The Riemann zeta function used in the inversion of the Laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Laguerre polynomials. The main contribution of our work is the development of a new and very effective method to evaluate the Laguerre coefficients with the use of the Riemann zeta function. Some examples are illustrated.