Extended Zeilberger's Algorithm for Identities on Bernoulli and Euler Polynomials

Details Extended Zeilberger's Algorithm for Identities on Bernoulli and Euler Polynomials Extended Zeilberger's Algorithm for Identities on Bernoulli and Euler Polynomials

2008-10-02

arxiv.org/abs/0810.0438v3

J. Number Theory 129 (2009) 2111-2132

Mathematics

Combinatorics

22 pages; Final version. References updated and a typo in (8.1) corrected

Scientific paper

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.

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