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Possible to evaluate the gamma function analytically?

  1. Nov 22, 2003 #1
    Does anybody know if it's possible to evaluate the gamma function analytically? I know it becomes a factorial for integers, and there's a trick involving a switch to polar coordinates for half values, but what about any other number? I have tried using a Taylor expansion and residue integration, but neither seems to work. Just curious if it's possible.
     
  2. jcsd
  3. Nov 23, 2003 #2
    Yes, let me PM this to Ed Witten.
     
  4. Nov 23, 2003 #3

    mathman

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    There are several representations. The best known is in terms of an integral
    [tex]
    \Gamma (z) = \int_{0}^\infty t^{z-1} e^{-t} dt
    [/tex]
     
  5. Nov 23, 2003 #4
    I understand that, but I'm looking for a non-numerical solution to that integral for a value of z such as Pi. The integral is impossible to evaluate in closed form, but is there some other way?
     
  6. Nov 24, 2003 #5

    mathman

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    I can't claim expertize on the gamma function, but from what I have able to find, the only closed form values are for integer or half integer values of z.
     
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