Polydisc

Summary

A polydisc in $\C^n$ is a product of $n$ open discs of the complex plane, one in each coordinate. It is the basic domain of several complex variables, playing the role that the disc plays in one variable. The Cauchy integral formula on a polydisc follows from the one-variable formula applied in each coordinate, and it leads to power series expansions. Its distinguished boundary is a torus, much smaller than its topological boundary.