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{\bf J.~M.~Borwein,D.~M.~Bradley, and D.~J.~Broadhurst                                                                 
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Evaluations of $k$-fold Euler/Zagier sums:       
a compendium of results for arbitrary $k$ }
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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.  
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