(It should be ).
Yes, but the beautiful Gamma function is defined for complex numbers with real part positive as well.
But I am afraid I cannot do this. I do not even want to try. MathWorld has so many identities and non involving imaginary numbers.
Shouldn't the contour integration of this function should be the same as in the real case? I'm not even going to try it, but that might be a possible way to evaluate it.
I have the numerical value of Gamma(i). Its modulus is an elementary
function: Sqrt(pi/sinh(pi)).
So its real and imaginary parts COULD be elementary functions too, but
I haven't been able to find them.
Bob.
Last edited by bobbyk; September 24th 2007 at 02:53 PM.
Reason: Add signature.
Shouldn't the contour integration of this function should be the same as in the real case? I'm not even going to try it, but that might be a possible way to evaluate it.
(sigh) I can't find a picture of the contour on the net. But the gamma function may be integrated using complex integration. I was wondering if it could be used for this problem.