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

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 inclu...

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Bibliographic Details
Published in:Applied mathematics and computation 2017-11, Vol.313, p.52-73
Main Authors: Borrego-Morell, J., Rafaeli, F.R.
Format: Article
Language:English
Subjects:
Asymptotic expansions
Hypergeometric functions
Orthogonal polynomials
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Summary: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.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2017.05.070