Evaluations of k-fold Euler/Zagier sums: a compendium of results for arbitrary k
Evaluations of k-fold Euler/Zagier sums: a compendium of results for arbitrary k
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DOI：
10.37236/1320
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发表时间：
1996-10
期刊：
影响因子：
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通讯作者：
J. Borwein;D. Bradley;D. Broadhurst
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文献类型：
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作者：
J. Borwein;D. Bradley;D. Broadhurst
欧拉和（也称为Zagier和）出现在纽结理论和量子场论的背景下。有各种各样与这些和有关的命题，它们的不完整性表明数学界和物理界都还没有完全理解这个领域。在这里，我们组装结果欧拉/Zagier和（也称为多维zeta/谐波和）的任意深度，包括符号交替。我们的许多结果是经验性的，显然是新的。通过仔细编译和检查高精度数值评估的巨大数据库，我们可以有信心地声称某些类别的结果是详尽的。虽然许多证据缺乏，我们已经勾勒出推导的所有结果，迄今已被证明。
Euler sums (also called Zagier sums) occur within the context of knot theory and quantum field theory. There are various conjectures related to these sums whose incompletion is a sign that both the mathematics and physics communities do not yet completely understand the field. Here, we assemble results for Euler/Zagier sums (also known as multidimensional zeta/harmonic sums) of arbitrary depth, including sign alternations. Many of our results were obtained empirically and are apparently new. By carefully compiling and examining a huge data base of high precision numerical evaluations, we can claim with some confidence that certain classes of results are exhaustive. While many proofs are lacking, we have sketched derivations of all results that have so far been proved.