I'm looking at the proof that $\Gamma(x,y) = \Gamma(x+y)B(x,y)$:
In the proof it is is assumed that $| J(z,t) | = z$. Why is this the case? What is $J(z,t)$?
Attempt: The substitution from $dudv$ in terms of $t$ and $z$ is roughly:
$$dudv = |\det(D \varphi)(t, z) | dtdz$$
though I'm not sure how to express $\varphi$.