The distribution of zeros of the polynomial eigenfunctions of ordinary differential operators of arbitrary order

  • E. Buendia
  • J. S. Dehesa
  • F. J. Galvez
Part of the Lecture Notes in Mathematics book series (LNM, volume 1329)


The distribution of zeros of the polynomial eigenfunctions of ordinary differential operators of arbitrary order with polynomial coefficients is calculated via its moments directly in terms of the parameters which characterize the operators. Some results of K.M. Case and the authors are extended. In particular, the restriction for the degree of the polynomial coefficient of the ith-derivative to be not greater than i is relaxed. Applications to the Heine polynomials, the Generalized Hermite polynomials and the Bessel type orthogonal polynomials (which no trivial properties of zeros were known of) are shown.


Orthogonal Polynomial Arbitrary Order Ordinary Differential Equation Polynomial Coefficient Polynomial Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • E. Buendia
    • 1
  • J. S. Dehesa
    • 1
  • F. J. Galvez
    • 1
  1. 1.Departamento de Fisica NuclearUniversidad de GranadaGranadaSpain

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