Quasi-exactly solvable problems and the dual (q-)Hahn polynomials

Abstract

A second-order differential (q-difference) eigenvalue equation is constructed whose solutions are generating functions of the dual (q-)Hahn polynomials. The fact is noticed that these generating functions are reduced to the (little q-)Jacobi polynomials, and implications of this for quasi-exactly solvable problems are studied. A connection with the Azbel-Hofstadter problem is indicated.

15 pages, LaTex; final version, presentation improved, title changed, to appear in J.Math.Phys

References in corpus (5)

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• Quasi-Exactly Solvable Systems and Orthogonal Polynomials
• Lie-algebraic discretization of differential equations
• Algebraization of difference eigenvalue equations related to $U_q(s{l}_2)$
• Quasi-Exactly Solvable Potentials on the Line and Orthogonal Polynomials