Algebraic inversion of the Laplace transform

A new algebraic scheme for inverting Laplace transforms of smooth functions is presented. Expansion of the Laplace transform F(s) in descending powers of s is used to construct the Taylor series of the corresponding time function f(t). This is done through entirely algebraic evaluations of F(s) at s179-185c points around circles in the complex plane. Test functions are used to examine the method and the results show good convergence over a broad region near t = 0. The method is especially well-suited to computer-based inversion of Laplace transform.