CONVERGENCE OF PIESSEN METHOD FOR NUMERICAL INVERSION OF THE LAPLACE TRANSFORM ON THE REAL LINE

A method proposed by Piessens [J. Inst. Math. Appl., 10 (1972), pp. 185-192] for numerical inversion of the Laplace transform on the real line is shown to converge exponentially fast for transforms F(s) = s-γ G(s) with γ > 0 and G(s) analytic at ∞. The based on an orthogonal polynomial expansion for the transform F(s). Convergence is obtained for a broad class of orthogonal polynomials with the Jacobi polynomial expansions of the original formulation as a special case. Implications for practical use are discussed.