A note on orthogonal polynomials described by Chebyshev polynomials

The purpose of this note is to extend in a simple and unified way some results on orthogonal polynomials with respect to the weight function $$\frac{\mathrm{\mid }{T}_m(x){\mathrm{\mid }}^p}{\sqrt{1-x^2}},-1<x<1,$$ where $T_m$ is the Chebyshev polynomial of the first kind of degree $m$ and $p>-1$.