2024/11/01 by Paweł J. Szabłowski, Szabłowski, Paweł J.
Mathematics · #26C16 #33D50 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical functions and polynomials #Primary 33B15 #Secondary 33C45
paper · pdf · doi:10.48550/arxiv.2411.00647
openalex publication_date 2024/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.