On the \(q\)-extension of Apostol-Euler numbers and polynomials
type: Item
instance of: scholarly article
title: On the \(q\)-extension of Apostol-Euler numbers and polynomials
zbMATH Open document ID: 1247.11028
DOI: 10.1155/2008/296159
author: Young Hee Kim
author: L. C. Jang
author: Won-Joo Kim
published in: Abstract and Applied Analysis
publication date: 2009-03-30T00:00:00Z
review text: Summary: Recently, \textit{J. Choi} et al. [Appl. Math. Comput. 199, No. 2, 723--737 (2008; Zbl 1146.33001)] have studied the \(q\)-extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of order \(n\) and multiple Hurwitz zeta function. In this paper, we define Apostol's type \(q\)-Euler numbers \(E_{n,q,\xi }\) and \(q\)-Euler polynomials \(E_{n,q,\xi }(x)\). We obtain the generating functions of \(E_{n,q,\xi }\) and \(E_{n,q,\xi }(x)\), respectively. We also have the distribution relation for Apostol's type \(q\)-Euler polynomials. Finally, we obtain \(q\)-zeta function associated with Apostol's type \(q\)-Euler numbers and Hurwitz's type \(q\)-zeta function associated with Apostol's type \(q\)-Euler polynomials for negative integers.
Mathematics Subject Classification ID: 11B68
Mathematics Subject Classification ID: 11B65
Mathematics Subject Classification ID: 11M35
Mathematics Subject Classification ID: 11S40
zbMATH DE Number: 5534779
Wikidata QID: Q58644315
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2008/296159
OpenAlex ID: W2113221414
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description: scientific article; zbMATH DE number 5534779