Carson transform

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The result of transformation of a function defined for and vanishing when , into the function

where is a complex variable. The inversion formula is

The difference between the Carson transform of and its Laplace transform is the presence of the factor .


Two well-known references for the Laplace transformation are [a1], which stresses the theory, and [a2], which stresses applications.


[a1] D.V. Widder, "The Laplace transform" , Princeton Univ. Press (1972)
[a2] G. Doetsch, "Introduction to the theory and application of the Laplace transformation" , Springer (1974) (Translated from German)
How to Cite This Entry:
Carson transform. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article