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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Bibliographic Details
Published in:Constructive approximation 2020-02, Vol.51 (1), p.49-72
Main Authors: Cho, Yong-Kum, Chung, Seok-Young, Yun, Hera
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
Numerical Analysis
Online Access:Get full text
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Summary: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 .
ISSN:0176-4276
1432-0940
DOI:10.1007/s00365-019-09462-5