Following method is explained by my senior. I want to know whether I can use it in all cases or not. When I solve it manually, I come to same answer.
$T(n)= 4T(n/2) + \frac{n^2}{\lg n}$
In above recurrence master theorem fails. But he gave me this solution, when
for $T(n) = aT(n/b) + \Theta(n^d \lg^kn)$
if $d = \log_b a$
if $k\geq0$ then $T(n)=\Theta(n^d \lg^{k+1})$
if $k=-1$ then $T(n)=\Theta(n^d\lg\lg n)$
if $k<-1$ then $T(n)=\Theta(n^{\log_ba})$
using above formulae, the recurrence is solved to $\Theta(n^2\lg\lg n)$. When I solved manually, I come up with same answer. If it is some standard method, what it is called ?