## Abstract and Applied Analysis

### Some Identities on the Generalized q-Bernoulli, q-Euler, and q-Genocchi Polynomials

#### Abstract

Mahmudov (2012, 2013) introduced and investigated some $q$-extensions of the $q$-Bernoulli polynomials ${\scr B}_{n,q}^{(\alpha )}(x,y)$ of order $\alpha$, the $q$-Euler polynomials ${\scr E}_{n,q}^{(\alpha )}(x,y)$ of order $\alpha$, and the $q$-Genocchi polynomials ${\mathrm{\scr G}}_{n,q}^{(\alpha )}(x,y)$ of order $\alpha$. In this paper, we give some identities for ${\scr B}_{n,q}^{(\alpha )}(x,y)$, ${\mathrm{\scr G}}_{n,q}^{(\alpha )}(x,y)$, and ${\scr E}_{n,q}^{(\alpha )}(x,y)$ and the recurrence relations between these polynomials. This is an analogous result to the $q$-extension of the Srivastava-Pintér addition theorem in Mahmudov (2013).

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 293532, 6 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393443650

Digital Object Identifier
doi:10.1155/2013/293532

Mathematical Reviews number (MathSciNet)
MR3139461

Zentralblatt MATH identifier
1359.11024

#### Citation

Kim, Daeyeoul; Kurt, Burak; Kurt, Veli. Some Identities on the Generalized q -Bernoulli, q -Euler, and q -Genocchi Polynomials. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 293532, 6 pages. doi:10.1155/2013/293532. https://projecteuclid.org/euclid.aaa/1393443650

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