On the properties of the $(p,\nu )$-extension of the Whittaker function $M_{\kappa ,\mu }(z)$

Abstract

In this paper, we obtain a $(p,\nu )$-extension of the Whittaker function $M_{\kappa ,\mu }(z)$ by using the extended confluent hypergeometric function of the first kind ${\Phi }_{p,\nu }(b;c;z)$ introduced in Parmar et al. [J. Classical Anal. 11 (2017) 81--106]. Also, we derive some of the main properties of this function, namely several integral representations, a summation formula, the analogue of Kummer's transformation formula, an asymptotic representation, the Mellin transform, a differential formula and some inequalities.

11 pages, 0 figures

References in corpus (1)

• A $(p,\nu )$-extension of the Appell function $F_1(\cdot )$ and its properties