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1990•International Journal of Mathematical Education in Science and TechnologyRequires access

A note on the inversion of Laplace transforms

Amaresh Chakrabarti

Open publisher page 2 citations

Abstract

A direct method, using a Mellin transform technique, is presented to derive the solution of a special class of first kind integral equations over the positive real axis, and as a particular case, an inversion formula is deduced for the Laplace transform F(p) of a function f(x) (x>0), when F(p) is known only for p>0.

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What this paper is about

A direct method, using a Mellin transform technique, is presented to derive the solution of a special class of first kind integral equations over the positive real axis, and as a particular case, an inversion formula is deduced for the Laplace transform F(p) of a function f(x) (x>0), when F(p) is known only for p>0.

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OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

A direct method, using a Mellin transform technique, is presented to derive the solution of a special class of first kind integral equations over the positive real axis, and as a particular case, an inversion formula is deduced for the Laplace transform F(p) of a function f(x) (x>0), when F(p) is known only for p>0.

Key concepts: Mellin transform, Laplace transform, Post's inversion formula, Two-sided Laplace transform, Mellin inversion theorem, Inversion (geology), Laplace transform applied to differential equations, Inverse Laplace transform

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