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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Matrix Jacobi biorthogonal polynomials via Riemann–Hilbert problem
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by Amílcar Branquinho, Ana Foulquié-Moreno, Assil Fradi and Manuel Mañas
Proc. Amer. Math. Soc. 152 (2024), 193-208
Published electronically: October 6, 2023


We consider matrix orthogonal polynomials related to Jacobi type matrices of weights that can be defined in terms of a given matrix Pearson equation. Stating a Riemann–Hilbert problem we can derive first and second order differential-difference relations that these matrix orthogonal polynomials and the second kind functions associated to them verify. For the corresponding matrix recurrence coefficients, non-Abelian extensions of a family of discrete Painlevé d-P$_{IV}$ equations are obtained for the three term recurrence relation coefficients.
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Bibliographic Information
  • Amílcar Branquinho
  • Affiliation: CMUC, Departamento de Matemática, Universidade de Coimbra, Largo D. Dinis, 3000-143 Coimbra, Portugal
  • ORCID: 0000-0003-4685-1583
  • Email:
  • Ana Foulquié-Moreno
  • Affiliation: CIDMA, Departamento de Matemática, Universidade de Aveiro, 3810-193 Aveiro, Portugal
  • ORCID: 0000-0001-5097-950X
  • Email:
  • Assil Fradi
  • Affiliation: Mathematical Physics Special Functions and Applications Laboratory, The Higher School of Sciences and Technology of Hammam Sousse, University of Sousse, Sousse 4002, Tunisia
  • ORCID: 0000-0003-2398-990X
  • Email:
  • Manuel Mañas
  • Affiliation: Departamento de Física Teórica, Universidad Complutense de Madrid, 28040-Madrid, Spain; and Instituto de Ciencias Matematicas (ICMAT), Campus de Cantoblanco UAM, 28049-Madrid, Spain
  • ORCID: 0000-0003-3764-5737
  • Email:
  • Received by editor(s): August 29, 2022
  • Received by editor(s) in revised form: January 17, 2023, and January 20, 2023
  • Published electronically: October 6, 2023
  • Additional Notes: The first author acknowledges the Centro de Matemática da Universidade de Coimbra, UIDB/00324/2020, which is funded by the Portuguese Government through FCT/MECS.
    The second and third authors acknowledge CIDMA Center for Research and Development in Mathematics and Applications (University of Aveiro) and the Portuguese Foundation for Science and Technology (FCT) within project UIDB/04106/2020 and UIDP/04106/2020.
    The fourth author thanks financial support from the Spanish “Agencia Estatal de Investigación” research project [PGC2018-096504-B-C33], Ortogonalidad y Aproximación: Teoría y Aplicaciones en Física Matemática.
    The first, second, and fourth authors acknowledge “Agencia Estatal de Investigación” research project [PID2021- 122154NB-I00], Ortogonalidad y aproximación con aplicaciones en machine learning y teoría de la probabilidad.
    The second author is the corresponding author
  • Communicated by: Mourad Ismail
  • Journal: Proc. Amer. Math. Soc. 152 (2024), 193-208
  • MSC (2020): Primary 33C45, 33C47, 42C05, 47A56
  • DOI:
  • MathSciNet review: 4661074