An infinite plate with a curvilinear hole in S-plane

Cauchy integral method has been applied to derive exact and closed expressions for Goursat's functions for the first and second fundamental problems for the infinite plate weakened by a hole having arbitrary shape. The plate considered are conformally mapped on the area of the right half-plane. The work of many previous authors are considered as special cases of this work and the interesting cases when the the shape of the hole is an ellipse, a crescent, a triangle, or a cut having the shape of a circular are include as special cases.