On sequences of Hurwitz polynomials related to orthogonal polynomials

Noé Martínez, Luis E. Garza*, Baltazar Aguirre-Hernández

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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 languageEnglish
Pages (from-to)2191-2208
Number of pages18
JournalLinear and Multilinear Algebra
Issue number11
Publication statusPublished - 2 Nov 2019
Externally publishedYes

Bibliographical note

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

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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