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**public sources and our publisher partners.**Dynamical quantum groups were recently introduced by Etingof and Varchenko as an algebraic framework for studying the dynamical Yang–Baxter equation, which is precisely the Yang–Baxter equation… Expand

In this paper we present an explicit (rank one) function transform which contains several Jacobi-type function transforms and Hankel-type transforms as degenerate cases. The kernel of the transform,… Expand

For the Bessel function \begin{equation} \label{bessel} J_{\nu}(z) = \sum\limits_{k=0}^{\infty} \frac{(-1)^k \left( \frac{z}{2} \right)^{\nu+2k}}{k! \Gamma(\nu+1+k)} \end{equation} there exist… Expand

In a previous paper we have introduced matrix-valued analogues of the Chebyshev polynomials by studying matrix-valued spherical functions on SU(2)\times SU(2). In particular the matrix-size of the… Expand

The matrix-valued spherical functions for the pair (K×K,K), K=SU(2), are studied. By restriction to the subgroup A, the matrix-valued spherical functions are diagonal. For suitable set of spherical… Expand

The lectures contain an introduction to quantum groups, q-special functions and their interplay. After generalities on Hopf algebras, ortogonal polynomials and basic hypergeometric series we work out… Expand

The symmetric Al-Salam–Chihara polynomials for q > 1 are associated with an indeterminate moment problem. There is a self-adjoint second-order difference operator on ℓ2(Z) to which these polynomials… Expand

A general addition formula for a two-parameter family of Askey-Wilson polynomials is derived from the quantum $SU(2)$ group theoretic interpretation. This formula contains most of the previously… Expand

We introduce matrix-valued weight functions of arbitrary size, which are analogues of the weight function for the Gegenbauer or ultraspherical polynomials for the parameter $\nu>0$. The… Expand