Bromwich Integral

The inverse of the Laplace Transform, given by

$$F(t)={1\over 2\pi i}\int^{\gamma+i\infty}_{\gamma-i\infty} e^{st} f(s)\,ds,$$

where $\gamma$ is a vertical Contour in the Complex Plane chosen so that all singularities of $f(s)$ are to the left of it.

References

Arfken, G. ``Inverse Laplace Transformation.'' §15.12 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 853-861, 1985.