Possible to evaluate the gamma function analytically?

  • Thread starter LeBrad
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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.
 
Yes, let me PM this to Ed Witten.
 

mathman

Science Advisor
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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]
 
212
0
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?
 

mathman

Science Advisor
7,692
389
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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