17 September 2007

correction to multiple zeta values post: Hoffman's relation

On Friday I made a post about multiple zeta values and was frustrated by my inability to find, for example, ζ(2,1).

Sarah Carr has informed me of the missing relation, "Hoffman's relation", which is used for calculating non-convergent ζ values:
For any convergent sequence of positive integers, k = (k1, ... ,kd) and its
corresponding sequence of 0's and 1's, ε = (0k1-11,...,0kd-11), then Σσ ζ(σ) = 0 where σ runs over all the terms in (1)*k - (1) Ш ε

I'm not particularly interested in finding it anymore (I have bigger fish to fry at the moment), but in the interests of completeness I wanted to make sure I had this right.

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