| Euler多项式的若干对称恒等式 |
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| 引用本文： | 杨胜良,乔占科. Euler多项式的若干对称恒等式[J]. 数学研究及应用, 2010, 30(3): 457-464. DOI: 10.3770/j.issn:1000-341X.2010.03.010 |
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| 作者姓名： | 杨胜良 乔占科 |
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| 作者单位： | 兰州理工大学应用数学系, 甘肃 兰州 730050;苏州科技大学数学系, 江苏 苏州 215009 |
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| 基金项目： | 甘肃省自然科学基金(Grant No.3ZS041-A25-007) |
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| 摘 要： | Using the generating functions, we prove some symmetry identities for the Euler polynomials and higher order Euler polynomials, which generalize the multiplication theorem for the Euler polynomials. Also we obtain some relations between the Bernoulli polynomials, Euler polynomials, power sum, alternating sum and Genocchi numbers.
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| 关 键 词： | Euler polynomial Bernoulli number Bernoulli polynomial Genocchi number power sum alternating sum. |
| 收稿时间： | 2007-12-31 |
| 修稿时间： | 2008-07-07 |
Some Symmetry Identities for the Euler Polynomials |
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| Sheng Liang YANG and Zhan Ke QIAO. Some Symmetry Identities for the Euler Polynomials[J]. Journal of Mathematical Research with Applications, 2010, 30(3): 457-464. DOI: 10.3770/j.issn:1000-341X.2010.03.010 |
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| Authors: | Sheng Liang YANG and Zhan Ke QIAO |
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| Affiliation: | 1. Department of Applied Mathematics, Lanzhou University of Technology, Gansu 730050, P. R. China
2. Department of Mathematics, Suzhou University of Science and Technology,Jianqsu 215009, P. R. China |
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| Abstract: | Using the generating functions, we prove some symmetry identities for the Euler polynomials and higher order Euler polynomials, which generalize the multiplication theorem for the Euler polynomials. Also we obtain some relations between the Bernoulli polynomials, Euler polynomials, power sum, alternating sum and Genocchi numbers. |
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| Keywords: | Euler polynomial Bernoulli number Bernoulli polynomial Genocchi number power sum alternating sum. |
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