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

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1329)

Abstract

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.

Keywords

  • Orthogonal Polynomial
  • Arbitrary Order
  • Ordinary Differential Equation
  • Polynomial Coefficient
  • Polynomial Solution

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© 1988 Springer-Verlag

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Buendia, E., Dehesa, J.S., Galvez, F.J. (1988). The distribution of zeros of the polynomial eigenfunctions of ordinary differential operators of arbitrary order. In: Alfaro, M., Dehesa, J.S., Marcellan, F.J., Rubio de Francia, J.L., Vinuesa, J. (eds) Orthogonal Polynomials and their Applications. Lecture Notes in Mathematics, vol 1329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083361

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  • DOI: https://doi.org/10.1007/BFb0083361

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