integrate term for term ...
at , ...
Let , so
So
Now
So now consider
Now consdier that if this limit diverges to infinity, but if then
Now consider that
So
So now consider
Now we have shown that the interval of convergence of is , thus on thatinterval it is uniformly convergent, thus on the integral and summation be switched.
So
Now notice that this series interval of convergence is , so by abel's theorem