Zeros of the exceptional Laguerre and Jacobi polynomials

Details Zeros of the exceptional Laguerre and Jacobi polynomials Zeros of the exceptional Laguerre and Jacobi polynomials

2011-02-28

arxiv.org/abs/1102.5669v1

Physics

Mathematical Physics

25 pages, 10 figures

Scientific paper

An interesting discovery in the last two years in the field of mathematical physics has been the exceptional $X_\ell$ Laguerre and Jacobi polynomials. Unlike the well-known classical orthogonal polynomials which start with constant terms, these new polynomials have the lowest degree $\ell=1,2,...$, 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.

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