title: Calculate the recurrence use repeated unfolding
body: <p>I am trying to calculate T (n) = 2 T (n/2) + n (log n)^2.
  Following the step I got:</p>
  
  <pre><code>=2^kT(n/2^k)+ nlog2 (n/2^(k-1))+ nlog2 (n/2^(k-2))+…+ n(log (n/2))^2 + n (log2 n)^2
  </code></pre>
  
  <p>when n=2^k I got:</p>
  
  <p><a href="https://i.stack.imgur.com/jDhQf.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/jDhQf.png" alt="formula"></a></p>
  
  <p>But I have no idea about how to simplify the summation formula and get  Θ() notation.
  Any one can help? Thanks a lot</p>