Rational extension of Newton diagram for the positivity of ${}_1F_2$ hypergeometric functions and Askey-Szeg\"o problem

Yong-Kum Cho; Seok-Young Chung; Hera Yun

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arXiv · 1805.11855

Rational extension of Newton diagram for the positivity of ${}_1F_2$ hypergeometric functions and Askey-Szeg\"o problem

Yong-Kum Cho·Seok-Young Chung·Hera Yun

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Abstract

We present a rational extension of Newton diagram for the positivity of ${}_1F_2$ generalized hypergeometric functions. As an application, we give upper and lower bounds for the transcendental roots $\beta(\alpha)$ of \begin{align*} \int_0^{j_{\alpha, 2}} t^{-\beta} J_\alpha(t) dt = 0\qquad(-1<\alpha\le 1/2), \end{align*} where $j_{\alpha, 2}$ denotes the second positive zero of Bessel function $J_\alpha$.

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Yong-Kum Cho, Seok-Young Chung, Hera Yun. 2018-05-30. Rational extension of Newton diagram for the positivity of ${}_1F_2$ hypergeometric functions and Askey-Szeg\"o problem. https://arxiv.org/abs/1805.11855

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