As you have written: "If you only meant the definition should be clearly stated, that is fine." which is exactly what I meant. And the reason that I meant it, is because the usual definition is not always clearly understood - otherwise we would not be having this discussion because the question...
Reply to lurflurf:
In the following n is an integer, x is a continuous variable (complex if you want).
That is exactly the point, and it is a very important one that comes up many places - quantum field theory being a prime example. The business of generalizing a function over a new...
The factorial notation only defined for positive interger arguments. It is a special case of the Gamma function and is only defined for positive integers where the two coincide. So, as someone else has replied (-1/2)! is meaningless on its own, so don't try to understand it as an infinite...
Hi:
Does anyone know of an explicit formula for the Real and Imaginary parts of GAMMA(1/2+I*y) as functions of y ?
I know about
|GAMMA(1/2+I*y)|^2 =Re(GAMMA(1/2+I*y))^2+Im(GAMMA(1/2+I*y))^2= Pi/cosh(Pi*y)
but can't find anything about each of the Real and Imaginary terms...