On the Condition of Orthogonal Polynomials via Modified Moments

Abstract

We consider the condition of orthogonal polynomials, encoded by the coefficients of their three-term recurrence relation, if the measure is given by modified moments (i.e. integrals of certain polynomials forming a basis). The results concerning various polynomial bases are illustrated by simple examples of generating (possibly shifted) Chebyshev polynomials of first and second kind.