Extension of incomplete gamma, beta and hypergeometric functions

Abstract

Recently, some extensions of the generalised gamma, beta, Gauss hypergeometric and confluent hypergeometric functions have been introduced. In this paper, we introduce generalisations of incomplete gamma, beta, Gauss, confluent and Appell's hypergeometric functions. Some integral representations, Mellin transforms, transformation formulae, differentiation formulae, difference formulae and fractional calculus formulae are obtained for these functions. © 2019 NSP.