This updated edition will continue to meet the needs for an authoritative comprehensive
analysis of the rapidly growing field of basic hypergeometric series, or q-series. It includes …

We consider the most general Dunkl shift operator L with the following properties:(i) L is of
first order in the shift operator and involves reflections;(ii) L preserves the space of …

The equivalence is found between high-energy QCD in the generalized leading logarithmic
approximation and the one-dimensional Heisenberg magnet. According to Regge theory …

We present some general results concerning so-called biorthogonal polynomials of RII type
introduced by M. Ismail and D. Masson. These polynomials give rise to a pair of rational …

A discrete-time chain, associated with the generalized eigenvalue problem for two Jacobi
matrices, is derived. Various discrete and continuous symmetries of this integrable equation …

A review of selected topics for Hirota's bilinear difference equation (HBDE) is given. This
famous three-dimensional difference equation is known to provide a canonical integrable …

Reflectionless defects in Hermitian tight-binding lattices, synthesized by the intertwining
operator technique of supersymmetric quantum mechanics, are generally not invisible and …

On the one hand the work of R. Askey and J. Wilson [3] shows that if one enters the “land of
g” and replaces derivatives by q-derivatives then one gets a much larger class of …

Skew-orthogonal polynomials (SOPs) arise in the study of the n-point distribution function for
orthogonal and symplectic random matrix ensembles. Motivated by the average of …

We consider some special reductions of generic Darboux–Crum dressing formulae and of
their difference versions. As a matter of fact, we obtain some new formulae for Darboux …