Some Results of Extended Beta Function and Hypergeometric Functions by Using Wiman’s Function

Abstract

The main aim of this research paper is to introduce a new extension of the Gauss hypergeometric function and confluent hypergeometric function by using an extended beta function. Some functional relations, summation relations, integral representations, linear transformation formulas, and derivative formulas for these extended functions are derived. We also introduce the logarithmic convexity and some important inequalities for extended beta function.

Keywords

• classical Euler beta function
• gamma function
• Gauss hypergeometric function
• confluent hypergeometric function
• Mittag-Leffler function