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Transactions of the American Mathematical Society

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On some open problems of P. Turán concerning Birkhoff interpolation


Author: A. K. Varma
Journal: Trans. Amer. Math. Soc. 274 (1982), 797-808
MSC: Primary 41A05
MathSciNet review: 675080
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Abstract: In 1974 P. Turán (see [6]) raised many interesting open problems in Approximation Theory some of which are on Birkhoff Interpolation. The object of this paper is to answer some of these problems (XXXVI-XXXIX). We obtain some new quadrature formulas where function values and second derivatives are only prescribed on the zeros of

$\displaystyle {\pi _n}(x) = {c_n}\int_{ - 1}^x {{P_{n - 1}}(t)\,dt} $

, $ {P_n}(x)$ being Legendre polynomial of degree $ n$.

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DOI: https://doi.org/10.1090/S0002-9947-1982-0675080-2
Article copyright: © Copyright 1982 American Mathematical Society