Stuffle Product Formulas of Multiple Zeta Values

Abstract

Using the combinatorial descriptions of stuffle product, we obtain recursive formulas for the stuffle product of multiple zeta values and of multiple zeta-star values. Then we apply the formulas to prove several stuffle product formulas with one or two strings of zp's. We also describe how to use our formulas in general cases.

Shuffle product formulas of multiple zeta values

“…There is another commutative product among multiple zeta values, which is called stuffle product [11]. If one can get the formula for the stuffle product x a1 y · · · x ar y * x b1 y · · · x bs y (we consider this product in [14]), then comparing with (2.2), one can get some double shuffle relations of multiple zeta values. While it seems that the obtained double shuffle relations are not terse and elegant.…”