Extended double shuffle relations and the generating function of triple zeta values of any fixed weight

Details Extended double shuffle relations and the generating function of triple zeta values of any fixed weight Extended double shuffle relations and the generating function of triple zeta values of any fixed weight

2012-04-18

arxiv.org/abs/1204.4085v1

Mathematics

Number Theory

21 pages

Scientific paper

Extended double shuffle relations among multiple zeta values are obtained by the fact that any product of multiple zeta values allowing divergent series has two different representations, and the case of two-fold product is considered in general. In this paper, we give two formulas for the generating function of the triple zeta values of any fixed weight by the use of the extended double shuffle relations obtained by not only two-fold products of double and single zeta values but also three-fold products of single zeta values. As applications of the formulas, we also obtain some parameterized, weighted and restricted sum formulas for triple zeta values.

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