Generalized \(q\)-Euler numbers and polynomials of higher order and some theoretic identities
type: Item
instance of: scholarly article
title: Generalized \(q\)-Euler numbers and polynomials of higher order and some theoretic identities
zbMATH Open document ID: 1222.11034
DOI: 10.1155/2010/682072
author: Taekyun Kim
author: Young Hee Kim
published in: Journal of Inequalities and Applications
publication date: 2010-12-06T00:00:00Z
full work available at URL: https://eudml.org/doc/226471
review text: The purpose of this paper is to give a new approach to the \(q\)-Euler numbers and polynomials of higher order attached to Dirichlet's character \(\chi\). From this, the authors derive some theoretic identities involving generalized \(q\)-Euler numbers and polynomials of higher order. In Section 2, they present new generating functions which are related to \(q\)-Euler numbers and polynomials of higher order attached to \(\chi\). They obtain distribution relations for the \(q\)-Euler polynomials attached to \(\chi\), and find some identities involving these \(q\)-Euler polynomials. Using the Cauchy residue theorem, it is shown that these \(q\)-extensions of the \(q\)-\(l\)-function of order \(r\) attached to \(\chi\) interpolate the \(q\)-Euler polynomials of order \(r\) at negative integers.
reviewed by: Florin Nicolae
Mathematics Subject Classification ID: 11B68
Mathematics Subject Classification ID: 11S80
zbMATH DE Number: 5823190
zbMATH Keywords: generalized Euler numbers and polynomials
MaRDI profile type: Publication
OpenAlex ID: W2132392188
Wikidata QID: Q59254223
cites work: Note on the Euler \(q\)-zeta functions
cites work: Some identities on the \(q\)-Euler polynomials of higher order and \(q\)-Stirling numbers by the fermionic \(p\)-adic integral on \(\mathbb Z_p\)
cites work: On a \(q\)-analogue of the \(p\)-adic log gamma functions and related integrals
cites work: q-Euler numbers and polynomials associated with p-adic q-integrals
cites work: On the \(q\)-extension of Euler and Genocchi numbers
cites work: On the multiple \(q\)-Genocchi and Euler numbers
cites work: \(q\)-generalized Euler numbers and polynomials
cites work: Reflection Symmetries of q-Bernoulli Polynomials
cites work: On interpolation functions of the generalized twisted \((h,q)\)-Euler polynomials
cites work: On Genocchi numbers and polynomials
cites work: On a \(p\)-adic interpolation function for the \(q\)-extension of the generalized Bernoulli polynomials and its derivative
cites work: On \(p\)-adic interpolating function for \(q\)-Euler numbers and its derivatives
cites work: Multiple twisted \(q\)-Euler numbers and polynomials associated with \(p\)-adic \(q\)-integrals
cites work: A note on Hölder type inequality for the fermionic \(p\)-adic invariant \(q\)-integral
cites work: Euler numbers and polynomials associated with zeta functions
description: scientific article; zbMATH DE number 5823190