Recursive Relationship.  

     The Chebyshev polynomials can be generated recursively in the following way.  First, set

          

  and use the recurrence relation

        .  

Exploration 1.

This is a "classic example" of recursion programming. Enter the following lines into Mathematica to recursively define Chebyshev polynomials.  

Now check it out and see how recursion works.

(c) John H. Mathews 2004