Communications of the
Korean Mathematical Society CKMS

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).