Inequalities for the gamma and polygamma functions
Author offers an extension, with new proof, of a result by \textit{G. D. Anderson} and \textit{S.-L. Qiu} [Proc. Am. Math. Soc. 125, No. 11, 3355-3362 (1997; Zbl 0881.33001)] of the strict increasing of \(\log (\Gamma(x+1))/(x\log x),\) from \(]1,\infty[\) to \(]0,\infty[,\) furthermore inequalities for \(\psi^{(n)}(x+1)-\psi^{(n)}(x+s) (\psi=\Gamma'/\Gamma)\) with \(s\in]0,1[\) and for Euler's \(C=\lim_{n\to\infty} (\sum_{k=1}^n(1/k) - \log n)\).
scientific article; zbMATH DE number 1416669
scientific article