Elementary Laplace

1. Oct 21, 2008

2RIP

Hi

1. The problem statement, all variables and given/known data
L[f] = (s)^(1/2)

3. The attempt at a solution
Is there actually an elementary laplace transform that can compute this? I tried using derivative to solve for it, but i'll always be stuck with a fractional exponent.

Thanks

2. Oct 22, 2008

jhicks

The best thing I could think of is using the convolution rule, i.e. (F(s)G(s) = f(t)*g(t)) where * is convolution. Let F(s)=G(s)=s^(1/2), then F(s)G(s) = s. Can you do the laplace transform of s?

3. Oct 22, 2008

2RIP

Oh, our class hasn't got to that section yet. Maybe I'll be able to solve it tomorrow then. Thanks.

4. Oct 22, 2008

2RIP

I think i might have just thought of something. Would it work if i first took the derivative. Then used the gamma function to compute the inverse laplace transform?

5. Oct 22, 2008

jhicks

The gamma function isn't in a form that is immediately obvious to me to see how it relates to what you have to evaluate.