Inequalities and monotonicity for the ratio of gamma functions. (Q1432837)
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scientific article; zbMATH DE number 2076838
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Inequalities and monotonicity for the ratio of gamma functions. |
scientific article; zbMATH DE number 2076838 |
Statements
Inequalities and monotonicity for the ratio of gamma functions. (English)
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22 June 2004
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Let \(\Gamma\) be the Euler gamma function. The authors prove that \[ f_y(x)= [\Gamma(x+ y+ 1)/\Gamma(y+ 1)]^{1/x}/(x+ y+ 1) \] is a decreasing function of \(x\geq 1\), for any fixed \(y\geq 0\).
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Euler's gamma function
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Stirling's formula
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