Explicit Calculation of Some Polynomials Introduced by W. Gautschi

Abstract

In his classical by now investigation of the numerical condition of methods for computing orthogonal polynomials from modified moments, Gautschi introduced some poly-nomials defined by the nodes and weights of a Gaussian quadrature formula for the measure of orthogonality. We show that these polynomials can be calculated explicitly for Chebyshev weights of first, second and third kinds.