Extended Zeilberger's algorithm for identities on Bernoulli and Euler polynomials

JOURNAL OF NUMBER THEORY

卷:129

Article

Chen, William Y. C.¹  Sun, Lisa H.¹ 

[1] Nankai Univ, Ctr Combinator, LPMC TJKLC, Tianjin 300071, Peoples R China

关键词: Bernoulli number;    Euler number;    Bernoulli polynomial;    Euler polynomial;    Zeilberger's algorithm;   

DOI  :  10.1016/j.jnt.2009.01.026

来源: Elsevier

【 摘 要 】

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. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free