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

Abstract

Extended double shuffle relations for multiple zeta values are obtained by the fact that any product of regularized multiple zeta values 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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Cited by in corpus (5)

• On Multiple Zeta Values of Even Arguments
• A study on multiple zeta values from the viewpoint of zeta-functions of root systems
• Weighted and Restricted Sum Formulas of Euler Sums
• Proof of Kaneko--Tsumura Conjecture on Triple T-Values
• A parameterized generalization of the sum formula for quadruple zeta values