New families of weighted sum formulas for multiple zeta values

Many [Formula: see text]-linear relations exist between multiple zeta values, the most interesting of which are the weighted sum formulas. In this paper, we generalize these to Euler sums and Kaneko and Tsumura’s multiple [Formula: see text]-values, a variant of the multiple zeta values, by considering generating functions of the Euler sums. Through this approach, we are able to re-prove a few known formulas, confirm a conjecture of Kaneko and Tsumura on triple [Formula: see text]-values, and discover many new identities.

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New families of weighted sum formulas for multiple zeta values

Abstract: Abstract. In this paper we use the generating functions and the double shuffle relations satisfied by the multiple zeta values to derive some new families of identities.

Cited by 4 publications

References 13 publications

Some weighted sum identities for double zeta values

Some weighted sum identities for double zeta values

Weighted sum formulas for finite multiple zeta values

Proof of Kaneko–Tsumura conjecture on triple T-values

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