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The matrix elements of unitary $SU_q(3)$ corepresentations, which are analogues of the symmetric powers of the natural repesentation, are shown to be the bivariate $q$-Krawtchouk orthogonal polynomials, thus providing an algebraic interpretation of these polynomials in terms of quantum groups.
S-Heun operators on linear and $q$-linear grids are introduced. These operators are special cases of Heun operators and are related to Sklyanin-like algebras. The Continuous Hahn and Big $q$-Jacobi polynomials are functions on which these S-Heun oper
The symbolic method is used to get explicit formulae for the products or powers of Bessel functions and for the relevant integrals.
A survey of recents advances in the theory of Heun operators is offered. Some of the topics covered include: quadratic algebras and orthogonal polynomials, differential and difference Heun operators associated to Jacobi and Hahn polynomials, connecti
We investigate polynomials, called m-polynomials, whose generator polynomial has coefficients that can be arranged as a matrix, where q is a positive integer greater than one. Orthogonality relations are established and coefficients are obtained for
We consider the time-dependent dynamical system $ddot{q}^{a}= -Gamma_{bc}^{a}dot{q}^{b}dot{q}^{c}-omega(t)Q^{a}(q)$ where $omega(t)$ is a non-zero arbitrary function and the connection coefficients $Gamma^{a}_{bc}$ are computed from the kinetic metri