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Volume 14
Issue 11
10.3390/axioms14110847
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Article

On the Application of a Hypergeometric Identity to Generate Generalized Hypergeometric Reduction Formulas

by
Juan Luis González-Santander
Department of Mathematics, University of Oviedo, C/Leopoldo Calvo Sotelo 18, 33007 Oviedo, Spain
Axioms 2025, 14(11), 847; https://doi.org/10.3390/axioms14110847 (registering DOI)
Submission received: 13 October 2025 / Revised: 8 November 2025 / Accepted: 15 November 2025 / Published: 18 November 2025
(This article belongs to the Special Issue Recent Advances in Special Functions and Applications, 2nd Edition)
Versions Notes

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 with finite sums involving the psi function and a recursive formula for Bateman’s G function are derived. Finally, all the results have been numerically checked with MATHEMATICA.
Keywords: gamma function; psi function; Bateman’s G function; beta function; incomplete beta function; summation formulas for generalized hypergeometric functions gamma function; psi function; Bateman’s G function; beta function; incomplete beta function; summation formulas for generalized hypergeometric functions

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MDPI and ACS Style

González-Santander, J.L. On the Application of a Hypergeometric Identity to Generate Generalized Hypergeometric Reduction Formulas. Axioms 2025, 14, 847. https://doi.org/10.3390/axioms14110847

AMA Style

González-Santander JL. On the Application of a Hypergeometric Identity to Generate Generalized Hypergeometric Reduction Formulas. Axioms. 2025; 14(11):847. https://doi.org/10.3390/axioms14110847

Chicago/Turabian Style

González-Santander, Juan Luis. 2025. "On the Application of a Hypergeometric Identity to Generate Generalized Hypergeometric Reduction Formulas" Axioms 14, no. 11: 847. https://doi.org/10.3390/axioms14110847

APA Style

González-Santander, J. L. (2025). On the Application of a Hypergeometric Identity to Generate Generalized Hypergeometric Reduction Formulas. Axioms, 14(11), 847. https://doi.org/10.3390/axioms14110847

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