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Bernoulli formula for integrals

  1. Nov 7, 2005 #1
    let be the Bernoulli formula for calculating an integral in the form:

    [tex]\int{f(x)dx}=C+\sum_{n=1}^{\infty}(-1)^{n}x^{n}\frac{d^{n}f}{dx^{n}}\frac{1}{\Gamma(n)} [/tex]

    my question is..could we calculate the integral from this series?..thanks.
  2. jcsd
  3. Nov 7, 2005 #2


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    It's actually a series for the antiderivative. I don't see why not...


    P.S. It's kinda mysterious that this formula involves Euler's gamma function and not Bernoulli's numbers.
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