Inequalities and monotonicity for the ratio of gamma functions.
Let \(\Gamma\) be the Euler gamma function. The authors prove that \[ f_y(x)= [\Gamma(x+ y+ 1)/\Gamma(y+ 1)]^{1/x}/(x+ y+ 1) \] is a decreasing function of \(x\geq 1\), for any fixed \(y\geq 0\).
scientific article; zbMATH DE number 2076838