Shuffle product formulas of multiple zeta values

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.

Higher Order Shuffle Regularization for Multiple Zeta Values

We study the higher order shuffle regularization for multiple zeta values and define higher order regularized shuffle relations. We find that higher order regularized shuffle relations can be deduced from the group-like property of the Drinfel’d associator.

An exotic shuffle relation for multiple zeta values

In this short note we will provide a new proof of the following exotic shuffle relation of multiple zeta values: ζ({2}x{3, 1}) = ( 2n+m m ) π (2n+ 1) · (4n+ 2m+ 1)! . This was proved by Zagier when n = 0, by Broadhurst when m = 0, and by Borwein, Bradley, and Broadhurst when m = 1. In general this was proved by Bowman and Bradley. Our new idea is to use the method of Borwein et al. to reduce th...

A New Shuffle Convolution for Multiple Zeta Values

Recently, interest in shuffle algebra has been renewed due to their connections with multiple zeta values. In this paper, we prove a new shuffle convolution that implies a reduction formula for the multiple zeta value ζ ({5, 1}n).

New Families of Weighted Sum Formulas for Multiple Zeta Values