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Angular Spheroidal Functions as a Function of Spheroidicity


	This Demonstration shows how the angular spheroidal functions, , vary over the interval . For comparison we also show the corresponding Legendre functions, , to which the spheroidal ones reduce when . The controls allow to be varied: for (real ) we have the so-called prolate functions, while for (imaginary ) we have the oblate functions.


	Contributed by: Peter Falloon

Snapshot 1: in the prolate limit

(where the spheroid becomes an infinite cylinder), the angular spheroidal functions become more concentrated around the origin (

), and less concentrated around the edges (

)

Snapshot 2: the reverse holds in the oblate limit

, in which the spheroid becomes a flat disk

Snapshot 3: in the oblate limit, both even and odd functions vanish at

; the even functions tend to the same form as the next higher odd function, with a sign change on one half of the interval (compare this picture, for

, with Snapshot 2, where

)

Contributed by: Peter Falloon

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