Certain Properties Associated with Generalized $M$-Series using Hadamard Product

Abstract

The generalized $M$-series is a hybrid function of generalized Mittag-Leffler function and generalized hypergeometric function. The principal aim of this paper is to investigate certain properties resembling those of the Mittag-Leffler and Hypergeometric functions including various differential and integral formulas associated with generalized $M$-series. Certain corollaries involving the generalized hypergeometric function are also discussed. Further, in view of Hadamard product of two analytic functions, we have represented our main findings in Hadamard product of two known functions.

Keywords

• beta function
• gamma function
• mittag-leffler function
• hypergeometric function
• generalized $m$-series
• hadamard product