User blog comment:Planterobloon/The Fast-Growing Hierarchy Explained/@comment-32697988-20180401194338/@comment-32697988-20180401211646

\(\omega\downarrow\downarrow n = \omega^{\omega^{n-1}}\)

\(W_{\omega^{\omega^\omega}}(n)=n+2^{n^{n^2}}\approx f^2_2(n^2)\)

\(W_{\omega^{\omega^{\omega^\omega}}}(n)=n+2^{n^{n^3}}\approx f^2_2(n^3)\)

\(W_{\varepsilon_0}=W_{\omega\downarrow\downarrow n}=n+2^{n^{n^(n-1)}}\approx f^3_2(n)\)

\(W_{\varepsilon_1}=W_{\omega\downarrow\downarrow n^2}=n+2^{n^{n^(n^2-1)}}\approx f^3_2(n^2)\)

\(W_{\varepsilon_\omega}=W_{\omega\downarrow\downarrow n^{n+1}}=n+2^{n^{n^(n^{n+1}-1)}}\approx f^4_2(n)\)

\(W_{\varepsilon_{\varepsilon_0}}=W_{\omega\downarrow\downarrow n \downarrow\downarrow }\approx 2^{n\uparrow\uparrow5}\approx f^5_2(n)\)

\(W_{\zeta_0}\approx f_3(n)\)