Inversion Formula by Application of Laplace & Mellin transforms

U. K. Bajpai, Manish Kumar Srivastava

Abstract: In this paper, we have established proof of two theorems on inversion formula by application of Laplace operators & Fox's method. The given integral equation can be reduced in terms of the inverse Mellin transforms of the unknown function and consequently the solution is then readily obtained by repeated applications of Laplace and inverse Laplace operators. The result established in this paper, further acts as the key formula for a large number of integral equations associated with Gauss's hypergeometric functions due to the general character of the H-function.

Keywords: H-Transformation, Laplace Transforms, Mellin Transforms, Contour, Inversion Formula