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Symmetry 2018, 10(8), 311; https://doi.org/10.3390/sym10080311

On p-Adic Fermionic Integrals of q-Bernstein Polynomials Associated with q-Euler Numbers and Polynomials

1
Graduate School of Education, Konkuk University, Seoul 143-701, Korea
2
Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea
3
Department of Mathematics, Sogang University, Seoul 121-742, Korea
4
Kwangwoon Institute for Advanced Studies, Kwangwoon University, Seoul 139-701, Korea
5
Institute of National Sciences, Far Eastern Federal University, 690950 Vladivostok, Russia
2010 Mathematics Subject Classication. 11B83; 11S80.
*
Author to whom correspondence should be addressed.
Received: 6 July 2018 / Revised: 19 July 2018 / Accepted: 23 July 2018 / Published: 1 August 2018
(This article belongs to the Special Issue Current Trends in Symmetric Polynomials with their Applications)
Full-Text   |   PDF [232 KB, uploaded 1 August 2018]

Abstract

We study a q-analogue of Euler numbers and polynomials naturally arising from the p-adic fermionic integrals on Zp and investigate some properties for these numbers and polynomials. Then we will consider p-adic fermionic integrals on Zp of the two variable q-Bernstein polynomials, recently introduced by Kim, and demonstrate that they can be written in terms of the q-analogues of Euler numbers. Further, from such p-adic integrals we will derive some identities for the q-analogues of Euler numbers. View Full-Text
Keywords: two variable q-Berstein polynomial; two variable q-Berstein operator; q-Euler number; q-Euler polynomial two variable q-Berstein polynomial; two variable q-Berstein operator; q-Euler number; q-Euler polynomial
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 (CC BY 4.0).
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Jang, L.-C.; Kim, T.; Kim, D.S.; Dolgy, D.V. On p-Adic Fermionic Integrals of q-Bernstein Polynomials Associated with q-Euler Numbers and Polynomials . Symmetry 2018, 10, 311.

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