On the application of a hypergeometric identity to generate generalized hypergeometric reduction formulas

2025/08/19 by Juan Luis González‐Santander, González-Santander, J. L.
Computer Science · Mathematics · #33B15 #33B20 #33C05 #33C10 #33C15 #33C20 #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2508.13897

openalex publication_date 2025/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We systematically exploit a new generalized hypergeometric identity to obtain new hypergeometric summation formulas. As a consistency test, alternative proofs for some special cases are also provided. As a byproduct new summation formulas involving finite sums involving the psi function, or a recursive formula for the Bateman's G function are derived. Finally, all the results have been numerically checked with MATHEMATICA.

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