Next Article in Journal
A Discussion on Random Meir-Keeler Contractions
Previous Article in Journal
Fuzzy Multi-Hypergroups
Previous Article in Special Issue
Eigenvalue Problem for Discrete Jacobi–Sobolev Orthogonal Polynomials
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.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop