Basic facts
- \(logn \in o(n^\epsilon)\) for any \(\epsilon > 0\)
- \(log^{c}n \in o(n^\epsilon)\) for any \(\epsilon > 0\)
- \(c_1^{n} \in o(c_2^{n})\) for all \(1 \leq c_1 < c_2\)
order
- \(1/\log n\)
- \(2^{2+1/n}\)
- \(\sqrt{\log \log n}\)
- \(\log n/\log \log n\)
- \(\log n\)
- \(\Theta(\log n) = 3^{\log\log n} < 3^{\sqrt{\log n}} < 3^{\log n} = \Theta(n)\)
- \(5(n+1/n)\)
- \(e^{\ln n} = n\)
- \(\log (n!) = n \log n\)
- \(n \log ^3 n\)
- \(4n^{3/2}\)
- \(4^{\log n} = n^2\)
- \(n^2 \log n\)
- \(n^3\)
- \(n^{100}\)
- \(3^{\sqrt{n}}\)
- \(4^{n} = 2^{2n}\)
- \(n!\)
- \(2^{n^2 \log n} = n^{n^2}\)