An extension of the Whittaker function
Commun. Korean Math. Soc.
Published online December 29, 2020
Junesang Choi, Kottakkaran Sooppy Nisar, and Gauhar Rahman
Dongguk University, Prince Sattam bin Abdulaziz University, Hazara University
Abstract : The Whittaker function and its diverse extensions have been
actively investigated. Here we aim to introduce an extension of
the Whittaker function by using the known extended confluent hypergeometric function
$\Phi_{p,v}$ and investigate some of its formulas such as
integral representations, a transformation formula, Mellin transform, and a differential formula.
Some special cases of our results are also considered.
Keywords : Beta function; Extended Beta function, Confluent hypergeometric function; Extended confluent hypergeometric function; Hypergeometric function; Extended hypergeometric function; Whittaker function; Extended Whittaker function; Mellin transform
MSC numbers : 33B20, 33C20, 33B15, 33C05
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