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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Vydáno v:Axioms Ročník 13; číslo 5; s. 317
Hlavní autoři: Li, Yue-Wu, Qi, Feng
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 01.05.2024
Témata:
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
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Popis
Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms13050317