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MOC
1998

Fast evaluation of multiple zeta sums

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Fast evaluation of multiple zeta sums
We show that the multiple zeta sum: ζ(s1, s2, ..., sd) = n1>n2>...>nd 1 ns1 1 ns2 2 ...n sd d , for positive integers si with s1 > 1, can always be written as a finite sum of products of rapidly convergent series. Perhaps surprisingly, one may develop fast summation algorithms of such efficiency that the overall complexity can be brought down essentially to that of one-dimensional summation. In particular, for any dimension d one may resolve D good digits of ζ in O(D log D/ log log D) arithmetic operations, with the implied big-O constant depending only on the set {s1, ..., sd}.
Richard E. Crandall
Added 22 Dec 2010
Updated 22 Dec 2010
Type Journal
Year 1998
Where MOC
Authors Richard E. Crandall
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