Possible to evaluate the gamma function analytically?

  • Thread starter LeBrad
  • Start date
  • #1
213
0
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.
 

Answers and Replies

  • #2
Yes, let me PM this to Ed Witten.
 
  • #3
mathman
Science Advisor
7,867
450
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]
 
  • #4
213
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?
 
  • #5
mathman
Science Advisor
7,867
450
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.
 

Related Threads on Possible to evaluate the gamma function analytically?

Replies
1
Views
1K
Replies
3
Views
716
Replies
11
Views
8K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
2
Views
830
Replies
6
Views
575
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
5
Views
2K
Top