUN
ma-115	473	10	,	,	PUNCT
ma-115	473	11	inter	inter	ADJ
ma-115	473	12	-	-	NOUN
ma-115	473	13	science	science	ADJ
ma-115	473	14	,	,	PUNCT
ma-115	473	15	new	new	PROPN
ma-115	473	16	york	york	PROPN
ma-115	473	17	,	,	PUNCT
ma-115	473	18	1968.[23	1968.[23	PROPN
ma-115	473	19	]	]	X
ma-115	473	20	d.	d.	PROPN
ma-115	473	21	zhang	zhang	PROPN
ma-115	473	22	,	,	PUNCT
ma-115	473	23	x.	x.	PROPN
ma-115	473	24	yuan	yuan	PROPN
ma-115	473	25	,	,	PUNCT
ma-115	473	26	n.	n.	PROPN
ma-115	473	27	ngo	ngo	PROPN
ma-115	473	28	,	,	PUNCT
ma-115	473	29	p.	p.	NOUN
ma-115	473	30	shum	shum	NOUN
ma-115	473	31	,	,	PUNCT
ma-115	473	32	fast	fast	ADJ
ma-115	473	33	hankel	hankel	NOUN
ma-115	473	34	transform	transform	NOUN
ma-115	473	35	and	and	CCONJ
ma-115	473	36	its	its	PRON
ma-115	473	37	application	application	NOUN
ma-115	473	38	for	for	ADP
ma-115	473	39	studying	study	VERB
ma-115	473	40	the	the	DET
ma-115	473	41	propagation	propagation	NOUN
ma-115	473	42	ofcylindrical	ofcylindrical	ADJ
ma-115	473	43	electromagnetic	electromagnetic	ADJ
ma-115	473	44	fields	field	NOUN
ma-115	473	45	,	,	PUNCT
ma-115	473	46	opt	opt	PROPN
ma-115	473	47	.	.	PUNCT
ma-115	474	1	express	express	VERB
ma-115	474	2	.	.	PUNCT
ma-115	475	1	10	10	NUM
ma-115	475	2	(	(	PUNCT
ma-115	475	3	2002	2002	NUM
ma-115	475	4	)	)	PUNCT
ma-115	475	5	,	,	PUNCT
ma-115	475	6	521	521	NUM
ma-115	475	7	-	-	SYM
ma-115	475	8	525	525	NUM
ma-115	475	9	.	.	PUNCT
ma-115	476	1	https://doi.org/10.1364/oe.10.000521	https://doi.org/10.1364/oe.10.000521	NOUN
ma-115	476	2	.	.	PUNCT
ma-115	477	1	https://doi.org/10.28924/ada/ma.3.6	https://doi.org/10.28924/ada/ma.3.6	PROPN
ma-115	477	2	https://doi.org/10.1016/j.sigpro.2005.10.001	https://doi.org/10.1016/j.sigpro.2005.10.001	PROPN
ma-115	477	3	https://doi.org/10.1090/s0002-9939-1969-0243294-0	https://doi.org/10.1090/s0002-9939-1969-0243294-0	AUX
ma-115	477	4	https://doi.org/10.1090/s0002-9939-1969-0243294-0	https://doi.org/10.1090/s0002-9939-1969-0243294-0	NOUN
ma-115	477	5	https://doi.org/10.1016/s0377-0427(02)00637-4	https://doi.org/10.1016/s0377-0427(02)00637-4	VERB
ma-115	477	6	https://doi.org/10.1080/10652460701827848	https://doi.org/10.1080/10652460701827848	PRON
ma-115	477	7	https://doi.org/10.1006/jmaa.1997.5351	https://doi.org/10.1006/jmaa.1997.5351	PROPN
ma-115	477	8	https://doi.org/10.1111/j.1365-2478.1986.tb00481.x	https://doi.org/10.1111/j.1365-2478.1986.tb00481.x	PROPN
ma-115	477	9	https://doi.org/10.1063/1.1666811	https://doi.org/10.1063/1.1666811	PROPN
ma-115	477	10	https://doi.org/10.1063/1.1666811	https://doi.org/10.1063/1.1666811	PROPN
ma-115	477	11	https://doi.org/10.1063/1.1666590	https://doi.org/10.1063/1.1666590	PROPN
ma-115	477	12	https://doi.org/10.1063/1.1666590	https://doi.org/10.1063/1.1666590	PROPN
ma-115	477	13	https://doi.org/10.1364/oe.10.000521	https://doi.org/10.1364/oe.10.000521	NOUN
ma-115	477	14	1	1	NUM
ma-115	477	15	.	.	PUNCT
ma-115	477	16	introduction	introduction	NOUN
ma-115	477	17	2	2	NUM
ma-115	477	18	.	.	PUNCT
ma-115	477	19	hankel	hankel	NOUN
ma-115	477	20	type	type	NOUN
ma-115	477	21	transforms	transform	VERB
ma-115	477	22	:	:	PUNCT
ma-115	477	23	3	3	X
ma-115	477	24	.	.	X
ma-115	477	25	hankel	hankel	NOUN
ma-115	477	26	-	-	PUNCT
ma-115	477	27	type	type	NOUN
ma-115	477	28	transforms	transform	NOUN
ma-115	477	29	of	of	ADP
ma-115	477	30	fractional	fractional	ADJ
ma-115	477	31	order	order	NOUN
ma-115	477	32	:	:	PUNCT
ma-115	477	33	4	4	X
ma-115	477	34	.	.	X
ma-115	477	35	properties	property	NOUN
ma-115	477	36	of	of	ADP
ma-115	477	37	a1,-,-2(+	a1,-,-2(+	NOUN
ma-115	477	38	)	)	PUNCT
ma-115	477	39	and	and	CCONJ
ma-115	477	40	a2,-,-2(+	a2,-,-2(+	NOUN
ma-115	477	41	):	):	PUNCT
ma-115	477	42	5	5	NUM
ma-115	477	43	.	.	PUNCT
ma-115	477	44	barut	barut	NOUN
ma-115	477	45	-	-	PUNCT
ma-115	477	46	girardello	girardello	NOUN
ma-115	477	47	-	-	PUNCT
ma-115	477	48	type	type	NOUN
ma-115	477	49	transformations	transformation	NOUN
ma-115	477	50	:	:	PUNCT
ma-115	477	51	6	6	NUM
ma-115	477	52	.	.	X
ma-115	477	53	barut	barut	NOUN
ma-115	477	54	-	-	PUNCT
ma-115	477	55	girardello	girardello	NOUN
ma-115	477	56	-	-	PUNCT
ma-115	477	57	type	type	NOUN
ma-115	477	58	transforms	transform	NOUN
ma-115	477	59	of	of	ADP
ma-115	477	60	fractional	fractional	ADJ
ma-115	477	61	order	order	NOUN
ma-115	477	62	:	:	PUNCT
ma-115	478	1	7	7	X
ma-115	478	2	.	.	NUM
ma-115	478	3	generalized	generalize	VERB
ma-115	478	4	hankel	hankel	NOUN
ma-115	478	5	transforms	transform	VERB
ma-115	478	6	:	:	PUNCT
ma-115	478	7	8	8	NUM
ma-115	478	8	.	.	PUNCT
ma-115	478	9	conclusions	conclusion	NOUN
ma-115	478	10	:	:	PUNCT
ma-115	478	11	references	reference	NOUN