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