Figure 1: Plot of Chebyshev polynomials [1] The leading coefficient of the

Figure 1: Plot of Chebyshev polynomials

[1] The leading coefficient of the is for as we can see from the recursive formula shown above. These polynomials are orthogonal with respect to the weight function on the interval ,

As we have mentioned, denotes the Chebyshev polynomial of degree . It has roots, which are also known as Chebyshev nodes. These nodes [5] can be calculated by the formula

A function can be approximated [4] by an n-th degree polynomial expressed in terms of ,

where

and are zeros of .
Since