Hamburger moment problems and orthogonal polynomials

Chihara, T. S.

doi:10.1090/S0002-9947-1989-0986686-1

Hamburger moment problems and orthogonal polynomials
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Trans. Amer. Math. Soc. 315 (1989), 189-203 Request permission

Abstract:

We consider a sequence of orthogonal polynomials given by the classical three term recurrence relation. We address the problem of deciding the determinacy or indeterminacy of the associated Hamburger moment problem on the basis of the behavior of the coefficients in the three term recurrence relation. Comparisons are made with other criteria in the literature. The efficacy of the criteria obtained is illustrated by application to many specific examples of orthogonal polynomials.

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