The Double Laplace Transform Expressed in terms of the Lerch Transcendent

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DOI:

https://doi.org/10.29020/nybg.ejpam.v14i3.3987

Keywords:

Laplace transform, Lerch Transcendent, Contour integral, definite integral

Abstract

In this manuscript, the authors derive a formula for the double Laplace transform expressed in terms of the Lerch Transcendent. The log term mixes the variables so that the integral is not separable except for special values of k. The method of proof follows the method used by us to evaluate single integrals. This transform is then used to derive definite integrals in terms of fundamental constants, elementary and special functions. A summary of the results is produced in the form of a table of definite integrals for easy referencing by readers.

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How to Cite

Reynolds, R., & Stauffer, A. (2021). The Double Laplace Transform Expressed in terms of the Lerch Transcendent. European Journal of Pure and Applied Mathematics, 14(3), 618–637. https://doi.org/10.29020/nybg.ejpam.v14i3.3987

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