A Further Extension of Gamma and Beta Functions Involving Generalized Mittag-Leffler Function and its Applications

Abstract

Recently, many researchers have proposed different extensions of gamma, beta, confluent hypergeometric, and Gauss hypergeometric functions. Our aim is to study another extension of gamma and beta functions related to the generalized Mittag-Leffler function. We also study some functional relations, integral representations and Mellin transforms.Some special cases of obtained results are considered and shown to further reduce to some known results.