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

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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

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Don't quote me but I think only if -h>-1. Gamma function

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(Happy)

Quote:

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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

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The Laplace operator is not going to converge if <-1

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