On the log-concavity of the Wright function (Q6629542)

The purpose of this article is to investigate the log-concavity on the half-line of the Wright function. First it is proved that a certain random variable is unimodal. Then it is proved that the density of this random variable is log-concave under certain conditions. The proofs use fractional integration, Fubini's theorem, Prékopa-Leindler theorem, Yamazato property, Legendre duplication, multiplicative convolution, Hölder's inequality, Cuculescu-Theodorescu theorem, Mittag-Leffler functions and some hypergeometric transformations.