Darstellung und Entwicklung des Restgliedes der Gregoryschen Quadraturformel mit Hilfe von Spline-Funktionen |
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| Authors: | Prof Dr Erich Martensen |
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| Institution: | (1) Mathematisches Institut II der Universität Karlsruhe (TH), Englerstr. 2, D-7500 Karlsruhe 1, Bundesrepublik Deutschland |
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| Abstract: | Summary Due to a theorem of Peano, the remainder term of Gregory's quadrature formula may be expressed by means of a polynomial spline-function. An explicite representation of this spline-function is given by a direct method, which does not make use of Peano's theorem. As an application the remainder term obtained is developed in terms of boundary derivations of the integrand, which leads to a general quadrature formula containing the Gregory formula and the Euler-MacLaurin summation formula as special cases.
Herrn Johannes Weissinger zum 60. Geburtstag am 12. 5. 1973 gewidmet |
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