Asymptotic iteration method for solving Hahn difference equations

Asymptotic iteration method for solving Hahn difference equations

Abstract Hahn’s difference operator D q ; w f ( x ) = ( f ( q x + w ) − f ( x ) ) / ( ( q − 1 ) x + w ) $D_{q;w}f(x) =({f(qx+w)-f(x)})/({(q-1)x+w})$ , q ∈ ( 0 , 1 ) $q\in (0,1)$ , w > 0 $w>0$ , x ≠ w / ( 1 − q ) $x\neq w/(1-q)$ is used to unify the recently established difference and q-asympto...

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Bibliographic Details
Main Authors: Lucas MacQuarrie, Nasser Saad, Md. Shafiqul Islam
Format: Article
Language:English
Published: SpringerOpen 2021-07-01
Series:Advances in Difference Equations
Subjects:
Hahn operator
Linear difference equations
q-difference equations
Polynomial solutions
Eigenvalue problems
Online Access:https://doi.org/10.1186/s13662-021-03511-9
Description
Summary:Abstract Hahn’s difference operator D q ; w f ( x ) = ( f ( q x + w ) − f ( x ) ) / ( ( q − 1 ) x + w ) $D_{q;w}f(x) =({f(qx+w)-f(x)})/({(q-1)x+w})$ , q ∈ ( 0 , 1 ) $q\in (0,1)$ , w > 0 $w>0$ , x ≠ w / ( 1 − q ) $x\neq w/(1-q)$ 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 ) $(q;w)$ -hypergeometric equation.
ISSN:1687-1847

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