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

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

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 introduce...

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Main Authors: Lee-Chae Jang, Taekyun Kim, Dae San Kim, Dmitry Victorovich Dolgy
Format: Article
Language:English
Published: MDPI AG 2018-08-01
Series:Symmetry
Subjects:
two variable q-Berstein polynomial
two variable q-Berstein operator
q-Euler number
q-Euler polynomial
Online Access:http://www.mdpi.com/2073-8994/10/8/311
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spelling doaj-0c12318c1e014d569cc333b1ee931ce32020-11-24T23:42:44ZengMDPI AGSymmetry2073-89942018-08-0110831110.3390/sym10080311sym10080311On p-Adic Fermionic Integrals of q-Bernstein Polynomials Associated with q-Euler Numbers and Polynomials †Lee-Chae Jang0Taekyun Kim1Dae San Kim2Dmitry Victorovich Dolgy3Graduate School of Education, Konkuk University, Seoul 143-701, KoreaDepartment of Mathematics, Kwangwoon University, Seoul 139-701, KoreaDepartment of Mathematics, Sogang University, Seoul 121-742, KoreaKwangwoon Institute for Advanced Studies, Kwangwoon University, Seoul 139-701, KoreaWe 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.http://www.mdpi.com/2073-8994/10/8/311two variable q-Berstein polynomialtwo variable q-Berstein operatorq-Euler numberq-Euler polynomial
collection DOAJ
language English
format Article
sources DOAJ
author Lee-Chae Jang
Taekyun Kim
Dae San Kim
Dmitry Victorovich Dolgy
spellingShingle Lee-Chae Jang
Taekyun Kim
Dae San Kim
Dmitry Victorovich Dolgy
On p-Adic Fermionic Integrals of q-Bernstein Polynomials Associated with q-Euler Numbers and Polynomials †
Symmetry
two variable q-Berstein polynomial
two variable q-Berstein operator
q-Euler number
q-Euler polynomial
author_facet Lee-Chae Jang
Taekyun Kim
Dae San Kim
Dmitry Victorovich Dolgy
author_sort Lee-Chae Jang
title On p-Adic Fermionic Integrals of q-Bernstein Polynomials Associated with q-Euler Numbers and Polynomials †
title_short On p-Adic Fermionic Integrals of q-Bernstein Polynomials Associated with q-Euler Numbers and Polynomials †
title_full On p-Adic Fermionic Integrals of q-Bernstein Polynomials Associated with q-Euler Numbers and Polynomials †
title_fullStr On p-Adic Fermionic Integrals of q-Bernstein Polynomials Associated with q-Euler Numbers and Polynomials †
title_full_unstemmed On p-Adic Fermionic Integrals of q-Bernstein Polynomials Associated with q-Euler Numbers and Polynomials †
title_sort on p-adic fermionic integrals of q-bernstein polynomials associated with q-euler numbers and polynomials †
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2018-08-01
description 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.
topic two variable q-Berstein polynomial
two variable q-Berstein operator
q-Euler number
q-Euler polynomial
url http://www.mdpi.com/2073-8994/10/8/311
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AT taekyunkim onpadicfermionicintegralsofqbernsteinpolynomialsassociatedwithqeulernumbersandpolynomials
AT daesankim onpadicfermionicintegralsofqbernsteinpolynomialsassociatedwithqeulernumbersandpolynomials
AT dmitryvictorovichdolgy onpadicfermionicintegralsofqbernsteinpolynomialsassociatedwithqeulernumbersandpolynomials
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