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2F1(a,b,c,z)= gamma function. What I mean is that the hypergeometric function converges to a set of gamme functions function in terms of (a,b,c)

where z is not 1,-1, or 1/2 ?

The hypergeometric identities in the mathworld summary which give gamma functions only have values of 1,-1, and 1/2 for Z but none others.

I have seen hypergeometric functions where z=1/8,1/3, 2/3 etc that give gamma functions but have no idea how to deive them despite many months of time and research.