2008 / September Volume 3 No.3
An elementary inequality for psi function
| Published Date |
2008 / September
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|---|---|
| Title | An elementary inequality for psi function |
| Author | |
| Keyword | |
| Download | |
| Pagination | 373-380 |
| Abstract | For $x>0$, let $\Gamma(x)$ be the Euler's gamma function, and $\Psi(x) = \frac {\Gamma'(x)}{\Gamma(x)}$ be the psi function. In this paper, we prove that $(b-L(a,b)) \Psi(b) + (L(a,b)-a) > (b-a) \Psi(\sqrt{ab})$ for $ b > a \ge 2$, where $L(a,b) = \frac {b-a}{\log b - \log a}$.
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| AMS Subject Classification |
33B15, 26D15
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| Received |
2007-10-30
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| Accepted |
2007-10-31
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