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arXiv · 2411.00647

A few finite and infinite identities involving Pochhammer and $q$- Pochhammer symbols obtained via analytical methods

Paweł J. Szabłowski
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Abstract

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.

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Paweł J. Szabłowski. 2024-11-01. A few finite and infinite identities involving Pochhammer and $q$- Pochhammer symbols obtained via analytical methods. https://arxiv.org/abs/2411.00647

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