What does the integration variable t represent in the gamma function definition?

[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.