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arXiv · 2311.04385

Partial fraction expansions and zeros of Hankel transforms

Yong-Kum Cho·Seok-Young Chung·Young Woong Park
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Abstract

It is proved by the method of partial fraction expansions and Sturm's oscillation theory that the zeros of certain Hankel transforms are all real and distributed regularly between consecutive zeros of Bessel functions. As an application, the sufficient or necessary conditions on parameters for which ${}_1F_2$ hypergeometric functions belong to the Laguerre-P\'olya class are investigated in a constructive manner.

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Yong-Kum Cho, Seok-Young Chung, Young Woong Park. 2023-11-07. Partial fraction expansions and zeros of Hankel transforms. https://arxiv.org/abs/2311.04385

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