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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...
$\displaystyle f(s)= \sum_{n=1}^{\infty} \frac{a_{n}}{n^{s}}$ (1)
My problem of undestanding is when I try to compute the $\displaystyle f^{'} (*)$ from (1). In the 'manual of mathematic' at my disposal is written...
$\displaystyle \frac{d}{dx} a^{u} = a^{u}\cdot \ln a \cdot \frac{du}{dx}$ (2)
... and setting $\displaystyle a=n$ , $\displaystyle u(x)=x$ the (2) becomes...
$\displaystyle \frac{d}{dx} n^{x} =  \ln x\cdot n^{x}$ (3)
... so that it would be...
$\displaystyle f^{'}(s)=  \sum_{n=1}^{\infty} \frac {a_{n}\cdot \ln n}{n^{s}}$ (4)
My problem is that in Wikipedia is written...
$\displaystyle f^{'}(s)= \sum_{n=1}^{\infty} \frac {a_{n}\cdot \ln n}{n^{s}}$ (5)
The question is easy: which is correct?... (4) or (5)? (Thinking)...
Thank in advance!...
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$

Looks like the result is: chisigma 1, Wikipedia 0.