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arXiv · 0912.4357

The tree method for multidimensional q-Hahn and q-Racah polynomials

Fabio Scarabotti
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Abstract

We develop a tree method for multidimensional q-Hahn polynomials. We define them as eigenfunctions of a multidimensional q-difference operator and we use the factorization of this operator as a key tool. Then we define multidimensional q-Racah polynomials as the connection coefficients between different bases of q-Hahn polynomials. We show that our multidimensional q-Racah polynomials may be expressed as product of ordinary one-dimensional q-Racah polynomial by means of a suitable sequence of transplantations of edges of the trees.

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Fabio Scarabotti. 2009-12-22. The tree method for multidimensional q-Hahn and q-Racah polynomials. https://doi.org/10.1007/s11139-010-9245-2

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