Asymptotic expansions of ratios of coefficients of orthogonal polynomials with exponential weights

Authors:
Attila Máté, Paul Nevai and Thomas Zaslavsky

Journal:
Trans. Amer. Math. Soc. **287** (1985), 495-505

MSC:
Primary 42C05; Secondary 05A15

DOI:
https://doi.org/10.1090/S0002-9947-1985-0768722-7

MathSciNet review:
768722

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Abstract | References | Similar Articles | Additional Information

Abstract: Let denote the th polynomial orthonormal with respect to the weight where is an even integer. G. Freud conjectured and Al. Magnus proved that, writing , the expression has a limit as . It is shown that this expression has an asymptotic expansion in terms of negative even powers of . In the course of this, a combinatorial enumeration problem concerning one-dimensional lattice walk is solved and its relationship to a combinatorial identity of J. L. W. V. Jensen is explored.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1985-0768722-7

Keywords:
Asymptotic expansion,
combinatorial enumerations,
combinatorial identities,
Freud's conjecture,
Jensen's identity,
orthogonal polynomials

Article copyright:
© Copyright 1985
American Mathematical Society