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We investigate polynomials satisfying a three-term recurrence relation of the form B n (x) = (x − β n)B n−1 (x) − α n xB n−2 (x), with positive recurrence coefficients α n+1 , β n (n = 1, 2,. . .). We show that the zeros are eigenvalues of a structured Hessenberg matrix and give the left and right eigenvectors of this matrix, from which we deduce Laurent… (More)

We study polynomials which satisfy the same recurrence relation as the Szeg˝ o polynomials, however, with the restriction that the (reflection) coefficients in the recurrence are larger than one in modulus. Para-orthogonal polynomials that follow from these Szeg˝ o polynomials are also considered. With positive values for the reflection coefficients, zeros… (More)