On the Zeros of $q$-Hankel Transform by Using P\'{o}lya-Hurwitz Partial Fraction Method
Number Theory
2025-12-11 v1 Complex Variables
Abstract
The technique of P\'{o}lya-Hurwitz of partial fractions is implemented to investigate the zeros of finite -Hankel transforms, which are defined in terms of the third -Bessel function of Jackson. The new approach, which is a -counterpart of P\'{o}lya-Hurwitz technique relaxes the restrictive conditions imposed on in the previously obtained results. In the present study, we use the -type sampling theorems of the -Hankel transforms, which lead directly to -partial fractions. Various experimental examples are established.
Keywords
Cite
@article{arxiv.2512.09002,
title = {On the Zeros of $q$-Hankel Transform by Using P\'{o}lya-Hurwitz Partial Fraction Method},
author = {Mahmoud Annaby and Shimaa Elsayed-Abdullah},
journal= {arXiv preprint arXiv:2512.09002},
year = {2025}
}
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14 pages