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 .

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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.
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