In this article, we obtain a new fundamental theorems for Nikiforov–Uvarov–Suslov complex difference equation of hypergeometric type by the method of Euler integral transformation, its expression is different from Suslov’s Theorem. We also 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 and other important results.

中文翻译：

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关于非均匀格上超几何型的复差分方程

在本文中，我们通过欧拉积分变换的方法得到了Nikiforov-Uvarov-Suslov 复数微分方程的一个新的基本定理，它的表达式不同于Suslov 定理。我们还建立了非均匀格子上的超几何型Nikiforov-Uvarov-Suslov差分方程的伴随方程，并证明它也是非均匀格子上的超几何型差分方程。然后获得伴随方程的特解。作为这些特解的应用，我们利用它们得到了非均匀格上超几何型原始差分方程的特解等重要结果。