We prove that many of beta, beta prime, gamma, inverse gamma, Student t- and ultraspherical distributions are freely infinitely divisible, but some of them are not. The latter negative result follows from a local property of probability density functions. Moreover, we show that the Gaussian, many of ultraspherical and Student t-distributions have free divisibility indicator 1.
"Free infinite divisibility for beta distributions and related ones." Electron. J. Probab. 19 1 - 33, 2014. https://doi.org/10.1214/EJP.v19-3448