Result: A note on $q$-Euler and Genocchi numbers: A note on \(q\)-Euler and Genocchi numbers

Title:
A note on $q$-Euler and Genocchi numbers: A note on \(q\)-Euler and Genocchi numbers
Authors:
Taekyun Kim, Hong Kyung Pak, Lee-Chae Jang
Source:
Proceedings of the Japan Academy, Series A, Mathematical Sciences. 77
Publisher Information:
Project Euclid, 2001.
Publication Year:
2001
Subject Terms:
Euler polynomials, \(q\)-calculus and related topics, Genocchi numbers, \(q\)-Euler numbers, 0101 mathematics, Bernoulli and Euler numbers and polynomials, 01 natural sciences
Document Type:
Academic journal Article<br />Other literature type
File Description:
application/xml
ISSN:
0386-2194
DOI:
10.3792/pjaa.77.139
Access URL:
https://projecteuclid.org/journals/proceedings-of-the-japan-academy-series-a-mathematical-sciences/volume-77/issue-8/A-note-on-q-Euler-and-Genocchi-numbers/10.3792/pjaa.77.139.pdf
https://zbmath.org/1800018
https://doi.org/10.3792/pjaa.77.139
http://ci.nii.ac.jp/naid/40005329317
https://projecteuclid.org/journals/proceedings-of-the-japan-academy-series-a-mathematical-sciences/volume-77/issue-8/A-note-on-q-Euler-and-Genocchi-numbers/10.3792/pjaa.77.139.full
Accession Number:
edsair.doi.dedup.....670d8e9ca19a38280de15615ebf614b9
Database:
OpenAIRE

Further Information

It is known that the Euler polynomials \(E_n(x)\) defined by the generating function \[ 2e^{tx}(e^t+1)^{-1}=\sum_{n=0}^\infty E_n(x)\frac{t^n}{n!} \] can be expressed via the Genocchi numbers corresponding to the generating function\break \(2t(e^t+1)^{-1}\). The authors find a \(q\)-analog of this relation. The resulting \(q\)-Euler numbers are different from those introduced by \textit{L. Carlitz} [Trans. Am. Math. Soc. 76, 332-350 (1954; Zbl 0058.01204)].