Extended Zeilberger's Algorithm for Identities on Bernoulli and Euler Polynomials
Extended Zeilberger's Algorithm for Identities on Bernoulli and Euler Polynomials
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DOI：
10.1016/j.jnt.2009.01.026
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发表时间：
2008-10
期刊：
影响因子：
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通讯作者：
William Y. C. Chen;L. H. Sun
中科院分区：
文献类型：
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作者：
William Y. C. Chen;L. H. Sun
利用Chen，Hou和Mu给出的推广Zeilberger算法，给出了Bernoulli多项式和Euler多项式恒等式的计算机代数证明方法.其核心思想是使用伯努利数和欧拉数的围道积分定义来建立被积函数的递推关系。这样的递归关系有一定的参数自由属性，导致所需的身份，而无需计算积分。此外，还得到了关于Bernoulli数的两个新恒等式.
We present a computer algebra approach to proving identities on Bernoulli polynomials and Euler polynomials by using the extended Zeilberger's algorithm given by Chen, Hou and Mu. The key idea is to use the contour integral definitions of the Bernoulli and Euler numbers to establish recurrence relations on the integrands. Such recurrence relations have certain parameter free properties which lead to the required identities without computing the integrals. Furthermore two new identities on Bernoulli numbers are derived.