# Closed Form Solutions for Spheroidal Functions

Closed Form Solutions for Spheroidal Functions

For general parameter values, the spheroidal functions (γ,z), (γ,z), (γ,z), and (γ,z) 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 .

PS

n,m

QS

n,m

(1)

S

n,m

(2)

S

n,m

m=1

n=1,2,…

γ=nπ/2

z