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Solutions of convex Bethe Ansatz equations and the zeros of (basic) hypergeometric orthogonal polynomials

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Abstract

Via the solutions of systems of algebraic equations of Bethe Ansatz type, we arrive at bounds for the zeros of orthogonal (basic) hypergeometric polynomials belonging to the Askey–Wilson, Wilson and continuous Hahn families.

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Notes

  1. Whereas a classical result of Bochner characterizes the Jacobi polynomials as “the most general orthogonal family satisfying a linear homogeneous second-order differential equation”, the Askey–Wilson polynomials are known to constitute “the most general orthogonal family satisfying a linear homogeneous second-order q-difference equation” [29].

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Acknowledgements

Thanks are due to the referees for pointing out some improvements of the presentation.

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Authors and Affiliations

  1. Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile

    J. F. van Diejen

  2. Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago, Chile

    E. Emsiz

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  1. J. F. van Diejen
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  2. E. Emsiz
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Correspondence to J. F. van Diejen.

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This work was supported in part by the Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT) Grants # 1170179 and # 1181046.

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van Diejen, J.F., Emsiz, E. Solutions of convex Bethe Ansatz equations and the zeros of (basic) hypergeometric orthogonal polynomials. Lett Math Phys 109, 89–112 (2019). https://doi.org/10.1007/s11005-018-1101-0

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