Stieltjes Polynomials

> n (x), the Chebyshev polynomial of the second kind, where E n+1 (x) = T n+1 (x), the Chebyshev polynomial of the first kind. For h(x) = (1 \Gamma x 2 ) \Gamma1=2 , P n (x) = T n (x) and E n+1 (x) = (1 \Gamma x 2 )U n\Gamma1 (x). A generalisation are the Bernstein-Szego weight functions h(x) = (1 \Gamma x 2 ) \Sigma1=2 =ae m (x), where ae m is a polynomial of degree m that is