Laplace transforms for superexponential functions

New Laplace transforms of Kummer's confluent hypergeometric functions

In this paper we aim to show how one can obtain so far unknown Laplace transforms of three rather general cases of Kummer’s confluent hypergeometric function 1F1(a; b; x) by employing generalizations of Gauss’s second summation theorem, Bailey’s summation theorem and Kummer’s summation theorem obtained earlier by Lavoie, Grondin and Rathie. The results established may be useful in theoretical p...

The h-Laplace and q-Laplace transforms

Article history: Received 12 May 2009 Available online 6 October 2009 Submitted by B.S. Thomson

Laplace Transforms for Numericalinversion via Continued

It is often possible to e ectively calculate cumulative distribution functions and other quantities of interest by numerically inverting Laplace transforms. However, to do so it is necessary to compute the Laplace transform values. Unfortunately, convenient explicit expressions for required transforms are often unavailable. In that event, we show that it is sometimes possible to nd continued-fr...

Algorithms for Unequally Spaced Fast Laplace Transforms

Vol. 1 (2013) pp. 37-46. ALGORITHMS FOR UNEQUALLY SPACED FAST LAPLACE TRANSFORMS FREDRIK ANDERSSON⇤ Abstract. We develop fast algorithms for unequally spaced discrete Laplace transforms with complex parameters, which are approximate up to prescribed choice of computational precision. The algorithms are based on modifications of algorithms for unequally spaced fast Fourier transforms using Gauss...

The Fekete-Szego Coefficient Functional for Transforms of Analytic Functions