Abstract
Chihara [On quasi orthogonal polynomials, Proc. Amer. Math. Soc. 8 (1957) , 765–767] has shown that quasi-orthogonal polynomials satisfy a three-term recurrence relation with polynomial coefficients. In this paper it is shown that, if a sequence of polynomial coefficients is given with some particular properties, then there exists a unique sequence of monic polynomials ({ U n } nϵN and U 0 = 1} which satisfies a three-term recurrence relation whose polynomial coefficients are those given. The polynomials are quasi-orthogonal of order 1 with respect to a unique linear functional of moments. Some new properties of the quasi-orthogonal polynomials of order 1 are also proved.
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