An Error Analysis and Convergence of a Quadrature Formula to Invert Laplace Transforms

The use of an expression for the exponential function exp(st)in Bromwich's integral, which incorporates a Padé approximation,yields a well known quadrature formula and its error terms.The error is then analysed for rational, transcendental andnon-rational Laplace transforms respectively and a convergencescheme is presented for rational transforms.