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Math Help - Laplace transform of t^-h

  1. #1
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    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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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by nuno almeida View Post
    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
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  3. #3
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    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
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  4. #4
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    Quote Originally Posted by nuno almeida View Post
    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
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  5. #5
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    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
    Last edited by nuno almeida; July 28th 2008 at 06:58 AM.
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