Some identities on the \(q\)-Bernoulli numbers and polynomials with weight \(0\)
type: Item
instance of: scholarly article
title: Some identities on the \(q\)-Bernoulli numbers and polynomials with weight \(0\)
zbMATH Open document ID: 1232.11027
DOI: 10.1155/2011/361484
author: Juan-Miguel Gracia
published in: Abstract and Applied Analysis
publication date: 2012-01-16T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 11B68
Mathematics Subject Classification ID: 11S80
zbMATH DE Number: 5997788
zbMATH Keywords: \(q\)-Bernoulli numbers with weight zero
zbMATH Keywords: \(q\)-Bernoulli polynomials with weight zero
zbMATH Keywords: \(p\)-adic \(q\)-integral representation of Bernstein polynomials
Wikidata QID: Q58654160
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/361484
OpenAlex ID: W2122888970
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description: scientific article; zbMATH DE number 5997788