International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 860280, 14 pages
doi:10.1155/2010/860280
Research Article

Some Identities on the 𝑞 -Genocchi Polynomials of Higher-Order and 𝑞 -Stirling Numbers by the Fermionic 𝑝 -Adic Integral on ℤ 𝑝

Seog-Hoon Rim, Jeong-Hee Jin, Eun-Jung Moon, and Sun-Jung Lee

Department of Mathematics, Kyungpook National University, Tagegu 702-701, Republic of Korea

Received 25 September 2010; Accepted 8 November 2010

Academic Editor: H. Srivastava

Copyright © 2010 Seog-Hoon Rim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A systemic study of some families of 𝑞 -Genocchi numbers and families of polynomials of Nörlund type is presented by using the multivariate fermionic 𝑝 -adic integral on ℤ 𝑝 . The study of these higher-order 𝑞 -Genocchi numbers and polynomials yields an interesting 𝑞 -analog of identities for Stirling numbers.