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On Differential Equations Associated with Perturbations of Orthogonal Polynomials on the Unit Circle

Author

Listed:
  • Lino G. Garza

    (Departamento de Física y Matemáticas, Universidad de Monterrey, San Pedro Garza García, Nuevo León 66238, Mexico)

  • Luis E. Garza

    (Facultad de Ciencias, Universidad de Colima, Colima 28045, Mexico)

  • Edmundo J. Huertas

    (Departamento de Física y Matemáticas, Universidad de Alcalá, Alcalá de Henares, Madrid 28801, Spain)

Abstract

In this contribution, we propose an algorithm to compute holonomic second-order differential equations satisfied by some families of orthogonal polynomials. Such algorithm is based in three properties that orthogonal polynomials satisfy: a recurrence relation, a structure formula, and a connection formula. This approach is used to obtain second-order differential equations whose solutions are orthogonal polynomials associated with some spectral transformations of a measure on the unit circle, as well as orthogonal polynomials associated with coherent pairs of measures on the unit circle.

Suggested Citation

  • Lino G. Garza & Luis E. Garza & Edmundo J. Huertas, 2020. "On Differential Equations Associated with Perturbations of Orthogonal Polynomials on the Unit Circle," Mathematics, MDPI, vol. 8(2), pages 1-19, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:246-:d:320484
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