Convexity and inequalities related to extended beta and confluent hypergeometric functions

Abstract

In the paper, the authors establish the logarithmic convexity and some inequalities for the extended beta function and, by using these inequalities for the extended beta function, find the logarithmic convexity and the monotonicity for the extended confluent hypergeometric function.

Keywords

• extended beta function
• extended confluent hypergeometric function
• inequality
• logarithmic convexity
• monotonicity