Zeros of Sobolev orthogonal polynomials following from coherent pairs

  • Authors:

  • H. G. Meijer;M. G. de Bruin

  • Affiliations:

  • Department of Applied Mathematical Analysis, Faculty of Information Technology and Systems, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, Netherlands;Department of Applied Mathematical Analysis, Faculty of Information Technology and Systems, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, Netherlands

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2002

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Abstract

Let {Snλ) denote the monic orthogonal polynomial sequence with respect to the Sobolev inner product (f,g)s = ∫-∞∞ fgdψ0 + λ ∫-∞∞ f'g'dψ1, where {dψ0, dψ1} is a so-called coherent pair and λ Snλ has n different, real zeros. The position of these zeros with respect to the zeros of other orthogonal polynomials (in particular Laguerre and Jacobi polynomials) is investigated. Coherent pairs are found where the zeros of Sn-1λ separte the zeros of Snλ.