Inequalities and monotonicity properties for the gamma function (Q5946611)
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scientific article; zbMATH DE number 1659286
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Inequalities and monotonicity properties for the gamma function |
scientific article; zbMATH DE number 1659286 |
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Inequalities and monotonicity properties for the gamma function (English)
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19 May 2002
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gamma function
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inequalities
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monotonicity
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ultraspherical polynomials
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history
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After an extensive survey of previous results by the authors and others, they offer the inequalities NEWLINE\[NEWLINE\Gamma[1+x+(1/x)]/2\leq \Gamma(1+x)\Gamma[1+(1/x)]<\Gamma[1+x+(1/x)]NEWLINE\]NEWLINE \((x>0; \) equality on the left at \(x=1\)), counter examples to the left inequality for more terms and factors, and proof of a weakened form of that generalization.
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