Sturm Liouville Theory and Orthogonal Polynomials

This is an evaluated Mathematica notebook. Since the notebook is intended to be interactive, it may be helpful to also view the unevaluated version

Copyright 1996
Gary S. Stoudt
Mathematics Department
Indiana University of PA
Indiana, PA 15705
GSSTOUDT@grove.iup.edu

It is assumed that you are acquainted with some of the aspects of Sturm-Liouville theory.

In[1]:=

  <<Calculus`DiracDelta`

This package allows us to use Dirac delta functions and Heaviside (step) functions.

Make sure you look at the notebook evenodd.ma before looking at this notebook.

The Sturm-Liouville form of a differential equation that we will use is
(ry')'+(q+Lp)y=0.
The functions p, q, r, and r' are continuous on the necessary interval and p and r are positive on the interval (except at possibly the endpoints).

Legendre Polynomials

Hermite Polynomials

Laguerre Polynomials

Chebychev Polynomials (of the First Kind)

Exercises

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