Series Solutions of the Non-Stationary Heun Equation
We consider the non-stationary Heun equation, also known as quantum Painlevé VI, which has appeared in different works on quantum integrable models and conformal field theory. We use a generalized kernel function identity to transform the problem to solve this equation into a differential-difference...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2018 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2018
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/209453 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Series Solutions of the Non-Stationary Heun Equation / F. Atai, E. Langmann // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 41 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862691825858379776 |
|---|---|
| author | Atai, F. Langmann, E. |
| author_facet | Atai, F. Langmann, E. |
| citation_txt | Series Solutions of the Non-Stationary Heun Equation / F. Atai, E. Langmann // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 41 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We consider the non-stationary Heun equation, also known as quantum Painlevé VI, which has appeared in different works on quantum integrable models and conformal field theory. We use a generalized kernel function identity to transform the problem to solve this equation into a differential-difference equation, which, as we show, can be solved by efficient recursive algorithms. We thus obtain series representations of solutions which provide elliptic generalizations of the Jacobi polynomials. These series reproduce, in a limiting case, a perturbative solution of the Heun equation due to Takemura, but our method is different in that we expand in non-conventional basis functions that allow us to obtain explicit formulas to all orders; in particular, for special parameter values, our series reduce to a single term.
|
| first_indexed | 2025-12-07T16:16:39Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209453 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:16:39Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Atai, F. Langmann, E. 2025-11-21T19:05:32Z 2018 Series Solutions of the Non-Stationary Heun Equation / F. Atai, E. Langmann // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 41 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33E20; 81Q05; 16R60 arXiv: 1609.02525 https://nasplib.isofts.kiev.ua/handle/123456789/209453 https://doi.org/10.3842/SIGMA.2018.011 We consider the non-stationary Heun equation, also known as quantum Painlevé VI, which has appeared in different works on quantum integrable models and conformal field theory. We use a generalized kernel function identity to transform the problem to solve this equation into a differential-difference equation, which, as we show, can be solved by efficient recursive algorithms. We thus obtain series representations of solutions which provide elliptic generalizations of the Jacobi polynomials. These series reproduce, in a limiting case, a perturbative solution of the Heun equation due to Takemura, but our method is different in that we expand in non-conventional basis functions that allow us to obtain explicit formulas to all orders; in particular, for special parameter values, our series reduce to a single term. We thank M. Hallnäs, O. Chalykh, and H. Rosengren for helpful discussions and comments, as well as an anonymous referee for carefully reading our paper. We gratefully acknowledge partial financial support by the Stiftelse Olle Engkvist Byggmästare (contract 184-0573). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Series Solutions of the Non-Stationary Heun Equation Article published earlier |
| spellingShingle | Series Solutions of the Non-Stationary Heun Equation Atai, F. Langmann, E. |
| title | Series Solutions of the Non-Stationary Heun Equation |
| title_full | Series Solutions of the Non-Stationary Heun Equation |
| title_fullStr | Series Solutions of the Non-Stationary Heun Equation |
| title_full_unstemmed | Series Solutions of the Non-Stationary Heun Equation |
| title_short | Series Solutions of the Non-Stationary Heun Equation |
| title_sort | series solutions of the non-stationary heun equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209453 |
| work_keys_str_mv | AT ataif seriessolutionsofthenonstationaryheunequation AT langmanne seriessolutionsofthenonstationaryheunequation |