An Extension of Beta Function by Using Wiman’s Function

Rahul Goyal,Shaher Momani,Praveen Agarwal,Michael Th Rassias

doi:10.3390/axioms10030187

Abstract

The main purpose of this paper is to study extension of the extended beta function by Shadab et al. by using 2-parameter Mittag-Leffler function given by Wiman. In particular, we study some functional relations, integral representation, Mellin transform and derivative formulas for this extended beta function.

Highlights

Introduction and PreliminariesSpecial functions play important roles in science and engineering due its variety of applications; that is why many researchers have been working on them for many years [1,2,3,4,5,6,7,8]
In the last few years, the extension of the classical Euler beta function and gamma function has been an interesting topic for researchers due to their pivot role in advanced research
In this paper, motivated by Pucheta [14], Shadab et al [15] and Atash et al [16], we extend the extended beta function defined as (19) by using the 2-parameter Mittag-leffler function Er1,r2 (z) (Wiman’s function) given by (21)

Summary

Introduction

Special functions play important roles in science and engineering due its variety of applications; that is why many researchers have been working on them for many years [1,2,3,4,5,6,7,8]. The classical beta function is one of the most important member of the class of special functions, and it is known as the Euler Integral of first kind. It has a wide range of applications in science, especially in engineering mathematics. In the last few years, the extension of the classical Euler beta function and gamma function has been an interesting topic for researchers due to their pivot role in advanced research.

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Conclusion