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arXiv · 1104.4442

Complete monotonicity of a function involving the gamma function and applications

Feng Qi
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Abstract

In the article we present necessary and sufficient conditions for a function involving the logarithm of the gamma function to be completely monotonic and apply these results to bound the gamma function $Γ(x)$, the $n$-th harmonic number $\sum_{k=1}^n\frac1k$, and the factorial $n!$.

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Feng Qi. 2011-04-22. Complete monotonicity of a function involving the gamma function and applications. https://doi.org/10.1007/s10998-014-0056-x

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