Math Help - Laplace transform of t^-h

1. Laplace transform of t^-h

Is there a closed form solution for the Laplace transform of a power function with a negative exponent?
Thanks much

2. Originally Posted by nuno almeida
Is there a closed form solution for the Laplace transform of a power function with a negative exponent?
Thanks much
Don't quote me but I think only if -h>-1. Gamma function

3. Yes, I've encoutered L{t^p} = Gamma(p+1) / s^(p+1) for p>-1 , but I'm dealing with a fractal dimension which most probably is <-1.
Thanks anyway

4. Originally Posted by nuno almeida
Is there a closed form solution for the Laplace transform of a power function with a negative exponent?
Thanks much
The Laplace operator is not going to converge if <-1

5. Ohhh, I see.
Any thoughts then about analytically solve x*x^-h, being h a real constant, x the dependent variable and * the convolution operation?
Thanks much