A note on an open problem

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Published: Jun 30, 2012
DOI: https://doi.org/10.5556/j.tkjm.43.2012.1184
Keywords:
Gamma function $ \psi $ function polygamma function complete monotonicity

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Miao-Qing An

Abstract

The function $\frac{\Gamma(x+1)^{\frac1x}}{(x+\beta)^{\alpha}}$ is logarithmically completely monotonic on $(0,\infty)$ for $\alpha\ge1$ and $0\le\beta\le1$, and is logarithmically completely monotonic in $(-1,0)$ for $0<\alpha\le \frac{2\beta}{1+2\beta}$ and $\beta>1$. This give an answer to an open problem proposed by Feng Qi.

Article Details

How to Cite
An, M.-Q. (2012). A note on an open problem. Tamkang Journal of Mathematics, 43(2), 281–287. https://doi.org/10.5556/j.tkjm.43.2012.1184
Issue
Vol. 43 No. 2 (2012)
Section
Papers

References

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