In this paper, we study power series with coefficients equal to a product of a generic sequence and an explicitly given function of a positive parameter expressible in terms of the Pochhammer symbols. Four types of such series are treated. We show that logarithmic concavity (convexity) of the generic sequence leads to logarithmic concavity (convexity) of the sum of the series with respect to the argument of the explicitly given function. The logarithmic concavity (convexity) is derived from a stronger property, namely, positivity (negativity) of the power series coefficients of the so-called generalized Tur\'{a}nian. Applications to special functions such as the generalized hypergeometric function and the Fox-Wright function are also discussed.

翻译：本文研究系数为一般序列与用Pochhammer符号表示的正参数显式函数之积的幂级数，并处理了四类此类级数。研究表明，一般序列的对数凹性（凸性）可导出其级数之和关于显式函数自变量的对数凹性（凸性）。该对数凹性（凸性）源于更强的性质，即广义Turán型幂级数系数的正性（负性）。本文还讨论了这些结果在广义超几何函数和Fox-Wright函数等特殊函数中的应用。