A cauchy-type integral equation arising in potential theory#x2020;

摘要

This note is concerned with the integral equationwhere 0c#x2264;1, the integral is the Cauchy principal value and #x3C6;0(y) is a prescribed continuous function, By changing the variables, the integral equation can be transformed to that of Cauchy type, whose solution is well-known. Reverting to the original variables, an elegant closed form solution for (*) is obtained