New operational relations between the original and the image for two-dimensional Laplace transforms involving a general class of polynomials, Fox’sH-function and the multivariableH-function are obtained. The result provides a unification of the bivariate Laplace transforms for theH-functions given by Chaurasia [2, 3].

A theorem concerning a product of a general class of polynomials and theH-function of several complex variables is given. Using this theorem certain integrals and expansion formula have been obtained. This general theorem is capable of giving a number of new, interesting and useful integrals, expansion formulae as its special cases.