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arXiv · 2003.06726

A discrete and $q$ Asymptotic Iteration Method

Mourad E. H. Ismail·Nasser Saad
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Abstract

We introduce a finite difference and $q$-difference analogues of the Asymptotic Iteration Method of Ciftci, Hall, and Saad. We give necessary, and sufficient condition for the existence of a polynomial solution to a general linear second-order difference or $q$-difference equation subject to a "terminating condition", which is precisely defined. When a difference or $q$-difference equation has a polynomial solution, we show how to find the second solution.

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Mourad E. H. Ismail, Nasser Saad. 2020-03-15. A discrete and $q$ Asymptotic Iteration Method. https://arxiv.org/abs/2003.06726

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