Families of weighted sum formulas for multiple zeta values

New Families of Weighted Sum Formulas for Multiple Zeta Values

Weighted Sum Formula for Multiple Zeta Values

Abstract. The sum formula is a basic identity of multiple zeta values that expresses a Riemann zeta value as a homogeneous sum of multiple zeta values of a given dimension. This formula was already known to Euler in the dimension two case, conjectured in the early 1990s for higher dimensions and then proved by Granville and Zagier independently. Recently a weighted form of Euler’s formula was o...

Shuffle Product Formulas of Multiple Zeta Values

Using the combinatorial description of shuffle product, we prove or reformulate several shuffle product formulas of multiple zeta values, including a general formula of the shuffle product of two multiple zeta values, some restricted shuffle product formulas of the product of two multiple zeta values, and a restricted shuffle product formula of the product of n multiple zeta values.

SUM OF MULTIPLE q-ZETA VALUES

The generating function of the sums of multiple q-zeta values with fixed weights, depths and 1-heights, 2-heights, . . . , r-heights is represented in terms of specializations of basic hypergeometric functions.

Sum relations for multiple zeta values and connection formulas for the Gauss hypergeometric functions

We give an explicit representation for the sums of multiple zetastar values of fixed weight and height in terms of Riemann zeta values.