Factorization method: new aspects

The factorization method [1,2], suggested by E. Schroedinger for 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 [4], is equivalent to the factorization method. The possibility to apply a similar approach to the finite difference equation depending on two discrete variables is discussed. as an example the particular 7-term finite difference equation is given which has the factorized solution in a form of the product of the two Hahn polynomials.