Gamma Function: Definition & Properties

[Tiiba]

The definition of this function is
Gamma(z) = integral(0, inf)(t^(z-1)e^(-t) dt)

Well, I can't understand what the t stands for. The only parameter is z... Is it an arbitrary number?

 

[arildno]

Your integrand is a function of TWO variables:
f(z,t)=t^{z-1}e^{-t}
When you integrate f(z,t) over the t-domain, (0\leq{t}<\infty) , what you are left with, is a function of z alone:
\Gamma(z)=\int_{0}^{\infty}f(z,t)dt

 

[Tiiba]

I think I get it. Thanks.