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

TL;DR

This paper introduces a new hypergeometric identity that enables the derivation of novel summation formulas, including those involving the psi function and Bateman's G function, with numerical validation.

Contribution

It presents a generalized hypergeometric identity that leads to new summation formulas and recursive relations, expanding the tools for hypergeometric function analysis.

Findings

New hypergeometric summation formulas derived

Recursive formula for Bateman's G function established

Numerical validation with MATHEMATICA confirms results

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.