Abstract
We find two-sided bounds and prove non-negativeness 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, the incomplete normalized beta-function and the generalized hypergeometric series. This communication continues the research of various authors who investigated logarithmic convexity and concavity of hypergeometric functions in parameters.
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