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, \ie, 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：本文研究了系数等于一般序列与一个可通过Pochhammer符号表示的正参数显式函数的乘积的幂级数。我们处理了四类此类级数，证明了一般序列的对数凹性（凸性）可导致级数之和关于该显式函数自变量的对数凹性（凸性）。这种对数凹性（凸性）是从更强的性质推导得出的，即所谓广义Turánian的幂级数系数的正性（负性）。此外，本文还讨论了其在广义超几何函数和Fox-Wright函数等特殊函数中的应用。