In this paper, we introduce a generalized form of Whittaker function with the help of generalized confluent k-hypergeometric function. We establish several interesting properties of the Whittaker k-function such as its integral representations, derivative, Laplace transform and Hankel transform. Further, we investigate the Riemann-Liouville fractional integral and k-Riemann-Liouville fractional integral of Whittaker k-function. Some intriguing particular cases of the main results are also mentioned.
Keywords and Phrases
k-Gamma function, k-Beta function, Confluent k-hypergeometric function, Whittaker function, Laplace transform, Hankel transform and Riemann-Liouville fractional integral.
A.M.S. subject classiﬁcation
33B15, 33C15, 26A33.