Advertisement

aequationes mathematicae

, Volume 21, Issue 1, pp 105–109 | Cite as

Some positive cotes numbers for the chebyshev weight function

  • Charles A. Micchelli
Research Papers

Abstract

We show that, for the Chebyshev weight function (1−x2)−1/2, the Cotes numbers for the quadrature rule with nodes at the zeros of the ultraspherical polynomialP n /(λ) are nonnegative if and only if −1/2<λ≤1.

AMS (1970) subject classification

Primary 41A55, 65D30 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Askey, R.,Positivity of the Cotes numbers for some Jacobi abscissas. Numer. Math.19 (1972), 46–48.Google Scholar
  2. [2]
    Askey, R.,Orthogonal polynomials and special functions. CBMS Regional Conference Series No. 21, SIAM, Philadelphia, 1975.Google Scholar
  3. [3]
    Askey, R. andFitch, J.,Positivity of the Cotes numbers for some ultraspherical abscissas. SIAM J. Numer. Anal.5 (1968), 199–201.Google Scholar
  4. [4]
    Horton, R.,Expansions using orthogonal polynomials. Ph.D. Thesis, Univ. of Wisconsin, Madison, 1973.Google Scholar
  5. [5]
    Locher, Franz,Norm bounds of quadrature processes. SIAM J. Numer. Anal.10 (1973), 553–558.Google Scholar
  6. [6]
    Pólya, G. andSzegö, G.,Problems and theorems in analysis. Vol. II, Springer-Verlag, New York, 1976.Google Scholar
  7. [7]
    Szegö, G.,Orthogonal polynomials. Amer. Math. Soc. Colloq. Publications, Vol. 23, revised edition, Amer. Math. Soc., Providence, R.I., 1959.Google Scholar

Copyright information

© Birkhäuser Verlag 1980

Authors and Affiliations

  • Charles A. Micchelli
    • 1
  1. 1.I.B.M. Corporation, Research DivisionYorktown HeightsUSA

Personalised recommendations