An extension of the Whittaker function Commun. Korean Math. Soc. 2021 Vol. 36, No. 4, 705-714 https://doi.org/10.4134/CKMS.c200311 Published online March 8, 2021 Printed October 31, 2021 Junesang Choi, Kottakkaran Sooppy Nisar, 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 : Primary 33B20, 33C20; Secondary 33B15, 33C05 Supported by : The authors would like express their deep-felt thanks for the reviewer's favorable and constructive comments. The first-named author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2020R111A1A01052440). Downloads: Full-text PDF   Full-text HTML