Complete monotonicity of a function involving the gamma function and applications

Details Complete monotonicity of a function involving the gamma function and applications Complete monotonicity of a function involving the gamma function and applications

2011-04-22

arxiv.org/abs/1104.4442v1

Mathematics

Classical Analysis and ODEs

11 pages

Scientific paper

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 $\Gamma(x)$, the $n$-th
harmonic number $\sum_{k=1}^n\frac1k$, and the factorial $n!$.

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