2024/07/24 by Nicolas Crampé, L. Frappat, Crampe, Nicolas +5 · 1 citation
Mathematics · #Advanced Mathematical Identities #Advanced Combinatorial Mathematics #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.2407.17016
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→1 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.