Griffiths polynomials of Racah type

Bivariate Griffiths polynomials of Racah type are constructed from univariate Racah polynomials. The bispectral properties of the former are deduced from simple properties of the latter. A duality relation and the orthogonality of these polynomials are provided. The domain of validity for the indice...

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Bibliographic Details
Published in:Journal of mathematical physics 2024-08, Vol.65 (8)
Main Authors: Crampé, Nicolas, Frappat, Luc, Gaboriaud, Julien, Ragoucy, Eric, Vinet, Luc, Zaimi, Meri
Format: Article
Language:English
Subjects:
Bivariate analysis
Mathematical Physics
Mathematics
Orthogonality
Polynomials
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Summary:Bivariate Griffiths polynomials of Racah type are constructed from univariate Racah polynomials. The bispectral properties of the former are deduced from simple properties of the latter. A duality relation and the orthogonality of these polynomials are provided. The domain of validity for the indices and variables of these polynomials is also determined. Particular limits on the parameters entering the polynomials allow to define several Griffiths polynomials of other types. One special limit connects them to the original Griffiths polynomials (of Krawtchouk type). Finally, a connection with the 9j symbols is made.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0209006