The Euler-MacLaurin Sum Formula

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


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


Fourier Expansion Recursion Formula Remainder Term Euler Number Bernoulli Number 
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Copyright information

© Springer-Verlag, Berlin • Heidelberg 1973

Authors and Affiliations

  • Hans Rademacher

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