Skip to main content
Log in

Sub-range Jacobi polynomials

  • Original Paper
  • Published:
Numerical Algorithms Aims and scope Submit manuscript

A Correction to this article was published on 07 May 2019

An Erratum to this article was published on 21 December 2016

This article has been updated

Abstract

Orthogonal polynomials relative to the Jacobi weight function, but orthogonal on a strict subinterval of [ − 1, 1], are studied, in particular with regard to their numerical computation. Related Gaussian quadrature rules are also considered.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Change history

  • 07 May 2019

    The first equation in Eq. (2.9) should read

  • 07 May 2019

    The first equation in Eq. (2.9) should read

References

  1. Da Fies, G., Vianello, M.: Trigonometric Gaussian quadrature on subintervals of the period (2011). http://www.math.unipd.it/∼marcov/pdf/trigauss.pdf. Accessed 8 March 2012

  2. Da Fies, G., Vianello, M.: Algebraic cubature on planar lenses and bubbles. Dolomites Res. Notes Approx. 5, 7–12 (2012)

    Google Scholar 

  3. Davis, P.J., Rabinowitz, P.: Some geometrical theorems for abscissas and weights of Gauss type. J. Math. Anal. Appl. 2, 428–437 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  4. Gautschi, W.: On generating orthogonal polynomials. SIAM J. Stat. Comput. 3, 289–317 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  5. Gautschi, W.: Computational aspects of orthogonal polynomials. In: Nevai, P. (ed.) Orthogonal Polynomials. NATO ASI Series, Series C: Mathematical and Physical Sciences, vol. 294, pp. 181–216. Kluwer, Dordrecht (1990)

    Chapter  Google Scholar 

  6. Gautschi, W.: Orthogonal Polynomials: Computation and Approximation. Numerical Mathematics and Scientific Computation, Oxford University Press, New York (2004)

    MATH  Google Scholar 

  7. Gautschi, W.: The circle theorem and related theorems for Gauss-type quadrature rules. Electr. Trans. Numer. Anal. 25, 129–137 (2006)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Walter Gautschi.

Additional information

An erratum to this article is available at http://dx.doi.org/10.1007/s11075-016-0257-x.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gautschi, W. Sub-range Jacobi polynomials. Numer Algor 61, 649–657 (2012). https://doi.org/10.1007/s11075-012-9556-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11075-012-9556-z

Keywords

Mathematics Subject Classifications (2010)

Navigation