Generating new classes of orthogonal polynomials (Q1922840)

Let \(\{P_n\}\) be a family of monic orthogonal polynomials that are orthogonal with respect to a quasi-definite linear functional \(u\). The paper under review deals with the problem of characterization of two sequences \(\{a_n\}\) and \(\{b_n\}\) for which the sequence \[ R_n=P_n+a_n P_{n-1}+b_nP_{n-2} \] \((n\geq 1\), \(P_{-1}(x)=0\), \(P_0(x)=1)\) is orthogonal to another quasi-definite linear functional \(v\). Applications to Hermite and Chebyshev polynomials of the second kind are included.