In this article, we obtain the adjoint difference equation for the 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 difference equation are then obtained. As an application of these particular solutions, we use them to obtain the particular solutions for the original difference equation of hypergeometric type on non-uniform lattices. In addition, we give another kind of fundamental theorems for the Nikiforov–Uvarov–Suslov difference equation of hypergeometric type, which are essentially new results and their expressions are different from the Suslov Theorem. Finally, we give an example to illustrate the application of the new fundamental theorems.

在本文中，我们获得了非均匀格上超几何型Nikiforov–Uvarov–Suslov差分方程的伴随差分方程，并证明它也是非均匀格上超几何型的差分方程。然后获得伴随差分方程的特定解。作为这些特定解的应用，我们使用它们来获得非均匀格上超几何类型原始差分方程的特定解。此外，我们为超几何类型的Nikiforov–Uvarov–Suslov差分方程提供了另一种基本定理，这些基本定理是新的结果，其表达式与Suslov定理不同。最后，我们给出一个例子来说明新的基本定理的应用。