An extension of the Whittaker function
Commun. Korean Math. Soc.
Published online March 8, 2021
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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