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 closedÃ¢ÂÂform 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 closedÃ¢ÂÂform expression and plotting over the standard domain of .
C. Flammer, Spheroidal Wave Functions, Stanford: Stanford University Press, 1957.
P. E. Falloon, "Theory and Computation of Spheroidal Harmonics with General Arguments," master's thesis, University of Western Australia, 2001.