TAILIEUCHUNG - Báo cáo hóa học: " Research Article Interpolation Functions of q-Extensions of Apostol’s Type Euler 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 Interpolation Functions of q-Extensions of Apostol’s Type Euler Polynomials | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 451217 12 pages doi 2009 451217 Research Article Interpolation Functions of q-Extensions of Apostol s Type Euler Polynomials Kyung-Won Hwang 1 Young-Hee Kim 2 and Taekyun Kim2 1 Department of General Education Kookmin University Seoul 136-702 South Korea 2 Division of General Education-Mathematics Kwangwoon University Seoul 139-701 South Korea Correspondence should be addressed to Young-Hee Kim yhkim@ and Taekyun Kim tkkim@ Received 16 May 2009 Accepted 25 July 2009 Recommended by Vijay Gupta The main purpose of this paper is to present new q-extensions of Apostol s type Euler polynomials using the fermionic p-adic integral on Zp. We define the q-l-Euler polynomials and obtain the interpolation functions and the Hurwitz type zeta functions of these polynomials. We define q-extensions of Apostol type s Euler polynomials of higher order using the multivariate fermionic p-adic integral on Zp. We have the interpolation functions of these q-l-Euler polynomials. We also give h q -extensions of Apostol s type Euler polynomials of higher order and have the multiple Hurwitz type zeta functions of these h q -l-Euler polynomials. Copyright 2009 Kyung-Won Hwang 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. 1. Introduction Definitions and Notations After Carlitz 1 gave q-extensions of the classical Bernoulli numbers and polynomials the q-extensions of Bernoulli and Euler numbers and polynomials have been studied by several authors. Many authors have studied on various kinds of q-analogues of the Euler numbers and polynomials cf. 1-39 .T Kim 7-23 has published remarkable research results for q-extensions of the Euler numbers and polynomials and their interpolation functions. In 13 T Kim .

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