Some identities on the \(q\)-Bernoulli numbers and polynomials with weight \(0\) (Q657114)
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scientific article; zbMATH DE number 5997788
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some identities on the \(q\)-Bernoulli numbers and polynomials with weight \(0\) |
scientific article; zbMATH DE number 5997788 |
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Some identities on the \(q\)-Bernoulli numbers and polynomials with weight \(0\) (English)
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16 January 2012
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Summary: Recently, the first author [Adv. Stud. Contemp. Math., Kyungshang 21, No. 2, 207--215 (2011; Zbl 1256.11017)] has introduced the \(q\)-Bernoulli numbers with weight \(\alpha\). In this paper, we consider the \(q\)-Bernoulli numbers and polynomials with weight \(\alpha = 0\) and give \(p\)-adic \(q\)-integral representation of Bernstein polynomials associated with \(q\)-Bernoulli numbers and polynomials with weight 0. From these integral representation on \(\mathbb Z_p\), we derive some interesting identities on the \(q\)-Bernoulli numbers and polynomials with weight 0.
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\(q\)-Bernoulli numbers with weight zero
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\(q\)-Bernoulli polynomials with weight zero
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\(p\)-adic \(q\)-integral representation of Bernstein polynomials
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