# (p, q)-EXTENSION OF THE WHITTAKER FUNCTION AND ITS CERTAIN PROPERTIES

• Dar, Showkat Ahmad (Department of Applied Sciences and Humanities Faculty of Engineering and Technology Jamia Millia Islamia (Central University)) ;
• Shadab, Mohd (Department of Applied Sciences and Humanities Faculty of Engineering and Technology Jamia Millia Islamia (Central University))
• Accepted : 2017.11.02
• Published : 2018.04.30

#### Abstract

In this paper, we obtain a (p, q)-extension of the Whittaker function $M_{k,{\mu}}(z)$ together with its integral representations, by using the extended confluent hypergeometric function of the first kind ${\Phi}_{p,q}(b;c;z)$ [recently extended by J. Choi]. Also, we give some of its main properties, namely the summation formula, a transformation formula, a Mellin transform, a differential formula and inequalities. In addition, our extension on Whittaker function finds interesting connection with the Laguerre polynomials.

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