Gamma

[LeBrad]

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.

[PrudensOptimus]

Yes, let me PM this to Ed Witten.

[mathman]

There are several representations. The best known is in terms of an integral

\Gamma (z) = \int_{0}^\infty t^{z-1} e^{-t} dt

[LeBrad]

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]

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.