A numerical method for locating the abscissa of convergence of a laplace transform function with no singularity at infinity

The knowledge of the abscissa of convergence σ0 of a Laplace Transform function F(s), is of primary interest in the field of the numerical inversion of the Laplace Transform itself. In this paper we propose a method for locating σ0 when F(s) has no singularity at infinity. The method actually finds an approximation of the real part of the rightmost singularity of F(s). The method is essentially based on a particular Moebius transformation which maps the extended complex plane into itself; this transformation allows us to build a sequence of values which converges to σ0.