Some Inequalities of Extended Hypergeometric Functions

Shilpi Jain, Rahul Goyal, Praveen Agarwal and Juan L. G. Guirao
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Shilpi Jain: Department of Mathematics, Poornima College of Engineering, Jaipur 302021, India
Rahul Goyal: Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India
Praveen Agarwal: Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India
Juan L. G. Guirao: Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, Hospital de Marina, 30203 Murcia, Spain

Mathematics, 2021, vol. 9, issue 21, 1-10

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.

Keywords: gamma function; classical Euler beta function; Gauss hypergeometric function; confluent hypergeometric function; Mittag–Leffler function; log-convexity; log-concavity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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