On the Zeros of $q$-Hankel Transform by Using Pólya-Hurwitz Partial Fraction Method
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918240663371776 |
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| author | Annaby, Mahmoud Elsayed-Abdullah, Shimaa |
| author_facet | Annaby, Mahmoud Elsayed-Abdullah, Shimaa |
| contents | The technique of Pólya-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 Pólya-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09002 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Zeros of $q$-Hankel Transform by Using Pólya-Hurwitz Partial Fraction Method Annaby, Mahmoud Elsayed-Abdullah, Shimaa Number Theory Complex Variables 30D10, 30C15, 30D45, 39A13 The technique of Pólya-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 Pólya-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. |
| title | On the Zeros of $q$-Hankel Transform by Using Pólya-Hurwitz Partial Fraction Method |
| topic | Number Theory Complex Variables 30D10, 30C15, 30D45, 39A13 |
| url | https://arxiv.org/abs/2512.09002 |