Any advanced mathematicians out there?

Question

I am trying to evaluate the Bromwich integral which computes the inverse Laplace transform of a given function. The integral is as follows:

/c+i*infinity
|
I F(s)*exp(s*t) dt
|
/ c-i*infinity

where F(s)= s^p/(s^2+1)^q
p and q are positive, c is greater than the real part of all the singularities of F(s), and i^2=-1.

So the integration is done along the vertical line x=c in the complex plane.

I appreciate all answers or hints. If you can't work with F(s), substitute values for p and q and work with that.

Basically we are taking the inverse laplace transform. So if a=1, p=0 and q=1 then the integral simply becomes sin(t). But I need to generalise the result for 00.

Answer 1

To be honest, I'm no mathmetician. Not even close! Apparently your quest for knowledge far exceeds my ability to give you the answer you're looking for. But you can look here:
http://www.allexperts.com/browse.cgi?catLvl=1&catID=37
Just select the right category, and ask the question. You will receive an answer to your email (generally within 3 days). Good luck!

Answer 2

http://mathworld.wolfram.com/BromwichIntegral.html

Substitute F(s) and the constraints and have a good time.