Infinite sum of logarithms Is there any closed form for this expression
$$
\sum_{n=0}^\infty\ln(n+x)
$$

Write it as $\sum_{n=0}^k \ln(n+x)=\ln\left(\prod_{n=0}^k \left(n+x\right)\right)=\ln\left(\frac{\Gamma(k+x+1)}{\Gamma(x)}\right)$. If $k$ goes to $\infty$ the expression diverges, if $x>0$ or $x$ is not equal to a negative integer.
