Coproduct Formula for Motivic Version of Yamamoto's Integral

Goncharov proved an explicit formula for the coproduct in the Hopf algebra of motivic iterated integrals. Yamamoto introduced Yamamoto’s integral which generalizes iterated integrals and gave a new integral expression for multiple zeta star values using Yamamoto’s integral. In this paper, we consider the motivic version of Yamamoto’s integral and generalize Goncharov’s coproduct formula to those motivic integrals. As an example, we will compute the coproduct of a certain type of Schur multiple zeta values.