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.
Bibliographical noteFunding Information:
Funding: The work of the first author was supported by Universidad de Monterrey under grant UIN19562. The work of the second author was supported by México’s Conacyt Grant 287523. The work of the third author (EJH) was supported by Dirección General de Investigación e Innovación, Consejería de Educación e Investigación of the Comunidad de Madrid (Spain), and Universidad de Alcalá under grant CM/JIN/2019-010, (Proyectos de I+D Para Jóvenes Investigadores de la Universidad de Alcalá 2019).
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