Resolution of Some Open Problems Concerning Multiple Zeta Evaluations of Arbitrary Depth
Resolution of Some Open Problems Concerning Multiple Zeta Evaluations of Arbitrary Depth
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DOI：
10.1023/b:comp.0000005036.52387.da
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发表时间：
2003-10
影响因子：
1.8
通讯作者：
D. Bowman;D. Bradley
中科院分区：
文献类型：
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作者：
D. Bowman;D. Bradley
We prove some new evaluations for multiple polylogarithms of arbitrary depth. The simplest of our results is a multiple zeta evaluation one order of complexity beyond the well-known Broadhurst–Zagier formula. Other results we provide settle three of the remaining outstanding conjectures of Borwein, Bradley, and Broadhurst. A complete treatment of a certain arbitrary depth class of periodic alternating unit Euler sums is also given.
