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Pré-Publication, Document De Travail Année : 2024

Griffiths polynomials of $q$-Racah type

Résumé

New bivariate Griffiths polynomials of $q$-Racah type are introduced and characterized. They generalize the polynomials orthogonal on the multinomial distribution introduced by R. Griffiths fifty years ago. They also correspond to a $q$-deformation of the Griffiths polynomials of Racah type introduced previously by the authors and collaborators. The latter are recovered from the former by a $q\to1$ limit. We show that these new polynomials are bispectral and biorthogonal. We also exhibit some symmetry relations that are essential in the proof of the bispectrality property.

Dates et versions

hal-04669703 , version 1 (09-08-2024)

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Nicolas Crampe, Luc Frappat, Julien Gaboriaud, Eric Ragoucy. Griffiths polynomials of $q$-Racah type. 2024. ⟨hal-04669703⟩
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