Multiple Zeta Values
نویسنده
چکیده
for any collection of positive integers s1, s2, . . . , sl. By definition, Lis(1) = ζ(s), s ∈ Z, s1 ≥ 2, s2 ≥ 1, . . . , sl ≥ 1. (4.2) Taking, as before for multiple zeta values, Lixs(z) := Lis(z), Li1(z) := 1, (4.3) let us extend action of the map Li : w 7→ Liw(z) by linearity on the graded algebra H (not H, since multi-indices are coded by words in H). Lemma 4.1. Let w ∈ H be an arbitrary non-empty word and xj the first letter in its record (that is w = xju for some word u ∈ H). Then d dz Liw(z) = d dz Lixju(z) = ωj(z) Liu(z), (4.4)
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