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Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials
Інший ID:
2010 Mathematics Subject Classification: 42C05; 33E30; 81Q05
http://dx.doi.org/10.3842/SIGMA.2011.107
http://dx.doi.org/10.3842/SIGMA.2011.107
Посилання:
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.
Підтримка:
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.
Дата:
2011
Переглядів:
336
Завантажень:
238
Анотація:
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.
