## Abstract and Applied Analysis

### Explicit Formulas Involving $q$-Euler Numbers and Polynomials

#### Abstract

We deal with $q$-Euler numbers and $q$-Bernoulli numbers. We derive some interesting relations for $q$-Euler numbers and polynomials by using their generating function and derivative operator. Also, we derive relations between the $q$-Euler numbers and $q$-Bernoulli numbers via the $p$-adic $q$-integral in the $p$-adic integer ring.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 298531, 11 pages.

Dates
First available in Project Euclid: 28 March 2013

https://projecteuclid.org/euclid.aaa/1364475903

Digital Object Identifier
doi:10.1155/2012/298531

Mathematical Reviews number (MathSciNet)
MR2994920

Zentralblatt MATH identifier
1257.11019

#### Citation

Araci, Serkan; Acikgoz, Mehmet; Seo, Jong Jin. Explicit Formulas Involving $q$ -Euler Numbers and Polynomials. Abstr. Appl. Anal. 2012 (2012), Article ID 298531, 11 pages. doi:10.1155/2012/298531. https://projecteuclid.org/euclid.aaa/1364475903

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