A formula to solve Laplace and Fourier Transforms

Among many contributions to science, Pierre-Simon Laplace developed his famous Transform as Jean-Baptiste Joseph Fourier with his very famous Fourier Transform. In this article a method is presented to easily solve the Fourier and Laplace Transform and their inverses. This General Formula is applica...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2023-10, Vol.431, p.115235, Article 115235
Main Authors: Morales-Castillo, Javier, Morales-Rodriguez, Eva M.
Format: Article
Language:English
Subjects:
Fourier Transform
Inverse symbolic operators
Laplace Transform
ODEs
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Summary:Among many contributions to science, Pierre-Simon Laplace developed his famous Transform as Jean-Baptiste Joseph Fourier with his very famous Fourier Transform. In this article a method is presented to easily solve the Fourier and Laplace Transform and their inverses. This General Formula is applicable to integrals that contain an exponential function multiplied by a derivable Function. Functions such as the Normal, Gamma and Beta could be solved too with some mathematical artifices. The methodology is presented step by step in this article. •A unique formula to solve Laplace Transform and the inverse.•This formula can be applicable to solve gamma, normal and other functions.•This formula can be applicable to solve Fourier Transform and the inverse Transform.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2023.115235