IJPAM: Volume 79, No. 4 (2012)

A NOTE ON THE TWISTED $q$-EULER NUMBERS AND
POLYNOMIALS WITH WEIGHT $( \alpha, \beta)$

Cheon Seoung Ryoo
Department of Mathematics
Hannam University
Daejeon 306-791, KOREA


Abstract. In this paper we construct a new type of the twisted $q$-Euler numbers $E_{n, q, w}^{(\alpha, \beta)}$ and polynomials $E_{n, q, w}^{(\alpha, \beta)}(x)$ with weight $( \alpha, \beta)$. Some interesting results and relationships are obtained.

Received: April 17, 2012

AMS Subject Classification: 11B68, 11S40, 11S80

Key Words and Phrases: Euler numbers and polynomials, twisted Euler numbers and polynomials, twisted $(h,q)$-Euler numbers and polynomials, twisted $q$-Euler numbers and polynomials with weight $( \alpha, \beta)$

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 79
Issue: 4