Some properties of the \(k\)-gamma function (Q2871250)
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scientific article; zbMATH DE number 6249033
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some properties of the \(k\)-gamma function |
scientific article; zbMATH DE number 6249033 |
Statements
22 January 2014
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\(k\)-gamma function
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inequalities
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completely monotonic functions
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Some properties of the \(k\)-gamma function (English)
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The authors study some new properties of a \(k\)-gamma function \(\Gamma_k\) \((k>0)\), introduced by \textit{R. Díaz} and \textit{E. Pariguan} [Divulg. Mat. 15, No. 2, 179--192 (2007; Zbl 1163.33300)]. They introduce also a \(k\)-analogue \(\zeta_k\) of Riemann's zeta function. By applying classical inequalities or a monotonicity theorem, the analogues of certain known results for the Euler gamma function are extended to the \(k\)-case.
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