Closed Form Solutions for Spheroidal Functions
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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 .
Contributed by: Peter Falloon (March 2011)
Open content licensed under CC BY-NC-SA
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.
"Closed Form Solutions for Spheroidal Functions"
Wolfram Demonstrations Project
Published: March 7 2011