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Sum of series factorial(n)*n^(-p)*factorial(q-1)/factorial(q+n)



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The solution

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