On the Application of a Hypergeometric Identity to Generate Generalized Hypergeometric Reduction Formulas

We systematically exploit a new generalized hypergeometric identity to obtain new hypergeometric summation formulas. As a consistency test, alternative proofs for some special cases are also provided. As a byproduct, new summation formulas with finite sums involving the psi function and a recursive...

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Vydáno v:Axioms Ročník 14; číslo 11; s. 847
Hlavní autor: González-Santander, Juan Luis
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 01.11.2025
Témata:
Bateman’s G function
beta function
Consistency tests
gamma function
incomplete beta function
psi function
Recursive functions
summation formulas for generalized hypergeometric functions
ISSN:2075-1680, 2075-1680
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Shrnutí:We systematically exploit a new generalized hypergeometric identity to obtain new hypergeometric summation formulas. As a consistency test, alternative proofs for some special cases are also provided. As a byproduct, new summation formulas with finite sums involving the psi function and a recursive formula for Bateman’s G function are derived. Finally, all the results have been numerically checked with MATHEMATICA.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms14110847