Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials
We present various results on the properties of the four infinite sets of the exceptional Xl polynomials discovered recently by Odake and Sasaki [Phys. Lett. B 679 (2009), 414-417; Phys. Lett. B 684 (2010), 173-176]. These Xl polynomials are global solutions of second order Fuchsian differential equ...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2011 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2011
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147992 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials / C. Ho, S. Odake, R. Sasaki // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 20 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862639443453673472 |
|---|---|
| author | Ho, C. Odake, S. Sasaki, R. |
| author_facet | Ho, C. Odake, S. Sasaki, R. |
| citation_txt | Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials / C. Ho, S. Odake, R. Sasaki // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 20 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We present various results on the properties of the four infinite sets of the exceptional Xl polynomials discovered recently by Odake and Sasaki [Phys. Lett. B 679 (2009), 414-417; Phys. Lett. B 684 (2010), 173-176]. These Xl polynomials are global solutions of second order Fuchsian differential equations with l+3 regular singularities and their confluent limits. We derive equivalent but much simpler looking forms of the Xl polynomials. The other subjects discussed in detail are: factorisation of the Fuchsian differential operators, shape invariance, the forward and backward shift operations, invariant polynomial subspaces under the Fuchsian differential operators, the Gram-Schmidt orthonormalisation procedure, three term recurrence relations and the generating functions for the Xl polynomials.
|
| first_indexed | 2025-12-01T01:21:17Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147992 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T01:21:17Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ho, C. Odake, S. Sasaki, R. 2019-02-16T12:46:59Z 2019-02-16T12:46:59Z 2011 Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials / C. Ho, S. Odake, R. Sasaki // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 20 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 42C05; 33E30; 81Q05 http://dx.doi.org/10.3842/SIGMA.2011.107 https://nasplib.isofts.kiev.ua/handle/123456789/147992 We present various results on the properties of the four infinite sets of the exceptional Xl polynomials discovered recently by Odake and Sasaki [Phys. Lett. B 679 (2009), 414-417; Phys. Lett. B 684 (2010), 173-176]. These Xl polynomials are global solutions of second order Fuchsian differential equations with l+3 regular singularities and their confluent limits. We derive equivalent but much simpler looking forms of the Xl polynomials. The other subjects discussed in detail are: factorisation of the Fuchsian differential operators, shape invariance, the forward and backward shift operations, invariant polynomial subspaces under the Fuchsian differential operators, the Gram-Schmidt orthonormalisation procedure, three term recurrence relations and the generating functions for the Xl polynomials. This work is supported in part by the National Science Council (NSC) of the Republic of China under Grant NSC 96-2112-M-032-007-MY3 (CLH), and in part by Grants-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology, No.19540179 (RS). Part of the work was done during CLH’s visit to the Yukawa Institute for Theoretical Physics (YITP), Kyoto University, and he would like to thank the staf f and members of YITP for the hospitality extended to him. RS wishes to thank National Taiwan University and NationalChiao-Tung University for the hospitality extended to him during his visits in which a part of the work was done. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials Article published earlier |
| spellingShingle | Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials Ho, C. Odake, S. Sasaki, R. |
| title | Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials |
| title_full | Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials |
| title_fullStr | Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials |
| title_full_unstemmed | Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials |
| title_short | Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials |
| title_sort | properties of the exceptional (xl) laguerre and jacobi polynomials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147992 |
| work_keys_str_mv | AT hoc propertiesoftheexceptionalxllaguerreandjacobipolynomials AT odakes propertiesoftheexceptionalxllaguerreandjacobipolynomials AT sasakir propertiesoftheexceptionalxllaguerreandjacobipolynomials |