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

Author

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  • Borrego-Morell, J.
  • Rafaeli, F.R.

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.

Suggested Citation

  • Borrego-Morell, J. & Rafaeli, F.R., 2017. "An asymptotic expansion for a class of biorthogonal polynomials with respect to a measure on the unit circle," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 52-73.
    • Handle: RePEc:eee:apmaco:v:313:y:2017:i:c:p:52-73
    DOI: 10.1016/j.amc.2017.05.070
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