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Asymptotic for Orthogonal Polynomials with Respect to a Rational Modification of a Measure Supported on the Semi-Axis

Author

Listed:
  • Carlos Féliz-Sánchez

    (Instituto de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Santo Domingo, Av. Alma Mater, Santo Domingo 10105, Dominican Republic)

  • Héctor Pijeira-Cabrera

    (Departamento de Matemáticas, Universidad Carlos III de Madrid, Av. de la Universidad, 30, 28911 Leganés, Spain)

  • Javier Quintero-Roba

    (Departamento de Teoría de la Señal y Comunicaciones y Sistemas Telemáticos y Computación, Universidad Rey Juan Carlos, 28942 Fuenlabrada, Spain)

Abstract

Given a sequence of orthogonal polynomials { L n } n = 0 ∞ , orthogonal with respect to a positive Borel ν measure supported on R + , let { Q n } n = 0 ∞ be the the sequence of orthogonal polynomials with respect to the modified measure r ( x ) d ν ( x ) , where r is certain rational function. This work is devoted to the proof of the relative asymptotic formula Q n ( d ) ( z ) L n ( d ) ( z ) ⇉ n ∏ k = 1 N 1 a k + i z + a k A k ∏ j = 1 N 2 z + b j b j + i B j , on compact subsets of C ∖ R + , where a k and b j are the zeros and poles of r , and the A k , B j are their respective multiplicities.

Suggested Citation

  • Carlos Féliz-Sánchez & Héctor Pijeira-Cabrera & Javier Quintero-Roba, 2024. "Asymptotic for Orthogonal Polynomials with Respect to a Rational Modification of a Measure Supported on the Semi-Axis," Mathematics, MDPI, vol. 12(7), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:1082-:d:1369700
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    References listed on IDEAS

    as
    1. Héctor Pijeira-Cabrera & Javier Quintero-Roba & Juan Toribio-Milane, 2023. "Differential Properties of Jacobi-Sobolev Polynomials and Electrostatic Interpretation," Mathematics, MDPI, vol. 11(15), pages 1-20, August.
    2. Abel Díaz-González & Juan Hernández & Héctor Pijeira-Cabrera, 2023. "Sequentially Ordered Sobolev Inner Product and Laguerre–Sobolev Polynomials," Mathematics, MDPI, vol. 11(8), pages 1-15, April.
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