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Bernoulli formula for integrals...

by eljose
Tags: bernoulli, formula, integrals
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Nov7-05, 06:09 AM
P: 501
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.
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Nov7-05, 06:39 AM
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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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