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Polynomials Satisfying Functional and Differential Equations and Diophantine Properties of Their Zeros

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Abstract

By investigating the behavior of two solvable isochronous N-body problems in the immediate vicinity of their equilibria, functional equations satisfied by the para-Jacobi polynomial \({p_{N} \left(0, 1; \gamma; x \right)}\) and by the Jacobi polynomial \({P_{N}^{\left(-N-1,-N-1 \right)} \left(x \right)}\) (or, equivalently, by the Gegenbauer polynomial \({C_{N}^{-N-1/2}\left( x \right) }\)) are identified, as well as Diophantine properties of the zeros and coefficients of these polynomials.

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Authors and Affiliations

  1. Physics Department, University of Rome “La Sapienza”, Rome, Italy

    Francesco Calogero & Ge Yi

  2. Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Rome, Italy

    Francesco Calogero & Ge Yi

Authors
  1. Francesco Calogero
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  2. Ge Yi
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Correspondence to Francesco Calogero.

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Calogero, F., Yi, G. Polynomials Satisfying Functional and Differential Equations and Diophantine Properties of Their Zeros. Lett Math Phys 103, 629–651 (2013). https://doi.org/10.1007/s11005-013-0612-y

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  • DOI: https://doi.org/10.1007/s11005-013-0612-y

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