# What is the exact renormalization regularization for divergent harmonic serise?

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?