Some Inequalities of Extended Hypergeometric Functions

Hypergeometric functions and their inequalities have found frequent applications in various fields of mathematical sciences. Motivated by the above, we set up certain inequalities including extended type Gauss hypergeometric function and confluent hypergeometric function, respectively, by virtue of...

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Bibliographic Details
Published inMathematics (Basel) Vol. 9; no. 21; p. 2702
Main Authors Jain, Shilpi, Goyal, Rahul, Agarwal, Praveen, Guirao, Juan L. G.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.11.2021
Subjects
Chebyshev approximation
classical Euler beta function
Concavity
confluent hypergeometric function
Convexity
Food science
gamma function
Gauss hypergeometric function
Hypergeometric functions
Inequalities
Inequality
log-convexity
Mathematical functions
Mittag–Leffler function
Theorems
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Summary:Hypergeometric functions and their inequalities have found frequent applications in various fields of mathematical sciences. Motivated by the above, we set up certain inequalities including extended type Gauss hypergeometric function and confluent hypergeometric function, respectively, by virtue of Hölder integral inequality and Chebyshev’s integral inequality. We also studied the monotonicity, log-concavity, and log-convexity of extended hypergeometric functions, which are derived by using the inequalities on an extended beta function.
ISSN:2227-7390
2227-7390
DOI:10.3390/math9212702