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

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

1998-02-25

arxiv.org/abs/physics/9802045v3

J. Math. Phys. 41, 569 (2000)

Physics

Mathematical Physics

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

Scientific paper

10.1063/1.533143

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.

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