## Abstract

In this contribution, we explore the well-known connection between Hurwitz and orthogonal polynomials. Namely, given a Hurwitz polynomial, it is shown that it can be decomposed into two parts: a polynomial that is orthogonal with respect to some positive measure supported in the positive real axis and its corresponding second-kind polynomial. Conversely, given a sequence of orthogonal polynomials with respect to a positive measure supported in the positive real axis, a sequence of Hurwitz polynomials can be constructed. Based on that connection, we construct sequences of Hurwitz polynomials that satisfy a recurrence relation, in a similar way as the orthogonal polynomials do. Even more, we present a way to construct families of Hurwitz polynomials using two sequences of parameters and a recurrence relation that constitutes an analogue of Favard's theorem in the theory of orthogonal polynomials.

Original language | English |
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Pages (from-to) | 2191-2208 |

Number of pages | 18 |

Journal | Linear and Multilinear Algebra |

Volume | 67 |

Issue number | 11 |

DOIs | |

Publication status | Published - 2 Nov 2019 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.

## All Science Journal Classification (ASJC) codes

- Algebra and Number Theory