Constructive Approximation

, Volume 45, Issue 1, pp 65–81 | Cite as

An Orthogonality Property of the Legendre Polynomials

  • L. Bos
  • A. Narayan
  • N. Levenberg
  • F. Piazzon


We give a remarkable additional othogonality property of the classical Legendre polynomials on the real interval \([-1,1]\): polynomials up to degree n from this family are mutually orthogonal under the arcsine measure weighted by the normalized degree-n Christoffel function.


Legendre polynomials Christoffel function Equilibrium measure 

Mathematics Subject Classification

33C45 41A10 65C05 


  1. 1.
    Bos, L., Ware, A.F.: On the uniqueness of an orthogonality property of the Legendre polynomials (2015) (preprint)Google Scholar
  2. 2.
    Cohen, A., Davenport, M.A., Leviatan, D.: On the stability and accuracy of least squares approximations. Found. Comput. Math. 13(5), 819–834 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Freud, G.: Orthogonal Polynomials. Pergamon Press/Akadémiai Kiadó, Budapest (1971)zbMATHGoogle Scholar
  4. 4.
    Lubinsky, D.: Applications of new Geronimus type identities for real orthogonal polynomials. Proc. Am. Math. Soc. 138(6), 2125–2134 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Szegö, G.: Orthogonal Polynomials, 4th edn. American Mathematical Society, Providence (1975)zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of VeronaVeronaItaly
  2. 2.Mathematics Department, Scientific Computing and Imaging Institute (SCI)University of UtahSalt Lake CityUSA
  3. 3.Department of MathematicsIndiana UniversityBloomingtonUSA
  4. 4.Department of MathematicsUniversity of PaduaPaduaItaly

Personalised recommendations