Inverse Laplace transform problem

1. Aug 25, 2009

xlines

Hello!

I am trying to solve a PDE for it's Green function, I found myself in a position to know G(is) where "i" is imaginary unit, G(s) is a Laplace transform of g(t) and g(t) is the Green's function I am after. So, I've been snooping around and found Mellin's inverse formula at

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

Should I insert variable transform of s = -i*u over there and setting gamma to zero, I find that green's function g(t) is a Fourier transform of G(-iu) divided by a factor. If I can make sure I can set gamma to zero, is this procedure "legal"?

Any input or suggestion is appriciated!

Last edited: Aug 25, 2009