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Bromwich Integral




:\mathcal{L}\left\{ f(t) ight\} = F(s),

where \mathcal{L} 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 System s.

The Bromwich integral, also called the Fourier-Mellin integral, is a Path Integral defined by:

:f(t) = rac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}F(s)e^{st}\,ds,\quad t>0,

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).


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BIBLIOGRAPHY

  • A. D. Polyanin and A. V. Manzhirov, ''Handbook of Integral Equations'', CRC Press, Boca Raton, 1998. ISBN 0-8493-2876-4