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arXiv · 2512.09002

On the Zeros of $q$-Hankel Transform by Using P\'{o}lya-Hurwitz Partial Fraction Method

Mahmoud Annaby·Shimaa Elsayed-Abdullah
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Abstract

The technique of P\'{o}lya-Hurwitz of partial fractions is implemented to investigate the zeros of finite $q$-Hankel transforms, which are defined in terms of the third $q$-Bessel function of Jackson. The new approach, which is a $q$-counterpart of P\'{o}lya-Hurwitz technique relaxes the restrictive conditions imposed on $q$ in the previously obtained results. In the present study, we use the $q$-type sampling theorems of the $q$-Hankel transforms, which lead directly to $q$-partial fractions. Various experimental examples are established.

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Mahmoud Annaby, Shimaa Elsayed-Abdullah. 2025-12-09. On the Zeros of $q$-Hankel Transform by Using P\'{o}lya-Hurwitz Partial Fraction Method. https://arxiv.org/abs/2512.09002

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