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Symmetry, Integrability and Geometry: Methods and Applications, 2017, Volume 13, 020, 10 pp.
DOI: https://doi.org/10.3842/SIGMA.2017.020 (Mi sigma1220) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials

Satoru Odake, Ryu Sasaki

Faculty of Science, Shinshu University, Matsumoto 390-8621, Japan
Full-text PDF (338 kB) Citations (6)
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DOI: https://doi.org/10.3842/SIGMA.2017.020
Abstract: 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.
Keywords: multi-indexed orthogonal polynomials; Laguerre and Jacobi polynomials; Wronskian formula; determinant formula.
Funding agency Grant number
Ministry of Education, Culture, Sports, Science and Technology, Japan 25400395
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.
Received: December 30, 2016; in final form March 23, 2017; Published online March 29, 2017
Bibliographic databases:
Document Type: Article
MSC: 42C05; 33C45; 34A05
Language: English
Citation: Satoru Odake, Ryu Sasaki, “Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials”, SIGMA, 13 (2017), 020, 10 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
     
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