The Generalized Gamma Distribution has p.d.f. defined as follows (see e.g. here for reference):
$$ f(t; \theta, k, \beta)=\frac{\beta }{\Gamma (k)\cdot \theta }{{\left( \frac{t}{\theta } \right)}^{k\beta -1}}{{e}^{-{{\left( \frac{t}{\theta } \right)}^{\beta }}}} $$
It's reported almost everywhere (for example here) that the log normal distribution is a special case for $k\rightarrow\infty$.
Anyway no information is given on how this log normal is determined.
In fact, log normal distribution is determined by two parameters $\mu$ and $\sigma^2$.
Please, can you help me to understand how to determine these two parameters starting from a generalized gamma distribution with known parameters and $k\rightarrow \infty$?