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Simplified Expressions of the Multi-Indexed 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, 2017, том 13
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Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials
Інший ID:
2010 Mathematics Subject Classification: 42C05; 33C45; 34A05
DOI:10.3842/SIGMA.2017.020
DOI:10.3842/SIGMA.2017.020
Посилання:
Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials / S. Odake, R. Sasaki // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 24 назв. — англ.
Підтримка:
S.O. is supported in part by Grant-in-Aid for Scientific Research from the Ministry of Education,
Culture, Sports, Science and Technology (MEXT), No. 25400395.
Дата:
2017
Переглядів:
439
Завантажень:
243
Анотація:
The multi-indexed Laguerre and Jacobi polynomials form a complete set of orthogonal polynomials. They satisfy second-order differential equations but not three term recurrence relations, because of the 'holes' in their degrees. The multi-indexed Laguerre and Jacobi polynomials have Wronskian expressions originating from multiple Darboux transformations. For the ease of applications, two different forms of simplified expressions of the multi-indexed Laguerre and Jacobi polynomials are derived based on various identities. The parity transformation property of the multi-indexed Jacobi polynomials is derived based on that of the Jacobi polynomial.
