INTERNATIONAL JOURNAL OF ENGINEERING, SCIENCE AND - Volume 6, Issue 8, December 2017

Pages: 133-139
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A NOTE ON THE LAPLACE TRANSFORM OF THE GENERALIZED INCOMPLETE GAMMA FUNCTION

Author: Lalit Mohan Upadhyaya

Category: Engineering, Science and Mathematics

Abstract:

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.

Keywords: Generalized incomplete gamma function Laplace transform Humbert's function Confluent hypergeometric function