In the theory of functions of several complex variables, a branch of mathematics, a polydisc is a Cartesian product of discs.
the open disc of center z and radius r in the complex plane, then an open polydisc is a set of the form It can be equivalently written as One should not confuse the polydisc with the open ball in Cn, which is defined as Here, the norm is the Euclidean distance in Cn.
, open balls and open polydiscs are not biholomorphically equivalent, that is, there is no biholomorphic mapping between the two.
A polydisc is an example of logarithmically convex Reinhardt domain.
This article incorporates material from polydisc on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.