2024-03-29T11:24:00Z
https://soar-ir.repo.nii.ac.jp/oai
oai:soar-ir.repo.nii.ac.jp:00011687
2022-12-14T04:09:28Z
1169:1170
Properties of the Exceptional (X-l) Laguerre and Jacobi Polynomial
Ho, Choon Lin
Odake, Satoru
Sasaki, Ryu
exceptional orthogonal polynomials
Gram-Schmidt process
Rodrigues formulas
generating functions
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.
Article
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS. 7:107 (2011)
NATL ACAD SCI UKRAINE, INST MATH
2011
eng
journal article
VoR
http://hdl.handle.net/10091/18501
https://soar-ir.repo.nii.ac.jp/records/11687
https://doi.org/10.3842/SIGMA.2011.107
10.3842/SIGMA.2011.107
1815-0659
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
7
107
https://soar-ir.repo.nii.ac.jp/record/11687/files/Properties_of_the_Exceptional.pdf
application/pdf
482.9 kB
2015-09-28