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

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...

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Bibliographic Details
Published in:Axioms Vol. 13; no. 5; p. 317
Main Authors: Li, Yue-Wu, Qi, Feng
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.05.2024
Subjects:
Closed form solutions
closed-form formula
contiguous function
Equality
Euler integral representation
Exact solutions
Expressions (Mathematics)
Functions, Hypergeometric
Gauss hypergeometric function
Hypergeometric functions
Lerch transcendent
Power series
Series expansion
specific argument
China
ISSN:2075-1680, 2075-1680
Online Access:Get full text
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Summary: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.
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content type line 14
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms13050317