Applications Concerning Orthogonal Polynomials

  • Edward B. Saff
  • Vilmos Totik
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 316)


The analysis of the asymptotic behavior of orthogonal polynomials was one of the driving forces for the resurgence of interest in potentials with external fields. The relationship between the two subjects can be seen as follows: consider, for example, orthogonal polynomials with respect to the so-called Freud weights W(x) = exp(-|x|λ) =: exp(-Q(x)). On applying the substitution xn 1/λ x and the defining properties of orthogonal polynomials one arrives at monic polynomials P n minimizing the integral
$$ \int {{{{\left( {\left| {{{P}_{n}}} \right|{{e}^{{ - nQ}}}} \right)}}^{2}}} $$


Orthogonal Polynomial Monic Polynomial Orthonormal Polynomial Weighted Polynomial Zero Distribution 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Edward B. Saff
    • 1
  • Vilmos Totik
    • 2
    • 3
  1. 1.Department of MathematicsUniversity of South Florida Institute for Constructive MathematicsTampaUSA
  2. 2.Bolyai InstituteJozsef Attila UniversitySzegedHungary
  3. 3.Department of MathematicsUniversity of South FloridaTampaUSA

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