Department of Mathematics, Municipal Post Graduate College, Mussoorie, Dehradun, Uttarakhand, India-248179
2010 AMS Mathematics Subject Classification: Primary: 33 B15, 33B 20, 33B 99, 33C 15, 33 C 65, 33 C 70, 33 C 99. Secondary: 35 A 22, 44 A 10
A few days back, while working on the Extended Beta and Gamma functions of matrix arguments [1], the present author has found a relation between the generalized incomplete gamma function of Chaudhry and Zubair [2] and one of the Humbert's confluent hypergeometric functions of two variables. We show in the present note that the Laplace transform of the generalized incomplete gamma function of Chaudhry and Zubair [2] can be evaluated in terms of this Humbert's function. The result which we establish in this paper for the special functions concerned with scalar arguments will be generalized to the case of matrix arguments in a further communication of this author in the near future.
Generalized incomplete gamma function, Laplace transform, Humbert's function-Confluent hypergeometric function
