# Bromwich integral

In

mathematics, the

**Bromwich integral** 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)*.

See also Inverse Fourier transform.