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Monotonicity results for the Gamma function. (English) Zbl 1059.33004
After exhaustive background description, the authors offer the following results. The fuctions \(x\mapsto \Gamma(x+1)^{1/x}(x+1)^{-1/2}\) and \(x\mapsto \Gamma(x+1)^{1/x}x^{-1/2}\) are strictly increasing on \([1,\infty[\) or \([2,\infty[,\) respectively, while \(x\mapsto \Gamma(x+1)^{1/x}(x+1)^{-1}\) is strictly decreasing on \([1,\infty[.\) The paper closes with 29 references.

MSC:
33B15 Gamma, beta and polygamma functions
26A48 Monotonic functions, generalizations
26D07 Inequalities involving other types of functions
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