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Rational Extension of the Newton Diagram for the Positivity of 1F2 Hypergeometric Functions and Askey–Szegö Problem
We present a rational extension of the Newton diagram for the positivity of 1 F 2 generalized hypergeometric functions. As an application, we give upper and lower bounds for the transcendental roots β ( α ) of ∫ 0 j α , 2 t - β J α ( t ) d t = 0 ( - 1 < α ≤ 1 / 2 ) , where j α , 2 denotes the sec...
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| Published in: | Constructive approximation 2020-02, Vol.51 (1), p.49-72 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| container_end_page | 72 |
| container_issue | 1 |
| container_start_page | 49 |
| container_title | Constructive approximation |
| container_volume | 51 |
| creator | Cho, Yong-Kum Chung, Seok-Young Yun, Hera |
| description | We present a rational extension of the Newton diagram for the positivity of
1
F
2
generalized hypergeometric functions. As an application, we give upper and lower bounds for the transcendental roots
β
(
α
)
of
∫
0
j
α
,
2
t
-
β
J
α
(
t
)
d
t
=
0
(
-
1
<
α
≤
1
/
2
)
,
where
j
α
,
2
denotes the second positive zero of Bessel function
J
α
. |
| doi_str_mv | 10.1007/s00365-019-09462-5 |
| format | article |
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1
F
2
generalized hypergeometric functions. As an application, we give upper and lower bounds for the transcendental roots
β
(
α
)
of
∫
0
j
α
,
2
t
-
β
J
α
(
t
)
d
t
=
0
(
-
1
<
α
≤
1
/
2
)
,
where
j
α
,
2
denotes the second positive zero of Bessel function
J
α
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1
F
2
generalized hypergeometric functions. As an application, we give upper and lower bounds for the transcendental roots
β
(
α
)
of
∫
0
j
α
,
2
t
-
β
J
α
(
t
)
d
t
=
0
(
-
1
<
α
≤
1
/
2
)
,
where
j
α
,
2
denotes the second positive zero of Bessel function
J
α
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1
F
2
generalized hypergeometric functions. As an application, we give upper and lower bounds for the transcendental roots
β
(
α
)
of
∫
0
j
α
,
2
t
-
β
J
α
(
t
)
d
t
=
0
(
-
1
<
α
≤
1
/
2
)
,
where
j
α
,
2
denotes the second positive zero of Bessel function
J
α
.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00365-019-09462-5</doi><tpages>24</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0176-4276 |
| ispartof | Constructive approximation, 2020-02, Vol.51 (1), p.49-72 |
| issn | 0176-4276 1432-0940 |
| language | eng |
| recordid | cdi_springer_journals_10_1007_s00365_019_09462_5 |
| source | Springer Link |
| subjects | Analysis Mathematics Mathematics and Statistics Numerical Analysis |
| title | Rational Extension of the Newton Diagram for the Positivity of 1F2 Hypergeometric Functions and Askey–Szegö Problem |
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