NEW SEVEN-PARAMETER MITTAG-LEFFLER FUNCTION WITH CERTAIN ANALYTIC PROPERTIES

Abstract

In this paper, a new seven-parameter Mittag-Leffler function of a single complexvariable is proposed as a generalization of the standard Mittag-Leer function, certaingeneralizations of Mittag-Leffler function, hypergeometric function and conuent hypergeometricfunction. Certain essential analytic properties are mainly discussed, such as radiusof convergence, order, type, differentiation, Mellin-Barnes integral representation and Eulertransform in the complex plane. Its relation to Fox-Wright function and H-function is alsodeveloped.