Stable convergence acceleration using Laplace transforms

Summary We consider the general class of power series where the terms may be expressed as the Laplace transforms of known functions. The sum of the series can then be evaluated efficiently and accurately by means of quadrature schemes, recently published by Frank Stenger. The method works also far outside the region of convergence as will be illustrated by numerical examples.Dedicated to Professor Lothar Collatz on the occasion of his 75th birthday