Asymptotic iteration method for solving Hahn difference equations

Advances in Difference Equations

article

MacQuarrie, Lucas¹  Saad, Nasser¹  Islam, Md. Shafiqul¹ 

[1] School of Mathematical and Computational Sciences, University of Prince Edward Island

关键词: Hahn operator;    Linear difference equations;    q -difference equations;    Polynomial solutions;    Eigenvalue problems;   

DOI  :  10.1186/s13662-021-03511-9

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

Hahn’s difference operator$D_{q;w}f(x) =({f(qx+w)-f(x)})/({(q-1)x+w})$ ,$q\in (0,1)$ ,$w>0$ ,$x\neq w/(1-q)$ is used to unify the recently established difference and q-asymptotic iteration methods (DAIM, qAIM). The technique is applied to solve the second-order linear Hahn difference equations. The necessary and sufficient conditions for polynomial solutions are derived and examined for the$(q;w)$ -hypergeometric equation.

【 授权许可】

CC BY