The Padé table and its connection with some weak exponential function approximations to laplace transform inversion
The Padé table to the Laplace transform is considered, the equivalence of the approximate Laplace transform inversion by the use of Padé approximants and some weak exponential function approximations to the inverse transform, is shown, and an oscillation theorem for the error is proved. A generalization to cover the case of multi-point Padé approximants and ordinary rational interpolation to the Laplace transform is also suggested. Prony's method of solving some non-linear equations is generalized.
Unable to display preview. Download preview PDF.