Adjoint difference equation for the Nikiforov–Uvarov–Suslov difference equation of hypergeometric type on non-uniform lattices

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 diff...

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Bibliographic Details
Published in:The Ramanujan journal 2020-11, Vol.53 (2), p.285-318
Main Authors: Cheng, Jinfa, Dai, Weizhong
Format: Article
Language:English
Subjects:
Combinatorics
Difference equations
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Lattices
Mathematics
Mathematics and Statistics
Number Theory
Theorems
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Summary: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.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-020-00298-3