| 高阶Bernoulli多项式和高阶Euler多项式的关系 |
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| 引用本文： | 雒秋明,马韵新,祁锋.高阶Bernoulli多项式和高阶Euler多项式的关系[J].数学杂志,2005,25(6):631-636. |
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| 作者姓名： | 雒秋明 马韵新 祁锋 |
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| 作者单位： | 1. 焦作大学数学系,河南,焦作,454003
2. 焦作工学院应用数学与信息科学系,河南,焦作,454001 |
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| 基金项目： | 国家自然科学基金（10001016）;河南省自然科学基金（00405180） |
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| 摘 要： | 利用发生函数的方法，讨论了高阶Bernoulli数和高阶Euler数，高阶Bernoulli多项式和高阶Euler多项式之间的关系，得到了经典Bernoulli数和Euler数，经典Bernoulli多项式和Euler多项式之间的新型关系。
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| 关 键 词： | Bernoulli-Euler数 Bernoulli-Euler多项式 高阶Bernoulli-Euler数 高阶BernoullliEuler多项式 关系 |
| 文章编号： | 0255-7797（2005）06-0631-06 |
| 收稿时间： | 2002-10-15 |
| 修稿时间： | 2002-10-152003-12-11 |
THE RELATIONS BETWEEN HIGHER ORDER BERNOULLI POLYNOMIALS AND HIGHER ORDER EULER POLYNOMIALS |
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| LUO Qiu-ming,MA Yun-xin,QI Feng.THE RELATIONS BETWEEN HIGHER ORDER BERNOULLI POLYNOMIALS AND HIGHER ORDER EULER POLYNOMIALS[J].Journal of Mathematics,2005,25(6):631-636. |
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| Authors: | LUO Qiu-ming MA Yun-xin QI Feng |
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| Institution: | 1. Dept. of Math., Jiaozuo University, Jiaozuo 454003, China;2. Dept. of Math. , Jiaozuo Institute of Technology, Jiaozuo 454000,China |
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| Abstract: | In this paper, we comprehensively discuss the relationships between the Bernoulli numbers of higher order and Euler numbers of higher order, between the Bernoulli polynomials of higher order and Euler polynomials of higher order, by using the method of generating functions, and we obtain some new results. Furthermore, we obtain several new relationships between the classical Bernoulli numbers and Euler numbers, between the classical Bernoulli polynomials and Euler polynomials. |
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| Keywords: | Bernoulli-Euler numbers Bernoulli-Euler polynomials Bernoulli-Euler numbers of higher order Bernoulli-Euler polynomials of higher order |
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