On free infinite divisibility for classical Meixner distributions

Abstract: We prove that symmetric Meixner distributions, whose probability densities are proportional to $|\Gamma(t+ix)|^2$, are freely infinitely divisible for $0<t\leq\frac{1}{2}$. The case $t=\frac{1}{2}$ corresponds to the law of L\'evy's stochastic area whose probability density is $\frac{1}{\cosh(\pi x)}$. A logistic distribution, whose probability density is proportional to $\frac{1}{\cosh^2(\pi x)}$, is freely infinitely divisible too.