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).