THE EVALUATION OF INVERSE LAPLACE TRANSFORMS WITHOUT THE AID OF CONTOUR INTEGRATION.

摘要

A method due to van der Pol is extended to give a simple procedure for the evalua¬tion of the inverse Laplace transform of functions satisfying linear ordinary differential equations with polynomial coefficients. The range of transforms that can be dealt with using the method is quite wide, and no recourse is made to the normal Bromwich integral and contour integration techniques. Considerable use is made of the Tauber and Abel theorems, and extensions of the method are made to the inverse Laplace and Mellin transforms of a function that satisfies a linear difference equation with polynomial coefficients, and to the derivation of an operational rule that does not appear to have been given previously in the literature. A number of illustrative examples are included.