Linearization and connection coefficients of orthogonal polynomials

Let {P_n}_n^=0/ be a system of orthogonal polynomials.Lasser [5] observed that if the linearization coefficients of {P_n}_n^=0/ are nonnegative then each of theP_n(x) is a linear combination of the Tchebyshev polynomials with nonnegative coefficients. The aim of this paper is to give a partial converse to this statement. We also consider the problem of determining when the polynomialsP_ncan be expressed in terms ofQ_nwith nonnegative coefficients, where {Q_n}_n^=0/ is another system of orthogonal polynomials. New proofs of well known theorems are given as well as new results and examples are presented.