  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.
