On the Complex Difference Equation of Hypergeometric Type on Non-uniform Lattices

Abstract

In this article, we establish the adjoint equation for Nikiforov-Uvarov-Suslov difference equation of hypergeometric type on non-uniform lattices, and prove it to be a difference equation of hypergeometric type on non-uniform lattices as well. The particular solutions of the adjoint equation are then obtained. As an appliction of these particular solutions, we use them to obtain the particular solutions for the original difference equation of hypergeometric type on non-uniform lattices. Finally, we prove another kind of fundamental theorems for Nikiforov-Uvarov-Suslov difference equation of hypergeometric type, which are essentially new results, its expression is different from Suslov's Theorem. equation of hypergeometric type; Non-uniform lattice MSC 2010: 33D20,33D45, 33C45.