What do we mean when we say a gamma function has index v?

What is the density function of a gamma distribution with mean u and index v? I know this may be a very simple question, but there are so many parametrisations of the gamma distribution that it's confusing me. Thanks!

(I'm trying to show that the variance of a gamma distribution with mean u and index v is u^2 / v. I think this should be fairly manageable if I knew what the distribution was in the first place, and I haven't managed to find it elsewhere.)