-Hypergeometric Orthogonal Polynomials with = −1

We obtain some properties of a class of -hypergeometric orthogonal polynomials with = −1, described by a uniform parametrization of the recurrence coefficients. We construct a class of complementary −1 polynomials by means of the Darboux transformation with a shift. We show that our classes conta...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2025
Main Author: Verde-Star, Luis
Format: Article
Language:English
Published: Інститут математики НАН України 2025
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/214203
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:-Hypergeometric Orthogonal Polynomials with = −1. Luis Verde-Star. SIGMA 21 (2025), 083, 19 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Verde-Star, Luis
author_facet Verde-Star, Luis
citation_txt -Hypergeometric Orthogonal Polynomials with = −1. Luis Verde-Star. SIGMA 21 (2025), 083, 19 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We obtain some properties of a class of -hypergeometric orthogonal polynomials with = −1, described by a uniform parametrization of the recurrence coefficients. We construct a class of complementary −1 polynomials by means of the Darboux transformation with a shift. We show that our classes contain the Bannai-Ito polynomials, their complementary polynomials, and other known −1 polynomials. We introduce some new examples of −1 polynomials and also obtain matrix realizations of the Bannai-Ito algebra.
first_indexed 2026-03-21T12:22:35Z
format Article
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2026-03-21T12:22:35Z
publishDate 2025
publisher Інститут математики НАН України
record_format dspace
spelling Verde-Star, Luis
2026-02-20T08:04:16Z
2025
-Hypergeometric Orthogonal Polynomials with = −1. Luis Verde-Star. SIGMA 21 (2025), 083, 19 pages
1815-0659
2020 Mathematics Subject Classification: 33C45; 33D45
arXiv:2410.14068
https://nasplib.isofts.kiev.ua/handle/123456789/214203
https://doi.org/10.3842/SIGMA.2025.083
We obtain some properties of a class of -hypergeometric orthogonal polynomials with = −1, described by a uniform parametrization of the recurrence coefficients. We construct a class of complementary −1 polynomials by means of the Darboux transformation with a shift. We show that our classes contain the Bannai-Ito polynomials, their complementary polynomials, and other known −1 polynomials. We introduce some new examples of −1 polynomials and also obtain matrix realizations of the Bannai-Ito algebra.
I am very grateful to the anonymous referees for their many suggestions, which helped improve the paper.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
-Hypergeometric Orthogonal Polynomials with = −1
Article
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spellingShingle -Hypergeometric Orthogonal Polynomials with = −1
Verde-Star, Luis
title -Hypergeometric Orthogonal Polynomials with = −1
title_full -Hypergeometric Orthogonal Polynomials with = −1
title_fullStr -Hypergeometric Orthogonal Polynomials with = −1
title_full_unstemmed -Hypergeometric Orthogonal Polynomials with = −1
title_short -Hypergeometric Orthogonal Polynomials with = −1
title_sort -hypergeometric orthogonal polynomials with = −1
url https://nasplib.isofts.kiev.ua/handle/123456789/214203
work_keys_str_mv AT verdestarluis hypergeometricorthogonalpolynomialswith1