Absolutely monotonic functions involving the zero-balanced Gaussian hypergeometric functions with applications

Let F ( a , b ; a + b ; x ) be the Gaussian hypergeometric function and F p ( x ) = ( 1 − x ) p exp ( F ( a , b ; a + b ; x ) ) . This article aims to extend the work of Zhen-Hang Yang and Jing-Feng Tian to a more generalized case involving zero-balanced Gaussian hypergeometric functions. We prove t...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2025; no. 1; pp. 25 - 15
Main Authors Sun, Chuanlong, Wang, Zixuan, Huang, Tiren
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 27.02.2025
Springer Nature B.V
SpringerOpen
Subjects
Absolute monotonicity
Analysis
Applications of Mathematics
Gaussian hypergeometric function
Hypergeometric functions
Inequality
Mathematics
Mathematics and Statistics
Monotone functions
Zero-balanced
Absolute monotonicity
40A05
26A48
33E05
29B62
Gaussian hypergeometric function
Zero-balanced
Inequality
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Summary:Let F ( a , b ; a + b ; x ) be the Gaussian hypergeometric function and F p ( x ) = ( 1 − x ) p exp ( F ( a , b ; a + b ; x ) ) . This article aims to extend the work of Zhen-Hang Yang and Jing-Feng Tian to a more generalized case involving zero-balanced Gaussian hypergeometric functions. We prove the sufficient and necessary conditions for the absolute monotonicity of − ( ln F p ) ′ , ln F p , − ( F p ) ′ and F p . These results ultimately yield several new inequalities involving the zero-balanced Gaussian hypergeometric functions.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-025-03275-w