Hypergeometric ₄F₃(1) with integral parameter differences

2022/02/09 by Dmitrii Karp, Karp, Dmitrii, E. G. Prilepkina +1
Mathematics · #33C20 #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2202.04388

openalex publication_date 2022/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we continue investigation of the hypergeometric function ₄F₃(1) as the function of its seven parameters. We deduce several reduction formulas for this function under additional conditions that one of the top parameters exceeds one of the bottom parameters by a positive integer or reversely one of the bottom parameters exceeds one of the top parameters by a positive integer or both. We show that all such cases reduce to the case of the unit parameter difference. The latter case, in turn, can be expressed in terms of certain linear combination of two series involving the logarithmic derivative of the gamma function.

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