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Math Help - Non integer factorial

  1. #1
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    Non integer factorial

    Hi all

    First thanks alot for all the help people offer on this forum, its really well appreciated

    I was wondering does anyone know how to evaluate a non integer factorial like 0.35! or 7.213!

    I was thinking of using the gamma function, but how to evaluate the recursive integral numerically?

    I welcome any advice

    chogo
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by chogo View Post
    Hi all

    First thanks alot for all the help people offer on this forum, its really well appreciated

    I was wondering does anyone know how to evaluate a non integer factorial like 0.35! or 7.213!

    I was thinking of using the gamma function, but how to evaluate the recursive integral numerically?

    I welcome any advice

    chogo
    As always the Wikipedia page is a good place to start.

    RonL
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  3. #3
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    Quote Originally Posted by chogo View Post
    Hi all

    First thanks alot for all the help people offer on this forum, its really well appreciated

    I was wondering does anyone know how to evaluate a non integer factorial like 0.35! or 7.213!

    I was thinking of using the gamma function, but how to evaluate the recursive integral numerically?

    I welcome any advice

    chogo
    As CaptainBlank said it is Euler's Grammer Function. It is really remarkable. It has great applications in applied math.

    Some interesting properties....
    1) (.5)!=\frac{\sqrt{\pi}}{2}.
    (I can prove this is you are familar with Multi-variable Calculus).

    2)(For differencial equations). The generalization of the Laplace transform for the power function y=x^n for n>-1 for non-integer values is,
    \mathcal{L} \{x^n\}=\frac{\Gamma(n+1)}{s^{n+1}}.

    This is really a remarkable function, one of my favorites (my favorite is the most ugliest function, Dirichlet Function).
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  4. #4
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    thanks for the help, its much appreciated.

    that euler grammer function is amazing thanks!, except im writting code which should be computationally efficient

    i found an approximation derived by Lanczos
    JSTOR: Options for Access to JSTOR

    i cant for the life of me understand that, but perhaps one of you guys might be interested. I think ill just stick with using eulers function even though it may be computationally inefficient

    thanks again guys
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