On p-adic Integral Representation of q-Bernoulli Numbers Arising from Two Variable q-Bernstein Polynomials

被引：2
作者：
San Kim, Dae [1 ]
Kim, Taekyun [2 ,3 ]
Ryoo, Cheon Seoung [4 ]
Yao, Yonghong [2 ,5 ]
机构：
[1] Sogang Univ, Dept Math, Seoul 121742, South Korea
[2] Tianjin Polytech Univ, Dept Math, Tianjin 300387, Peoples R China
[3] Kwangwoon Univ, Dept Math, Seoul 139701, South Korea
[4] Hannam Univ, Dept Math, Daejeon 306791, South Korea
[5] Univ Elect Sci & Technol China, Inst Fundamental & Frontier Sci, Chengdu 610054, Sichuan, Peoples R China
来源：
SYMMETRY-BASEL | 2018年 / 10卷 / 10期
基金：
新加坡国家研究基金会;
关键词：
q-Bernoulli numbers; q-Bernoulli polynomials; two variable q-Bernstein polynomials; two variable q-Bernstein operators; p-adic integral on Z(p);
D O I：
10.3390/sym10100451
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
The q-Bernoulli numbers and polynomials can be given by Witt's type formulas as p-adic invariant integrals on Z(p). We investigate some properties for them. In addition, we consider two variable q-Bernstein polynomials and operators and derive several properties for these polynomials and operators. Next, we study the evaluation problem for the double integrals on Z(p) of two variable q-Bernstein polynomials and show that they can be expressed in terms of the q-Bernoulli numbers and some special values of q-Bernoulli polynomials. This is generalized to the problem of evaluating any finite product of two variable q-Bernstein polynomials. Furthermore, some identities for q-Bernoulli numbers are found.
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页数：11
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