Sergei Kalmykov (Shanghai Jiao Tong University & Keldysh Institute): Log-convexity and log-concavity for series in gamma ratios and applications

We discuss bounds of Taylor coefficients for the Turán determinants of power series with coefficients involving the ratio of gamma-functions. We consider these series as functions of simultaneous shifts of the arguments of the gamma-functions located in the numerator and the denominator. The results are then applied to derive new inequalities for the Gauss hypergeometric function, modified Bessel function, the incomplete normalized beta-function, and the generalized hypergeometric series. It is based on joint research with D. Karp

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