On a new (p,q)-Mtahieu type power series and its applications

Abstract

Our aim in this paper, is to establish certain new integrals for the the (p,q)-Mathieu--power series. In particular, we investigate the Mellin-Barnes type integral representations for a particular case of thus special function. Moreover, we introduce the notion of the (p,q)-Mittag-Leffler functions and we present a relationships between thus two functions. Some other applications are proved, in particular two Tur\'an type inequalities for the (p,q)-Mathieu series are proved.