A Practical Method for Computation of Laplace Inverses by Post–Widder’s Formula

Abstract

In this note, a novel method for parametric inversion of Laplace transforms by means of the Post–Widder formula is developed. In brief, the coefficients of the MacLaurin series equivalent of the sequence, which converges to Post–Widder's formula at infinity, are calculated by means of the iterated Aitken transform. Subsequently, the asymptotic values of such coefficients are obtained using the diagonal Padé approximants in a computationally efficient manner. Our method revives the classical Post–Widder formula from the practical viewpoint.

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