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Letters in Mathematical Physics

, Volume 109, Issue 1, pp 89–112 | Cite as

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

  • J. F. van DiejenEmail author
  • E. Emsiz
Article

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.

Keywords

(Basic) hypergeometric orthogonal polynomials Zeros of orthogonal polynomials Convex Bethe Ansatz equations 

Mathematics Subject Classification

Primary 33D45 Secondary 26C10 33C45 81R12 82B23 

Notes

Acknowledgements

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

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Authors and Affiliations

  1. 1.Instituto de Matemática y FísicaUniversidad de TalcaTalcaChile
  2. 2.Facultad de MatemáticasPontificia Universidad Católica de ChileSantiagoChile

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