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Math Help - Sign uncertainty...

  1. #1
    MHF Contributor chisigma's Avatar
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    Sign uncertainty...

    Informations about Diriclet series can be found, among other sources, here...

    Dirichlet series - Wikipedia, the free encyclopedia

    The 'formal definition' of a Diriclet series is given as...

    f(s)= \sum_{n=1}^{\infty} \frac{a_{n}}{n^{s}} (1)

    My problem of undestanding is when I try to compute the f^{'} (*) from (1). In the 'manual of mathematic' at my disposal is written...

    \frac{d}{dx} a^{u} = a^{u}\cdot \ln a \cdot \frac{du}{dx} (2)

    ... and setting a=n , u(x)=-x the (2) becomes...

    \frac{d}{dx} n^{-x} = - \ln x\cdot n^{-x} (3)

    ... so that it would be...

    f^{'}(s)= - \sum_{n=1}^{\infty} \frac {a_{n}\cdot \ln n}{n^{s}} (4)

    My problem is that in Wikipedia is written...

    f^{'}(s)= \sum_{n=1}^{\infty} \frac {a_{n}\cdot \ln n}{n^{s}} (5)

    The question is easy: which is correct?... (4) or (5)? ...

    Thank in advance!...

    Kind regards

    \chi \sigma
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  2. #2
    MHF Contributor
    Opalg's Avatar
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    Looks like the result is: chisigma 1, Wikipedia 0.
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