Suma de la serie lg^nx/n

/                         /      -1       \
|-log(1 - log(x))  for And\x >= e  , x < E/
|                                          
|   oo                                     
| ____                                     
| \   `                                    
<  \       n                               
|   \   log (x)                            
|   /   -------           otherwise        
|  /       n                               
| /___,                                    
| n = 1                                    
\                                          

$$\begin{cases} - \log{\left(1 - \log{\left(x \right)} \right)} & \text{for}\: x \geq e^{-1} \wedge x < e \\\sum_{n=1}^{\infty} \frac{\log{\left(x \right)}^{n}}{n} & \text{otherwise} \end{cases}$$

Piecewise((-log(1 - log(x)), (x < E)∧(x >= exp(-1))), (Sum(log(x)^n/n, (n, 1, oo)), True))