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

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