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In this article, we establish the adjoint equation forNikiforov-Uvarov-Suslov difference equation of hypergeometric type onnon-uniform lattices, and prove it to be a difference equation ofhypergeometric type on non-uniform lattices as well. The particular solutionsof the adjoint equation are then obtained. As an appliction of these particularsolutions, we use them to obtain the particular solutions for the originaldifference equation of hypergeometric type on non-uniform lattices. Finally, weprove another kind of fundamental theorems for Nikiforov-Uvarov-Suslovdifference equation of hypergeometric type, which are essentially new results,its expression is different from Suslov's Theorem.

Adjoint Difference Equation for a Nikiforov-Uvarov-Suslov difference equation of hypergeometric type on Non-uniform Lattices