| 广义高阶Bernoulli多项式的一些恒等式及其应用 |
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| 引用本文： | 王念良.广义高阶Bernoulli多项式的一些恒等式及其应用[J].商洛学院学报,2014(6):3-5. |
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| 作者姓名： | 王念良 |
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| 作者单位： | 商洛学院数学与计算机应用学院/应用数学研究所 |
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| 基金项目： | 陕西省教育厅专项科研计划项目(2013JK0570) |
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| 摘 要： | Bernoulli多项式及其多种推广形式在组合数学、解析数论等领域中起着十分重要的作用。广义Bernoulli多项式Bn,χ(x)与Euler多项式、Dirichlet级数有密切的联系。应用绝对收敛Laurent级数的卷积公式,给出了广义高阶Bernoulli多项式的一些表达式和一个推论。
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| 关 键 词： | Bernoulli数 广义高阶Bernoulli多项式 Laurent级数 |
Some Identities Involving Generalized Higher-order Bernoulli Polynomials and Its Applications |
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| WANG Nian-liang.Some Identities Involving Generalized Higher-order Bernoulli Polynomials and Its Applications[J].Journal of Shangluo University,2014(6):3-5. |
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| Authors: | WANG Nian-liang |
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| Institution: | WANG Nian-liang;College of Mathematics and Computer Application, Shangluo University/Institute of Applied Mathematics; |
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| Abstract: | Bernoulli polynomials and its variety generalizations play a central role in the theory of Combination and Analytic Number Theory. It is well- known that the generalized Bernoulli polynomial Bn,χ（x） closely related to Euler polynomials and Dirichlet series. By the product formulas of the absolute convergence Laurent expansion, a representation of generalized Higher-order Bernoulli polynomial and a corollary are obtained. |
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| Keywords: | Bernoulli number generalized higher-order Bernoulli polynomial Laurent series |
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