How to generate unknown orthogonal polynomials out of known orthogonal polynomials (Q1195724)

The aim of this paper is to present algorithms for generating the three- term recursion coefficients of orthogonal polynomials for a weight function \(v(t)=r(t)w(t)\). The weight function is obtained by modifying a given weight function \(w\) by a rational function \(r\). The authors describe a modified Chebyshev algorithm and apply it to the construction of orthogonal polynomials. Three algorithms are presented for the computation of orthogonal polynomials relative to weight functions \(v\) obtained by modifying \(w\) by a linear divisor or by a quadratic divisor. Some experiments with the derived methods are presented and discussed.