# Construction of complex potentials for multiply connected domains

## TL;DR

This paper develops a generalized method to construct complex potentials in multiply connected domains, enabling the mapping of such domains onto slit planes with a focus on computational simplicity.

## Contribution

It introduces a generalized approach to construct complex potentials in multiply connected domains, extending previous methods to more complex geometries.

## Key findings

- The method effectively constructs complex potentials with explicit formulas.
- It maps multiply connected domains onto slit planes.
- The approach is computationally straightforward.

## 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 infinite 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 infinite 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.