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- All the applications I have found for physical applications of the gamma seem to be, to my untrained eye, only for real z (and mostly positive), with the Riemann zeta function being the only obvious exception. What am I missing?

An example of physical applications for the gamma (or beta) function(s) is

http://sces.phys.utk.edu/~moreo/mm08/Riddi.pdf

(I refer to the beta function related to the gamma function, not the other functions with this name)

The applications in Wikipedia

https://en.wikipedia.org/wiki/Gamma_function#Applications

https://en.wikipedia.org/wiki/Beta_function#Applications

seem also to be for real numbers (without non-positive integers), and mostly positive, except of course for the Riemann zeta function.

This is likely due to a lack of depth on my part, so could anyone indicate at least briefly where non-real complex values might be in the domain of a gamma function used in a physical application? Associated links with fuller explanations, while not absolutely necessary, are always an appreciated extra bonus. Thanks.

http://sces.phys.utk.edu/~moreo/mm08/Riddi.pdf

(I refer to the beta function related to the gamma function, not the other functions with this name)

The applications in Wikipedia

https://en.wikipedia.org/wiki/Gamma_function#Applications

https://en.wikipedia.org/wiki/Beta_function#Applications

seem also to be for real numbers (without non-positive integers), and mostly positive, except of course for the Riemann zeta function.

This is likely due to a lack of depth on my part, so could anyone indicate at least briefly where non-real complex values might be in the domain of a gamma function used in a physical application? Associated links with fuller explanations, while not absolutely necessary, are always an appreciated extra bonus. Thanks.