Inversion of the multi-dimensional Laplace transform-expansion by Laguerre series

In this paper an algorithm to numerically invert two-dimensional Laplace transform known in closed form as an analytic function is presented. The method is based on expanding the inverse function in a series of products of (generalized) Laguerre polynomials. It is based on the method by Weeks (1966) and the generalized version presented by Piessens and Branders (1971) for the one-dimensional case.