\(q\)-Bernoulli numbers and polynomials. (Q2767899)
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scientific article; zbMATH DE number 1698737
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(q\)-Bernoulli numbers and polynomials. |
scientific article; zbMATH DE number 1698737 |
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10 October 2002
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\(q\)-Bernoulli numbers
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\(q\)-Bernoulli polynomials
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\(p\)-adic \(q\)-integral
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\(q\)-Bernoulli numbers and polynomials. (English)
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The authors define \(q\)-Bernoulli numbers and polynomials of higher order using the \(p\)-adic \(q\)-integral of the Volkenborn type introduced by \textit{T. Kim} [J. Number Theory 76, 320--329 (1999; Zbl 0941.11048)]. Then higher \(q\)-Bernoulli numbers are expressed as linear combinations of products of the first order \(q\)-Bernoulli numbers. As \(q\to 1\), this implies the formulas for the classical Bernoulli numbers found by \textit{K. Dilcher} [ibid. 60, 23--41 (1996; Zbl 0863.11011)] and \textit{I. C. Huang} and \textit{S. Y. Huang} [ibid. 76, 178--193 (1999; Zbl 0940.11009)].NEWLINENEWLINEFor the entire collection see [Zbl 0972.00006].
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