Wendel's and Gautschi's inequalities: refinements, extensions, and a class of logarithmically completely monotonic functions (Q2378765)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Wendel's and Gautschi's inequalities: refinements, extensions, and a class of logarithmically completely monotonic functions |
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Wendel's and Gautschi's inequalities: refinements, extensions, and a class of logarithmically completely monotonic functions (English)
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14 January 2009
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Sufficient and necessary conditions are presented that a class of functions involving ratios of Euler's gamma function and originating from Wendel's and Gautschi's inequalities are logarithmically completely monotonic. From this, Wendel's, Gautschi's, Kershaw's, Laforgia's, Bustoz-Ismail's, Merkle's and Elezović-Giordano-Pečarić's inequalities are refined, extended and sharpened, and a double inequality on the divided differences of the psi and polygamma function is deduced straightforwardly.
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sufficient and necessary condition
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logarithmically completely monotonic function
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inequality
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ratio of gamma functions
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exponential function
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psi function
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polygamma function
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