Advertisement

Analysis Mathematica

, Volume 9, Issue 3, pp 235–245 | Cite as

An interpolation process on the roots of the integrated Legendre polynomials

  • L. Szili
Article

Keywords

Legendre Polynomial Interpolation Process Integrate Legendre Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Об одном интерполяци онном процессе с узла ми в корнях интегрированных мно гочленов Лежандра

Abstract

Пусть −1=х n,n <xn−1,n<...<x1,n=1 корн и многочлена
$$\Pi _n \left( x \right) = - \left( {n - 1} \right)n\mathop \smallint \limits_{ - 1}^x P_{n - 1} \left( t \right)dt,$$
гдеPn−1 — многочлен Леж андра степени (n−1) иx i,n * (i=1, 2, ...,n − 1) корни многочлен аΠ n ′.
В работе доказываетс я теорема о сходимост и многочленовR n (n=2, 4, 6, ...), удо влетворяющих следующим условиям:
гдеy i,n иy i,n - заданные си стемы значений. Неулучшаемость теор емы также доказана.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    J. Balázs andP. Turán, Notes on interpolation. II,Acta Math. Acad. Sci. Hungar.,8 (1957) 201–215.Google Scholar
  2. [2]
    J. Balázs andP. Turán, Notes on interpolation. III,Acta Math. Acad. Sci. Hungar.,9 (1958), 195–214.Google Scholar
  3. [3]
    J. Balázs andP. Turán, Notes on interpolation. IV,Acta Math. Acad. Sci. Hungar.,9 (1958), 243–258.Google Scholar
  4. [4]
    E. Egerváry andP. Turán, Notes on interpolation. V,Acta Math. Acad. Sci. Hungar.,9 (1958), 259–267.Google Scholar
  5. [5]
    L. G. Pál, A new modification of the Hermite—Fejér interpolation,Analysis Math.,1 (1975), 197–205.Google Scholar
  6. [6]
    G. Szegő,Orthogonal polynomials, Amer. Math. Soc. Coll. Publ. (New York, 1959).Google Scholar
  7. [7]
    P. O. H. Vértesi, On certain linear operators. IV,Acta Math. Acad. Sci. Hungar.,23 (1972), 115–125.Google Scholar

Copyright information

© Akadémiai Kiadó 1983

Authors and Affiliations

  • L. Szili
    • 1
  1. 1.Department of MathematicsEötvös Loránd UniversityBudapestHungary

Personalised recommendations