Closed Form Solutions for Spheroidal Functions

For general parameter values, the spheroidal functions , , , and are difficult to compute and are calculated via infinite series representations involving simpler special functions. However, for the special set of parameter values , , and , simple closed-form solutions can be found involving trigonometric functions. These provide a useful check on the accuracy of numerical solutions. In this Demonstration we illustrate these solutions by showing both the closed-form expression and plotting over the standard domain of .