Any non-elementary gamma fcn formulas?

[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 Gauss multiplication formula, Stirling's asymptotic series for complex arguments, the Bohr-Mollerup Thm, the Residues at the poles... did I miss anything?

 

[shmoe]

How about the Hankel contour integral for 1/Gamma?

 

[benorin]

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

 

[tehno]

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 Gauss multiplication formula, Stirling's asymptotic series for complex arguments, the Bohr-Mollerup Thm, the Residues at the poles... did I miss anything?

To summarize all these approximations and take mean value?