Master Theorem

For the recurrence relation T(n) = aT(n/b) + f(n) with a $\geq$ 1, b > 1 and T(n) on non-negative integers, T(n) can be asymptotically bounded as follows:

1.

If f(n) = O( ) for some constant $\epsilon>0$, then T(n) = .

2.

If f(n) = , then T(n) = .

3.

If f(n) = for some constant , and if af(n/b) $\leq$ cf(n) for some constant c < 1 and large n, then T(n) = $\Theta(f(n))$.

Which is larger, f(n) or n^{log_b a}?

By a factor of $n^\epsilon$, or polynomially larger...