Abstract: We give a short account on the methods for numerical inversion of the Laplace transform and also propose a new method. Our method is inspired and motivated from a problem of the evaluation of the M\" untz polynomials (see [1]), as well as the construction of the generalized Gaussian quadrature rules for the M\"untz systems (see [2]). As an illustration of our method we consider an example with 100 real poles distributed uniformly on (-1/2,100). A numerical investigation shows the efficiency of the proposed method.
Keywords: Laplace transform, Bromwich integral, orthogonal polynomials, Gaussian quadrature formula.