A New Closed-Form Formula of the Gauss Hypergeometric Function at Specific Arguments-Reference-Cited by-同舟云学术

A New Closed-Form Formula of the Gauss Hypergeometric Function at Specific Arguments

Published:2024-05-10 Issue:5 Volume:13 Page:317
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Li Yue-Wu¹^ORCID,Qi Feng²³^ORCID

Affiliation:

1. School of Mathematics and Physics, Hulunbuir University, Hulunbuir 021008, China

2. School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, China

3. Independent Researcher, University Village, Dallas, TX 75252, USA

Abstract

In this paper, the authors briefly review some closed-form formulas of the Gauss hypergeometric function at specific arguments, alternatively prove four of these formulas, newly extend a closed-form formula of the Gauss hypergeometric function at some specific arguments, successfully apply a special case of the newly extended closed-form formula to derive an alternative form for the Maclaurin power series expansion of the Wilf function, and discover two novel increasing rational approximations to a quarter of the circular constant.

Funder

Doctors Foundation of Hulunbuir University

Publisher

MDPI AG

Link

https://www.mdpi.com/2075-1680/13/5/317/pdf

Reference38 articles.

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