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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-07-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-021-03511-9 |
| _version_ | 1818909184489422848 |
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| author | Lucas MacQuarrie Nasser Saad Md. Shafiqul Islam |
| author_facet | Lucas MacQuarrie Nasser Saad Md. Shafiqul Islam |
| author_sort | Lucas MacQuarrie |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-19T22:22:53Z |
| format | Article |
| id | doaj.art-87070bd2ccd84d70912cbda8bd79e011 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-19T22:22:53Z |
| publishDate | 2021-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-87070bd2ccd84d70912cbda8bd79e0112022-12-21T20:03:35ZengSpringerOpenAdvances in Difference Equations1687-18472021-07-012021112310.1186/s13662-021-03511-9Asymptotic iteration method for solving Hahn difference equationsLucas MacQuarrie0Nasser Saad1Md. Shafiqul Islam2School of Mathematical and Computational Sciences, University of Prince Edward IslandSchool of Mathematical and Computational Sciences, University of Prince Edward IslandSchool of Mathematical and Computational Sciences, University of Prince Edward IslandAbstract 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.https://doi.org/10.1186/s13662-021-03511-9Hahn operatorLinear difference equationsq-difference equationsPolynomial solutionsEigenvalue problems |
| spellingShingle | Lucas MacQuarrie Nasser Saad Md. Shafiqul Islam Asymptotic iteration method for solving Hahn difference equations Advances in Difference Equations Hahn operator Linear difference equations q-difference equations Polynomial solutions Eigenvalue problems |
| title | Asymptotic iteration method for solving Hahn difference equations |
| title_full | Asymptotic iteration method for solving Hahn difference equations |
| title_fullStr | Asymptotic iteration method for solving Hahn difference equations |
| title_full_unstemmed | Asymptotic iteration method for solving Hahn difference equations |
| title_short | Asymptotic iteration method for solving Hahn difference equations |
| title_sort | asymptotic iteration method for solving hahn difference equations |
| topic | Hahn operator Linear difference equations q-difference equations Polynomial solutions Eigenvalue problems |
| url | https://doi.org/10.1186/s13662-021-03511-9 |
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