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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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An algebraic description of the bispectrality of the biorthogonal rational functions of Hahn type
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by Satoshi Tsujimoto, Luc Vinet and Alexei Zhedanov PDF
Proc. Amer. Math. Soc. 149 (2021), 715-728 Request permission


The biorthogonal rational functions of ${_3}F_2$ type on the uniform grid provide the simplest example of rational functions with bispectrality properties that are similar to those of classical orthogonal polynomials. These properties are described by three difference operators $X,Y,Z$ which are tridiagonal with respect to three distinct bases of the relevant finite-dimensional space. The pairwise commutators of the operators $X,Y,Z$ generate a quadratic algebra which is akin to the algebras of Askey–Wilson type attached to hypergeometric polynomials.
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Additional Information
  • Satoshi Tsujimoto
  • Affiliation: Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Kyoto, Japan 606-8501
  • MR Author ID: 339527
  • Luc Vinet
  • Affiliation: Centre de recherches mathématiques, Université de Montréal, P. O. Box 6128, Centre-ville Station, Montréal (Québec), Canada H3C 3J7
  • MR Author ID: 178665
  • ORCID: 0000-0001-6211-7907
  • Alexei Zhedanov
  • Affiliation: School of Mathematics, Renmin University of China, Beijing 100872, People’s Republic of China
  • MR Author ID: 234560
  • Received by editor(s): May 7, 2020
  • Received by editor(s) in revised form: May 30, 2020
  • Published electronically: November 30, 2020
  • Additional Notes: The first author’s work was partially supported by JSPS KAKENHI (Grant Numbers 19H01792, 17K18725).
    The research of the second author was funded in part by a Discovery Grant from the Natural Sciences and Engineering Council (NSERC) of Canada.
    The third author gratefully acknowledges the award of a CRM-Simons Professorship and was supported by the National Science Foundation of China (Grant No.11771015).
  • Communicated by: Mourad Ismail
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 715-728
  • MSC (2010): Primary 33C45, 33C80
  • DOI:
  • MathSciNet review: 4198077