The New Mittag-Leffler Function and Its Applications

Abstract

In this paper, we investigate some properties of the Pochhammer p,s,k-symbol ξn,k,sp and gamma p,s,k-function Γs,kpξ. We then prove several identities for newly defined symbol ξn,k,sp and the function Γs,kpξ. The integral representations for the gamma p,s,k-function and beta p,s,k-function are presented. Also, we define a new Mittag-Leffler p,s,k-function and study its analytic properties and its transforms.