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<p>In this article, using the method of Euler integral transforms, we obtain a new fundamental theorem for the Nikiforov-Uvarov-Suslov difference equation of hypergeometric type, which are essentially new results and their expressions are different from the Suslov Theorem. Meanwhile, we give two important examples to illustrate the applications of the new fundamental theorem. These indicate that the new fundamental theorem gives more general special functions which include the well-known Askey-Wilson polynomial as their particular case.</p>

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A New Fundamental Theorem for the Hypergeometric Difference Equation on Non-uniform Lattices and Its Application

  • 期刊论文

  • 发表日期：

    2026年1月22日

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  • Jin-fa Cheng

摘要

In this article, using the method of Euler integral transforms, we obtain a new fundamental theorem for the Nikiforov-Uvarov-Suslov difference equation of hypergeometric type, which are essentially new results and their expressions are different from the Suslov Theorem. Meanwhile, we give two important examples to illustrate the applications of the new fundamental theorem. These indicate that the new fundamental theorem gives more general special functions which include the well-known Askey-Wilson polynomial as their particular case.