Angular Spheroidal Functions as a Function of Spheroidicity

This Demonstration shows how the angular spheroidal functions,

PS

n,m

(γ,x)

, vary over the interval

-1≤x≤1

. For comparison we also show the corresponding Legendre functions,

m

P

n

(x)

, to which the spheroidal ones reduce when

γ=0

. The controls allow

2

γ

to be varied: for

2

γ

>0

(real

γ

) we have the so-called prolate functions, while for

2

γ

<0

(imaginary

γ

) we have the oblate functions.