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 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