Factorization of the hypergeometric-type difference equation on the uniform lattice. (English) Zbl 1176.33008

Álvarez-Nodarse, R.; Atakishiyev, N. M.; Costas-Santos, R. S.

ETNA, Electron. Trans. Numer. Anal. 27, 34-50 (2007).

Summary: We discuss factorization of the hypergeometric-type difference equations on the uniform lattices and show how one can construct a dynamical algebra, which corresponds to each of these equations. Some examples are exhibited, in particular, we show that several models of discrete harmonic oscillators, previously considered in a number of publications, can be treated in a unified form.

MSC:

33C45	Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
33C90	Applications of hypergeometric functions
39A13	Difference equations, scaling (\(q\)-differences)

Keywords:

discrete polynomials; factorization method; discrete oscillators