# Laplace transformation t^(3/2)

1. Nov 29, 2009

### jrsweet

1. The problem statement, all variables and given/known data
Just a quick question concerning a Laplace transformation...
Find the Laplace transform of the following function:
f(t)=10t3/2-e(-7t)

2. Relevant equations

3. The attempt at a solution
I wasn't sure what to do with the t3/2 so I just followed the formula for t1/2 and I got this:

(10pi(3/2))/(2s5/2)-(1/(s+7))

Is there anything wrong with this?

2. Nov 30, 2009

### Staff: Mentor

t1/2 and t3/2 are different functions, so it should be expected that their Laplace transforms would be different.
L{tk - 1} = $\Gamma$(k)/sk, where $\Gamma$ represents the gamma function.

$$\Gamma(z)~=~\int_0^{\infty} t^{z - 1}~e^{-t}dt$$
Hope that helps.