A class of integral equations

It was pointed out by Copson(1) in 1947 that the solution of the integral equation for the electrostatic problem for a circular disc could be reduced to the solution of Abel integral equations and hence a solution obtained in a fairly elementary manner. This result was obtained independently by Lebedev(2), who also obtained a similar result for the electrostatic problem for the spherical cap. The solution for the spherical cap was also obtained independently by Collins (3). In view of the relative simplicity of the approach it seems to be of interest to examine whether there exist other integral equations which can be treated in a similar fashion. In the present paper one such class of integral equations will be considered.