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Sum of series ln^n(x)/n!



=

The solution

You have entered [src]
  oo         
____         
\   `        
 \       n   
  \   log (x)
  /   -------
 /       n!  
/___,        
n = 1        
$$\sum_{n=1}^{\infty} \frac{\log{\left(x \right)}^{n}}{n!}$$
Sum(log(x)^n/factorial(n), (n, 1, oo))
The answer [src]
/    1        x   \       
|- ------ + ------|*log(x)
\  log(x)   log(x)/       
$$\left(\frac{x}{\log{\left(x \right)}} - \frac{1}{\log{\left(x \right)}}\right) \log{\left(x \right)}$$
(-1/log(x) + x/log(x))*log(x)

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