Work

Hypergeometric ${}_4F_3(1)$ with integral parameter differences

Year: 2022

Type: preprint

Abstract: In this paper we continue investigation of the hypergeometric function ${}_4F_3(1)$ 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2202.04388

Authors: Karp, Dmitrii, Prilepkina, Elena

Institution: Holon Institute of Technology

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Russian Foundation for Basic Research, Ministry of Science and Higher Education of the Russian Federation

Awards: G1524342187, G3366096296, G6116214918

OpenAlex ID: W4221151133

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