# 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¢Â€Âform 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¢Â€Âform expression and plotting over the standard domain of .

Contributed by: Peter Falloon (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

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.

## Permanent Citation

"Closed Form Solutions for Spheroidal Functions"

http://demonstrations.wolfram.com/ClosedFormSolutionsForSpheroidalFunctions/

Wolfram Demonstrations Project

Published: March 7 2011