Closed Form Solutions for Spheroidal Functions

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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 .

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.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.