We give an explicit formula for the shuffle relation in a general double shuffle framework that specializes to double shuffle relations of multiple zeta values and multiple polylogarithms. As an application, we generalize the well-known decomposition formula of Euler that expresses the product of two Riemann zeta values as a sum of double zeta values to a formula that expresses the product of two multiple polylogarithm values as a sum of other multiple polylogarithm values.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Double shuffle relation
- Euler's decomposition formula
- Multiple polylogarithm values
- Multiple zeta values