Re: [math-fun] The function g(z) = e*(GAMMA(z+1/2)/sqrt(2*pi))^(1/z)... two amazing observations

Also, all you need to do is to prove all the CF coefficients are positive -- in order instantly to prove that the sequence of odd-numbered convergents, and the sequence of even-numbered convergents, of the CF both converge for all positive z. (The two might converge to two different values; proving the two limits are the same, or assessing the rate of convergence, both will be tougher.) For practical purposes I think this CF converges, in the sense that if it diverges, it doesn't happen for quite a while :)