A note on orthogonal polynomials described by Chebyshev polynomials

Abstract 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 | T m ( x ) | p 1 − x 2 , − 1 x 1 , where T m is the Chebyshev polynomial of the first kind of degree m and p > − 1 . Namely, this note provides an explicit representation of the recurrence coefficients for polynomials orthogonal with respect to the above weight function and an explicit representation for these polynomials in terms of known functions.