Orthogonal polynomials for exponential weights x2ρe-2Q(x) on [0, d)

  • Authors:

  • Eli Levin;Doron Lubinsky

  • Affiliations:

  • Mathematics Department, The Open University of Israel, P.O. Box 808, Raanana 43107, Israel;The School of Mathematics, Georgia Institute of Technology, Atlanta, GA

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2005

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Abstract

Let I = [0, d), where d is finite or infinite. Let Wρ (x) = xρ exp (-Q (x)), where ρ - ½ and Q is continuous and increasing on I, with limit ∞ at d. We study the orthonormal polynomials associated with the weight Wρ2, obtaining bounds on the orthonormal polynomials, zeros, and Christoffel functions. In addition, we obtain restricted range inequalities.