The Double Laplace Transform Expressed in terms of the Lerch Transcendent
DOI:
https://doi.org/10.29020/nybg.ejpam.v14i3.3987Keywords:
Laplace transform, Lerch Transcendent, Contour integral, definite integralAbstract
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.Downloads
Published
2021-08-05
Issue
Section
Nonlinear Analysis
License
Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.
By agreeing to this statement, you acknowledge that:
- You retain full copyright over your work.
- The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
- This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.
How to Cite
The Double Laplace Transform Expressed in terms of the Lerch Transcendent. (2021). European Journal of Pure and Applied Mathematics, 14(3), 618-637. https://doi.org/10.29020/nybg.ejpam.v14i3.3987