Some inequalities of extended hypergeometric functions

Shilpi Jain; Rahul Goyal; Praveen Agarwal; Juan L.G. Guirao

doi:10.3390/math9212702

Some inequalities of extended hypergeometric functions

Shilpi Jain
, Rahul Goyal
, Praveen Agarwal
, Juan L.G. Guirao

Poornima College of Engineering
International College of Engineering
Harish Chandra Research Institute
International Center for Basic and Applied Sciences
Technical University of Cartagena
Faculty of Sciences, King Abdulaziz University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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.

Original language	English
Article number	2702
Journal	Mathematics
Volume	9
Issue number	21
DOIs	https://doi.org/10.3390/math9212702
State	Published - 1 Nov 2021
Externally published	Yes

Keywords

Classical Euler beta function
Confluent hypergeometric function
Gamma function
Gauss hypergeometric function
Log-concavity
Log-convexity
Mittag–Leffler function

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10.3390/math9212702

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title = "Some inequalities of extended hypergeometric functions",

abstract = "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 H{\"o}lder integral inequality and Chebyshev{\textquoteright}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.",

keywords = "Classical Euler beta function, Confluent hypergeometric function, Gamma function, Gauss hypergeometric function, Log-concavity, Log-convexity, Mittag{\textendash}Leffler function",

author = "Shilpi Jain and Rahul Goyal and Praveen Agarwal and Guirao, \{Juan L.G.\}",

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AU - Jain, Shilpi

AU - Goyal, Rahul

AU - Agarwal, Praveen

AU - Guirao, Juan L.G.

PY - 2021/11/1

Y1 - 2021/11/1

N2 - 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.

AB - 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.

KW - Classical Euler beta function

KW - Confluent hypergeometric function

KW - Gamma function

KW - Gauss hypergeometric function

KW - Log-concavity

KW - Log-convexity

KW - Mittag–Leffler function

UR - https://www.scopus.com/pages/publications/85118278109

U2 - 10.3390/math9212702

DO - 10.3390/math9212702

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AN - SCOPUS:85118278109

SN - 2227-7390

VL - 9

JO - Mathematics

JF - Mathematics

IS - 21

M1 - 2702

ER -

Some inequalities of extended hypergeometric functions

Abstract

Keywords

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