English

A discrete and $q$ Asymptotic Iteration Method

Classical Analysis and ODEs 2020-07-13 v2

Abstract

We introduce a finite difference and qq-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 qq-difference equation subject to a "terminating condition", which is precisely defined. When a difference or qq-difference equation has a polynomial solution, we show how to find the second solution.

Keywords

Cite

@article{arxiv.2003.06726,
  title  = {A discrete and $q$ Asymptotic Iteration Method},
  author = {Mourad E. H. Ismail and Nasser Saad},
  journal= {arXiv preprint arXiv:2003.06726},
  year   = {2020}
}

Comments

17 pages

R2 v1 2026-06-23T14:14:59.068Z