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We study the nonnegative product linearization property for polynomials with even- tually constant Jacobi parameters. For some special cases a necessary and sucient condition for this property is provided. 1. Introduction. LetfPng 1=0 be a sequence of polynomials defined by the following recurrence relation: P0(x) = 1 and for n 0 xPn(x) = Pn+1(x) + nPn(x) + n 1Pn 1(x) (1) (under the convention thatP 1(x) = 0), wheref ng 1=0 andf ng 1=0 are sequences of real numbers, called Jacobi parameters, and n > 0. Then all Pn are monic and degPn = n. We denote byL the linear functional on R(x) defined by:L(P0) = 1 andL(Pn) = 0 for n 1. Then we have

Nonnegative linearization for orthogonal polynomials with eventually constant Jacobi parameters