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given the harmonic series

$$ \sum_{n=0}^{\infty}\frac{1}{n+a} $$

what is the correct option for the regularization ?

a) $ \sum_{n=0}^{\infty}\frac{1}{n+a}= -\Psi (a) $ Digamma function

b) $ \sum_{n=0}^{\infty}\frac{1}{n+a}= -\Psi(a)+\log a $

for $ a=1 $ the solution is the same $ \sum_{n=0}^{\infty}\frac{1}{n+1}= \gamma $

but for any other positive a? where can i find info on the Harmonci generalized series and physics?

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