Editing Inverse Laplace transform (section)

==Mellin's inverse formula==
An integral formula for the inverse [[Laplace transform]], called the ''Mellin's inverse formula'', the ''[[Thomas John I'Anson Bromwich|Bromwich]] integral'', or the ''[[Joseph Fourier|Fourier]]–[[Hjalmar Mellin|Mellin]] integral'', is given by the [[line integral]]:
:<math>f(t) = \mathcal{L}^{-1} \{F(s)\}(t) =  \frac{1}{2\pi i}\lim_{T\to\infty}\int_{\gamma-iT}^{\gamma+iT}e^{st}F(s)\,ds</math>
where the integration is done along the vertical line <math>\textrm{Re}(s) = \gamma</math> in the [[complex plane]] such that <math>\gamma</math> is greater than the real part of all [[Mathematical singularity|singularities]] of <math>F(s)</math> and <math>F(s)</math> is bounded on the line, for example if the contour path is in the [[region of convergence]]. If all singularities are in the left half-plane, or <math>F(s)</math> is an [[entire function]], then <math>\gamma</math> can be set to zero and the above inverse integral formula becomes identical to the [[inverse Fourier transform]].

In practice, computing the complex integral can be done by using the [[Cauchy residue theorem]].