Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials
|
|
| Creator |
Ho, C.
Odake, S. Sasaki, R. |
|
| 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.
|
|
| Date |
2019-02-16T12:46:59Z
2019-02-16T12:46:59Z 2011 |
|
| Type |
Article
|
|
| Identifier |
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 http://dspace.nbuv.gov.ua/handle/123456789/147992 |
|
| Language |
en
|
|
| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
|
|
| Publisher |
Інститут математики НАН України
|
|