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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)