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The Euler-MacLaurin Sum Formula

  • Hans Rademacher
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 169)

Abstract

Let f(x) be continuous with as many continuous derivatives as required. Noticing B1(x) =l we obtain through integration by parts
$$\int\limits_0^1 {f(x)\,dx\, = \,[{B_1}(x)f(x)]_0^1 - } \int\limits_0^1 {{B_1}(x)f'(x)dx.} $$

Keywords

Fourier Expansion Recursion Formula Remainder Term Euler Number Bernoulli Number 
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.

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Copyright information

© Springer-Verlag, Berlin • Heidelberg 1973

Authors and Affiliations

  • Hans Rademacher

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