Monotonicity, convexity properties and inequalities involving Gaussian hypergeometric functions with applications

Abstract

In this paper, we mainly prove monotonicity and convexity properties of certain functions involving zero-balanced Gaussian hypergeometric function F(a,b;a+b;x). We generalize conclusions of elliptic integral to Gaussian hypergeometric function, and get some accurate inequalities about Gaussian hypergeometric function.

Keywords

• gaussian hypergeometric function
• monotonicity
• convexity