I can't figure out how to solve this recurrence relation:
$T(n)=25T(n/5)+n^2\cdot(\log(n))^2$.
I can't use here in the iteration method. I also tried to use the Master Theorem but I figured out that I can't use this method here. I don't have any more ideas.
Thanks for the help
The sequence $$x_k=\frac{T(5^k)}{25^k}$$ solves the recursion $$x_k=x_{k-1}+(\log5)^2\cdot k^2$$ hence $$x_k=x_0+(\log5)^2\sum_{m=1}^km^2=\Theta(k^3)$$ which implies $$T(5^k)=25^k\cdot x_k=\Theta((5^k)^2\cdot k^3)$$ result from which one often deduces (although the consequence does not hold in full rigor) that $$T(n)=\Theta(n^2\cdot(\log n)^3)$$
