On free infinite divisibility for classical Meixner distributions

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

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