Consider:
Note that:
So we have: (1)
Now: (see here )
The integral on the right clearly converges, thus: where . Hence
Recall that: .
Thus, going back to (1) :
So finally: Hence your series is:
Consider:
Note that:
So we have: (1)
Now: (see here )
The integral on the right clearly converges, thus: where . Hence
Recall that: .
Thus, going back to (1) :
So finally: Hence your series is: