Numerical laplace inversion of (s2+a2)−(n+½)(s2+b2)−m

Abstract

A numerical method is developed for the computation of a function H _mn (t) which is the Laplace-inverse function of (s ²+a ²)^−(n−½)(s ²+b ²)^−m The method consists of expanding the function H _mn (t) in a series whose typical term is associated with a Bessel-like functions G _i (a t). A simple technique, suitable for the purpose, is developed for the computation of the function G _i (a t). A few typical results for H _mn (t) are given.