We demonstrate a Markov duality between the dynamic asymmetric simple exclusion
process (ASEP) and the standard ASEP. We then apply this to step initial data, as well as a …

The J-matrix method is extended to difference and q-difference operators and is applied to
several explicit differential, difference, q-difference and second order Askey-Wilson type …

For a class of orthogonal polynomials related to the q-Meixner polynomials corresponding to
an indeterminate moment problem we give a one-parameter family of orthogonality …

Many special functions are eigenfunctions to explicit operators, such as difference and
differential operators, which is in particular true for the special functions occurring in the …

We give new derivations of properties of the functions of the second kind of the Jacobi, little
and big q-Jacobi polynomials, and the symmetric Al-Salam–Chihara polynomials for q> 1 …

The complex zeros of the orthogonal Laguerre polynomials L n (a)(x) for a<− n,
ultraspherical polynomials P n (λ)(x) for λ<− n, Jacobi polynomials P n (a, β)(x) for a<− n, β< …

We study the q-hypergeometric difference operator L on a particular Hilbert space. In this
setting L can be considered as an extension of the Jacobi operator for q− 1-Al-Salam …

We study a limiting case of the Askey–Wilson polynomials when one of the parameters goes
to infinity, namely continuous dual q-Hahn polynomials when q> 1. Solutions to the …

We study the spectral properties of a class of Sturm-Liouville type operators on the real line
where the derivatives are replaced by aq-difference operator which has been introduced in …