Elliptic Racah polynomials

The q-Racah-Krall-type polynomials

Bispectrality of Multivariable Racah-wilson Polynomials

We construct a commutative algebra Ax of difference operators in R, depending on p + 3 parameters which is diagonalized by the multivariable Racah polynomials Rp(n; x) considered by Tratnik [27]. It is shown that for specific values of the variables x = (x1, x2, . . . , xp) there is a hidden duality between n and x. Analytic continuation allows us to construct another commutative algebra An in ...

2 00 8 Leonard pairs and the q - Racah polynomials ∗

Let K denote a field, and let V denote a vector space over K with finite positive dimension. We consider a pair of linear transformations A : V → V and A : V → V that satisfy the following two conditions: (i) There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A is diagonal. (ii) There exists a basis for V with respec...

Poisson Kernels as Expansions in q-Racah Polynomials

This note concerns stochastic processes on chains of arbitrary length whose Poisson kernel can be expressed in terms of the q-Racah polynomials, the most general q-deformed orthogonal polynomials in the discrete series of the Askey scheme. We give a new interpretation of this kernel as the probability transition density for a subordinated Markov process with only nearest neighbor hops. As an ap...

On the Limit from q-Racah Polynomials to Big q-Jacobi Polynomials

A limit formula from q-Racah polynomials to big q-Jacobi polynomials is given which can be considered as a limit formula for orthogonal polynomials. This is extended to a multi-parameter limit with 3 parameters, also involving (q-)Hahn polynomials, little q-Jacobi polynomials and Jacobi polynomials. Also the limits from Askey–Wilson to Wilson polynomials and from q-Racah to Racah polynomials ar...