Analysis Mathematica

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

An interpolation process on the roots of the integrated Legendre polynomials

  • L. Szili


Legendre Polynomial Interpolation Process Integrate Legendre Polynomial 
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Об одном интерполяци онном процессе с узла ми в корнях интегрированных мно гочленов Лежандра


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.


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Copyright information

© Akadémiai Kiadó 1983

Authors and Affiliations

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

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