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Bromwich integral

In mathematics, the Bromwich integral of F(s) is the function f(t) which has the property


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.