Logarithmic convexity and inequalities for the gamma function
We propose a method, based on logarithmic convexity, for producing sharp bounds for the ratio \(\Gamma(x+ \beta)/\Gamma(x)\). As an application, we present an inequality that sharpens and generalizes some previously known ones, in particular the well known one due to \textit{W. Gautschi} [J. Math. Phys. 38, 77-81 (1959; Zbl 0094.04104)].
scientific article; zbMATH DE number 944359