# Bromwich integral

From Example Problems

In mathematics, the **Bromwich integral** or inverse Laplace transform of *F(s)* is the function *f(t)* which has the property

where is the Laplace transform. The Bromwich integral is thus sometimes simply called the **inverse Laplace transform**.

The Laplace transform and the inverse Laplace transform together have a number of properties that make them useful for analysing linear dynamic systems.

The Bromwich integral, also called the **Fourier-Mellin integral**, is a path integral defined by:

where the integration is done along the vertical line *x*=*c* in the complex plane such that *c* is greater than the real part of all singularities of *F(s)*.

The name is for Thomas John I'Anson Bromwich (1875-1929).

## See also

## External links

- Tables of Integral Transforms at EqWorld: The World of Mathematical Equations.

## Bibliography

- A. D. Polyanin and A. V. Manzhirov,
*Handbook of Integral Equations*, CRC Press, Boca Raton, 1998. ISBN 0-8493-2876-4nl:Inverse laplacetransformatie