Recurrence Formula

$$\begin{array}{r}T(n)=aT(n/b)+f(n)\\ a\ge 1,b>1\end{array}$$

1. if $f(n)=\theta (n^c)$ where $c<lo{g}_{b}a$ then $T(n)=\theta (n^{lo{g}_{b}a})$
2. if $f(n)=\theta (n^c)$ where $c=lo{g}_{b}a$ then $T(n)=\theta (n^{c}logn)$
3. if $f(n)=\theta (n^c)$ where $c>lo{g}_{b}a$ then $T(n)=\theta (f(n))$