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Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials

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...

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Main Authors: Ho, C., Odake, S., Sasaki, R.
Format: Article
Language:English
Published: Інститут математики НАН України 2011
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/147992
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spelling irk-123456789-1479922019-02-17T01:24:35Z Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials Ho, C. Odake, S. Sasaki, R. 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. 2011 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
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.
format Article
author Ho, C.
Odake, S.
Sasaki, R.
spellingShingle Ho, C.
Odake, S.
Sasaki, R.
Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Ho, C.
Odake, S.
Sasaki, R.
author_sort Ho, C.
title Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials
title_short 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_sort properties of the exceptional (xl) laguerre and jacobi polynomials
publisher Інститут математики НАН України
publishDate 2011
url http://dspace.nbuv.gov.ua/handle/123456789/147992
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.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT hoc propertiesoftheexceptionalxllaguerreandjacobipolynomials
AT odakes propertiesoftheexceptionalxllaguerreandjacobipolynomials
AT sasakir propertiesoftheexceptionalxllaguerreandjacobipolynomials
first_indexed 2023-05-20T17:28:21Z
last_indexed 2023-05-20T17:28:21Z
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