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.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


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 )
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+