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Open AccessArticle

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

1
Departamento de Física y Matemáticas, Universidad de Monterrey, San Pedro Garza García, Nuevo León 66238, Mexico
2
Facultad de Ciencias, Universidad de Colima, Colima 28045, Mexico
3
Departamento de Física y Matemáticas, Universidad de Alcalá, Alcalá de Henares, Madrid 28801, Spain
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 246; https://doi.org/10.3390/math8020246
Received: 13 January 2020 / Revised: 3 February 2020 / Accepted: 5 February 2020 / Published: 14 February 2020
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. View Full-Text
Keywords: Orthogonal polynomials on the unit circle; holonomic differential equations; spectral transformations; coherent pairs of measures Orthogonal polynomials on the unit circle; holonomic differential equations; spectral transformations; coherent pairs of measures
MDPI and ACS Style

Garza, L.G.; Garza, L.E.; Huertas, E.J. On Differential Equations Associated with Perturbations of Orthogonal Polynomials on the Unit Circle. Mathematics 2020, 8, 246. https://doi.org/10.3390/math8020246

AMA Style

Garza LG, Garza LE, Huertas EJ. On Differential Equations Associated with Perturbations of Orthogonal Polynomials on the Unit Circle. Mathematics. 2020; 8(2):246. https://doi.org/10.3390/math8020246

Chicago/Turabian Style

Garza, Lino G.; Garza, Luis E.; Huertas, Edmundo J. 2020. "On Differential Equations Associated with Perturbations of Orthogonal Polynomials on the Unit Circle" Mathematics 8, no. 2: 246. https://doi.org/10.3390/math8020246

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