Some formulae for the \(q\)-Bernoulli and Euler polynomials of higher order
type: Item
instance of: scholarly article
title: Some formulae for the \(q\)-Bernoulli and Euler polynomials of higher order
zbMATH Open document ID: 1008.11005
DOI: 10.1016/S0022-247X(02)00203-2
author: Taekyun Kim
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-02-11T00:00:00Z
review text: Let \(q\in \mathbb C_p\), \(|q-1|_p<p^{-1/(p-1)}\). The author defines higher \(q\)-Bernoulli numbers via a \(q\)-analog of the Volkenborn integral [see also the author, Arch. Math. 76, 190--195 (2001; Zbl 0986.11010)], by analogy with a well-known representation for classical Bernoulli numbers. In a similar way, the \(q\)-Euler polynomials and \(q\)-Euler numbers are defined. Some formulas for sums of their products are proved. For the higher \(q\)-Bernoulli numbers, a Kummer-type congruence is obtained.
reviewed by: Anatoly N. Kochubei
Mathematics Subject Classification ID: 11B68
Mathematics Subject Classification ID: 11S40
Mathematics Subject Classification ID: 05A30
zbMATH DE Number: 1866610
zbMATH Keywords: \(q\)-Bernoulli numbers
zbMATH Keywords: \(q\)-Euler numbers
zbMATH Keywords: Volkenborn integral
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1866610