Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article On Some Arithmetical Properties of the Genocchi Numbers and Polynomials | Hindawi Publishing Corporation Advances in Difference Equations Volume 2008 Article ID i95049 14 pages doi 2008 195049 Research Article On Some Arithmetical Properties of the Genocchi Numbers and Polynomials Kyoung Ho Park1 and Young-Hee Kim2 1 Department of Mathematics Kyungpook National University Daegu 702-701 South Korea 2 Division of General Education-Mathematics Kwangwoon University Seoul 139-701 South Korea Correspondence should be addressed to Young-Hee Kim yhkim@ Received 31 October 2008 Revised 19 December 2008 Accepted 25 December 2008 Recommended by Martin J. Bohner We investigate the properties of the Genocchi functions and the Genocchi polynomials. We obtain the Fourier transform on the Genocchi function. We have the generating function of h q -Genocchi polynomials. We define the Cangul-Ozden-Simsek s type twisted h q -Genocchi polynomials and numbers. We also have the generalized twisted h q -Genocchi numbers attached to the Dirichlet s character X. Finally we define zeta functions related to h q -Genocchi polynomials and have the generating function of the generalized h q -Genocchi numbers attached to X. Copyright 2008 K. H. Park and . Kim. 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. 1. Introduction After Carlitz introduced an interesting q-analogue of Frobenius-Euler numbers in 1 q-Bernoulli and q-Euler numbers and polynomials have been studied by several authors. Recently many authors have an interest in the q-extension of the Genocchi numbers and polynomials cf. 2-5 . Kim et al. 5 defined the q-Genocchi numbers and the q-Genocchi polynomials. In 3 Kim derived the q-analogs of the Genocchi numbers and polynomials by constructing q-Euler numbers. He also gave some interesting relations between q-Euler and q-Genocchi numbers. The first author et al. 6 obtained the .
