### Resumen

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.

Idioma original | English |
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Número de artículo | 246 |

Publicación | Mathematics |

Volumen | 8 |

N.º | 2 |

DOI | |

Estado | Published - 1 feb 2020 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

## Huella Profundice en los temas de investigación de 'On differential equations associated with perturbations of orthogonal polynomials on the unit circle'. En conjunto forman una huella única.

## Citar esto

Garza, L. G., Garza, L. E., & Huertas, E. J. (2020). On differential equations associated with perturbations of orthogonal polynomials on the unit circle.

*Mathematics*,*8*(2), [246]. https://doi.org/10.3390/math8020246