Rational Extension of the Newton Diagram for the Positivity of 1 F 2 Hypergeometric Functions and Askey–Szegö Problem

초록

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 ∫0jα,2t-βJα(t)dt=0(-1<α≤1/2),where j α , 2 denotes the second positive zero of Bessel function J α . © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

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