# Carson transform

From Encyclopedia of Mathematics

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 .

#### Comments

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

#### References

[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: http://www.encyclopediaofmath.org/index.php?title=Carson_transform&oldid=17141

This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article