Yuri F. Smirnov, Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico and Moscow State University, Russia
e-mail:  smirnov@nucl-th.npi.msu.su

Finate Difference Equations and Factorization Method

Abstract

The factorization method, suggested by E. Schroedinger for the the solution of second order differential equations, is applied to the finite difference equations of hypergeometric type on the nonuniform lattice. It is shown that the method of the solution of these equations developed by Nikiforov, Suslov and Uvarov is equivalent to the factorization method. The possibility to apply a similar approach to the finite difference equations depending on two discrete variables is discussed. As an example the particular 7-term finite difference equation with a hidden SU(3) algebra is given. It has the factorized solution in a form of the product of the two Hahn polynomials.

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