/sci/ - Science & Math

a) Is it valide to write the Melling type inverse formula

<span class="math">f(t) = \frac{1}{2\pi i}\lim_{T\to\infty}\int_{\gamma-iT}^{\gamma+iT}e^{st}F(s)\,ds[/spoiler]

http://en.wikipedia.org/wiki/Inverse_Laplace_transform

as

<span class="math">f(t) = ie^{\gamma t} \frac{1}{2\pi i}\lim_{T\to\infty}\int_{-T}^{T}e^{iwt}F(iw+\gamma)\,dw[/spoiler]

?

b) I know that the general formula of the inverse Mellin transform relates to the Cauchy formula (I mean there is the 2pi i there, so that must be related to integrating around singularities in some way) but I really don't see it.
I've can someone shine light on this?

http://vimeo.com/41009719

he /sci/
what causes this amazing shit.