Various Representations of Holomorphic Functions by Cauchy and Analogous Integrals

Abstract

One of the most natural methods of solution of various boundary problems involving holomorphic functions consists of expressing the unknown holomorphic function in the form of a Cauchy or analogous integral; this expression, substituted into the boundary condition, reduces to an integral equation. In fact, such a method was used in the last section for the solution of the classical and modified Dirichlet problems.