Operational calculus in two variables and special functions

In this paper, we establish few operational relations between the original and the image for two dimensional Laplace transforms whose kernel involve the product of the general polynomials S-m1,...,mR(I1,...,IR) (x(1),...,x(R)), a general class of multivariable polynomials S-N1(Mr+1,...,Mr') (-y(r+1,...,-yr')), Fox' s H-function and the multivariable H-function. A unification of the bivariate Laplace transform for the H-function given by Chaurasia(2, 3) is provided by the results established here. The importance of the present study lies in the fact that it unifies and extends the results of a large number of authors.