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ISRN Mathematical Physics
Volume 2012 (2012), Article ID 920475, 27 pages
Research Article

Zeros of the Exceptional Laguerre and Jacobi Polynomials

1Department of Physics, Tamkang University, Tamsui 251, Taiwan
2Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan

Received 12 April 2012; Accepted 4 July 2012

Academic Editors: G. Goldin and R. Schiappa

Copyright © 2012 Choon-Lin Ho and Ryu Sasaki. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An interesting discovery in the last two years in the field of mathematical physics has been the exceptional 𝑋ℓ Laguerre and Jacobi polynomials. Unlike the well-known classical orthogonal polynomials which start with constant terms, these new polynomials have the lowest degree β„“=1,2,…, and yet they form complete sets with respect to some positive-definite measure. In this paper, we study one important aspect of these new polynomials, namely, the behaviors of their zeros as some parameters of the Hamiltonians change. Most results are of heuristic character derived by numerical analysis.