# Inverse Laplace Transform: 1/Sqrt[s-a]

• June 22nd 2008, 01:29 PM
Inverse Laplace Transform: 1/Sqrt[s-a]
How do I find the inverse Laplace transform of 1/Sqrt[s-a] ?

I'm completely stuck on this problem because I'm not even sure what transformation properties I should use to begin with.

Thanks.
• June 22nd 2008, 01:59 PM
CaptainBlack
Quote:

How do I find the inverse Laplace transform of 1/Sqrt[s-a] ?

I'm completely stuck on this problem because I'm not even sure what transformation properties I should use to begin with.

Thanks.

You look it up in a table of standard forms:

$\mathcal{L} \left(\frac{t^{n-1}e^{at}}{\Gamma (n)} \right) = \frac{1}{(s-a)^n}, \ n>0$

RonL