Asymptotic expansions for solutions of smooth recurrence equations
Authors:
ShingWhu Jha, Attila Máté and Paul Nevai
Journal:
Proc. Amer. Math. Soc. 110 (1990), 365370
MSC:
Primary 33C45; Secondary 39A10, 41A60
MathSciNet review:
1014646
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Abstract: Let be a convergent sequence of reals, where for each the tuple satisfies one of equations, depending on the residue class of , for some given and . Assume these equations are smooth, they have the same gradient in the first variables, and this gradient satisfies a certain nonmodularity condition. We then show that has asymptotic expansions, depending on the residue class of , in terms of powers of . This result enables us to discuss the asymptotic behavior of the recurrence coefficients associated with certain orthogonal polynomials. A key ingredient in the proof of the main result is a lemma involving exponential sums.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199010146467
PII:
S 00029939(1990)10146467
Keywords:
Asymptotic expansions,
exponential sums,
orthogonal polynomials,
recurrence equations
Article copyright:
© Copyright 1990 American Mathematical Society
