TAILIEUCHUNG - báo cáo hóa học:" Research Article On Multiple Interpolation Functions of the q-Genocchi Polynomials"

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 Multiple Interpolation Functions of the q-Genocchi Polynomials | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 351419 13 pages doi 2010 351419 Research Article On Multiple Interpolation Functions of the q-Genocchi Polynomials Seog-Hoon Rim 1 Jeong-Hee Jin 2 Eun-Jung Moon 2 and Sun-Jung Lee2 1 Department of Mathematics Education Kyungpook National University Tagegu 702-701 South Korea 2 Department of Mathematics Kyungpook National University Tagegu 702-701 South Korea Correspondence should be addressed to Seog-Hoon Rim shrim@ Received 14 December 2009 Accepted 29 March 2010 Academic Editor Wing-Sum Cheung 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. Recently many mathematicians have studied various kinds of the q-analogue of Genocchi numbers and polynomials. In the work New approach to q-Euler Genocchi numbers and their interpolation functions Advanced Studies in Contemporary Mathematics vol. 18 no. 2 pp. 105112 2009. Kim defined new generating functions of q-Genocchi q-Euler polynomials and their interpolation functions. In this paper we give another definition of the multiple Hurwitz type q-zeta function. This function interpolates q-Genocchi polynomials at negative integers. Finally we also give some identities related to these polynomials. 1. Introduction Let p be a fixed odd prime number. Throughout this paper Zp Qp C and Cp denote the ring of p-adic rational integers the field of p-adic rational numbers the complex number field and the completion of the algebraic closure of Qp respectively. Let N be the set of natural numbers and Z N u 0 . Let vp be the normalized exponential valuation of Cp with p p p-v-p p 1 p see 1 . When one talks of q-extension q is variously considered as an indeterminate a complex q e C or a p-adic number q e Cp. If q e C then one .

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