IJPAM: Volume 80, No. 2 (2012)

AN IDENTITY OF THE TWISTED $Q$-EULER
POLYNOMIALS ASSOCIATED WITH THE $p$-ADIC $q$-INTEGRALS ON $\Bbb Z_p$

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


Abstract. In [6], we studied the twisted $q$-Euler numbers and polynomials. By using these numbers and polynomials, we investigate the alternating sums of powers of consecutive integers. By applying the symmetry of the fermionic $p$-adic $q$-integral on $ \mathbb{Z}_p$, we give recurrence identities the twisted $q$-Euler polynomials.

Received: June 18, 2012

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

Key Words and Phrases: Euler numbers and polynomials, $q$-Euler numbers and polynomials, $q$-Euler numbers and polynomials, alternating sums, the twisted $q$-Euler polynomials

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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: 80
Issue: 2