Construction of complex potentials for multiply connected domain

Abstract

The method of reduction of a Fredholm integral equation to the linear system is generalized to construction of a complex potential - an analytic function in an unbounded multiply connected domain with a simple pole at infinity which maps the domain onto a plane with horizontal slits. We consider a locally sourceless, locally irrotational flow on an arbitrary given n-connected unbounded domain with impermeable boundary. The complex potential has the form of a Cauchy integral with one linear and n logarithmic summands. The method is easily computable.