Abstract Quasi-Exactly Solvable Schrödinger Equations occupy an intermediate place
between exactly-solvable (eg the harmonic oscillator and Coulomb problems, etc.) and non …

The basic properties of the polynomials pn (x) that satisfy the orthogonality relations (2.0.
1)\int_a^ b p_n (x) p_m (x) ρ (x) dx= 0\quad (m ≠ n) hold also for the polynomials that satisfy …

We list the so-called Askey-scheme of hypergeometric orthogonal polynomials. In chapter 1
we give the definition, the orthogonality relation, the three term recurrence relation and …

The purpose of this article is threefold. First, it provides the reader with a few useful and
efficient tools which should enable her/him to evaluate nontrivial determinants for the case …

We list the so-called Askey-scheme of hypergeometric orthogonal polynomials and we give
a qanalogue of this scheme containing basic hypergeometric orthogonal polynomials. In …

Abstract CONTENTS Introduction § 1. Preliminary information § 2. Construction of particular
solutions for a difference equation of hypergeometric type on non-uniform lattices § 3. Some …

The subject of special functions is often presented as a collection of disparate results, rarely
organized in a coherent way. This book emphasizes general principles that unify and …

Following the works of Nikiforov and Uvarov a review of the hypergeometric-type difference
equation for a function y (x (s)) on a nonuniform lattice x (s) is given. It is shown that the …

Theinterpretation of the Meixner--Pollaczek, Meixner, and Laguerre polynomials as overlap
coefficients in the positive discrete series representations of the Lie algebra su(1,1) and the …

Second-order (maximally) superintegrable systems in dimensions two and three are
essentially classified. With increasing dimension, however, the non-linear partial differential …