The Mexiner distribution with parameters
$\alpha$, $\beta$, $\delta$, and $\mu$
has density
$$f(x) = \kappa \,\exp(\beta(x-\mu)/\alpha)
\, |\Gamma\left(\delta+ i(x-\mu)/\alpha\right)|^2$$
where the normalization constant is given by
$$\kappa =
\frac{\left(2\cos\left(\beta/2\right)\right)^{2\delta}}{
2 \alpha \pi \, \Gamma\left(2 \delta\right)}$$ The symbol $i$ denotes the imaginary unit, that is, we have to
evaluate the gamma function $\Gamma(z)$ for complex
arguments $z= x + i\,y$.
Notice that $\alpha>0$, $|\beta| < \pi$
and $\delta>0$.
The domain of the distribution can be truncated to the
interval (lb,ub).