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. Our paper is inspired to the classical tree methods in the theory of Clebsch-Gordan coefficients and of hyperspherical coordinates. It is based on previous work of Dunkl, who considered two-dimensional q-Hahn polynomials. It is also related to a recent paper of Gasper and Rahman: we show that their multidimensional q-Racah polynomials correspond to a particular case of our construction.

The tree method for multidimensional q-Hahn and q-Racah polynomials / Scarabotti, Fabio. - In: RAMANUJAN JOURNAL. - ISSN 1382-4090. - STAMPA. - 25:1(2011), pp. 57-91. [10.1007/s11139-010-9245-2]

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

SCARABOTTI, Fabio
2011

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. Our paper is inspired to the classical tree methods in the theory of Clebsch-Gordan coefficients and of hyperspherical coordinates. It is based on previous work of Dunkl, who considered two-dimensional q-Hahn polynomials. It is also related to a recent paper of Gasper and Rahman: we show that their multidimensional q-Racah polynomials correspond to a particular case of our construction.
2011
basic hypergeometric series; factorization method; q-hahn polynomial; q-racah polynomial; tree method
01 Pubblicazione su rivista::01a Articolo in rivista
The tree method for multidimensional q-Hahn and q-Racah polynomials / Scarabotti, Fabio. - In: RAMANUJAN JOURNAL. - ISSN 1382-4090. - STAMPA. - 25:1(2011), pp. 57-91. [10.1007/s11139-010-9245-2]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/377277
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