I need help using the Gram-Schmidt orthogonalization process to derive the first four orthonormal Chebychev polynomials. Using the range $[-1,1]$ and the weight function $w(x)=(1-x^2)^\frac{1}{2}$.
I know I can follow the Gram-Schmidt process using this link but I am unsure how to start this problem with the Chebychev polynomials, meaning what would be my $u(1)$ and $u(2)$?
The Gram-Schmidt process can be used to orthonormalize any linearly independent family of vectors. Since you want to end up with polynomials, you could pick the family of monomials $\{1,x,x^2,x^3,\ldots\}$ and start orthonormalizing with respect to your inner product.