# Any non-elementary gamma fcn formulas?

1. Jun 5, 2006

### benorin

I'm writing a paper which includes a treatment of the gamma function, and I am taking suggestions for non-elementary formulae involving the gamma function. I have the usual limit of a product definition, two infinite products, the usual improper integrals for Re[z]>0, the Guass multiplication formula, Stirling's asymptotic series for complex arguements, the Bohr-Mollerup Thm, the Residues at the poles... did I miss anything?

2. Jun 6, 2006

### shmoe

How about the Hankel contour integral for 1/Gamma?

3. Jun 6, 2006

### benorin

Thanks, shmoe! I did miss one. I also got the reflection formula, though I forgot to mention it.

4. Jun 7, 2006

### tehno

:surprised
To summarize all these approximations and take mean value?

Last edited: Jun 7, 2006