English

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 qq-Hankel transforms, which are defined in terms of the third qq-Bessel function of Jackson. The new approach, which is a qq-counterpart of P\'{o}lya-Hurwitz technique relaxes the restrictive conditions imposed on qq in the previously obtained results. In the present study, we use the qq-type sampling theorems of the qq-Hankel transforms, which lead directly to qq-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