An asymptotic expansion for a class of biorthogonal polynomials with respect to a measure on the unit circle

J. Borrego-Morell and F.R. Rafaeli

Applied Mathematics and Computation, 2017, vol. 313, issue C, 52-73

Abstract: We consider the system of biorthogonal polynomials {Pn, Qn}n ≥ 0 with respect to a complex valued measure supported on the unit circle and give a uniform compound asymptotic expansion formula consisting of the sum of two inverse factorial series, giving the explicit expression of the terms and including error bounds. As a consequence we prove that the set of accumulation points of the zeros these polynomials is included in the unit circle. Some numerical experiments are included.

Keywords: Asymptotic expansions; Orthogonal polynomials; Hypergeometric functions (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:313:y:2017:i:c:p:52-73

DOI: 10.1016/j.amc.2017.05.070

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