Eigenvalues for a Centrally Loaded Circular Cylindrical Cavity

The general availability of large high-speed computers has made the use of series expansions in complicated field theory problems feasible even when these series do not converge rapidly. This paper outlines the method and illustrates its application to the solution of a problem in cylindrical coordinates. At the same time, the errors inherent in this method of solution are indicated and estimates are made of their magnitudes. A comparison of the method with Slater's perturbation theory is made.