A few finite and infinite identities involving Pochhammer and $q$- Pochhammer symbols obtained via analytical methods
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915267910565888 |
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| author | Szabłowski, Paweł J. |
| author_facet | Szabłowski, Paweł J. |
| contents | We present several identities with a form of polynomials or rational functions that involve Pochhammer and q-Pochhammer symbols and q-binomials (i.e. Gauss polynomials). All these identities were obtained by some analytical methods based on infinite expansions of the ratio of densities in a Fourier series of polynomials orthogonal with respect to the density in the denominator. We want a unified approach to justify many known and unknown identities. The purpose of studying these identities is to simplify calculations occurring while dealing with Pochhammer and q-Pochhammer symbols. Additional possible applications of the results presented in the paper are applications within the Combinatorics and the transformation formulae of hypergeometric and basic hypergeometric functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_00647 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A few finite and infinite identities involving Pochhammer and $q$- Pochhammer symbols obtained via analytical methods Szabłowski, Paweł J. Analysis of PDEs Primary 33B15, 33D50, Secondary 33C45, 26C16 We present several identities with a form of polynomials or rational functions that involve Pochhammer and q-Pochhammer symbols and q-binomials (i.e. Gauss polynomials). All these identities were obtained by some analytical methods based on infinite expansions of the ratio of densities in a Fourier series of polynomials orthogonal with respect to the density in the denominator. We want a unified approach to justify many known and unknown identities. The purpose of studying these identities is to simplify calculations occurring while dealing with Pochhammer and q-Pochhammer symbols. Additional possible applications of the results presented in the paper are applications within the Combinatorics and the transformation formulae of hypergeometric and basic hypergeometric functions. |
| title | A few finite and infinite identities involving Pochhammer and $q$- Pochhammer symbols obtained via analytical methods |
| topic | Analysis of PDEs Primary 33B15, 33D50, Secondary 33C45, 26C16 |
| url | https://arxiv.org/abs/2411.00647 |