Catching函数分析1：BO~EBO

本条目展示Catching函数的分析。以下左为FGH，右为SGH。均用MOCF表示。

\begin{align}.\\&f_3(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega+1)\\&f_4^n(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega+\Omega)\\&f_\omega^n(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega+\Omega^\Omega)\\&f_{\omega^\omega}^n(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega+\Omega^{\Omega^\Omega})\\&f_{\psi(0)}^n(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega+\psi_1(\Omega))\\&f_{\psi(\Omega)[n]}(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega+\psi_1(\Omega_2))\\&f_{\psi(\Omega_2)[n]}(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega+\psi_1(\Omega_3))\\&f_{\psi(\Omega_3)[n]}(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega+\psi_1(\Omega_4))\\&f_{\psi(\Omega_\omega)[n]}(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega+\psi_1(\Omega_\omega))\\&f_{\psi(\Omega_\omega)[n]}^2(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega+\psi_1(\Omega_\omega)\times2)\\&f_{\psi(\Omega_\omega)[n]+1}^n(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega+\psi_1(\Omega_\omega)\times\Omega)\\&f_{\psi(\Omega_\omega)[n]\times2}(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega+\psi_1(\Omega_\omega)^2)\\&f_{\psi(\Omega_\omega[n]+1)}(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega+\psi_1(\Omega_\omega+1))\\&f_{\psi(\Omega_\omega[n]+\omega)}^n(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega+\psi_1(\Omega_\omega+\Omega))\\&f_{\psi(\Omega_\omega[n]+\psi(0)[n])}(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega+\psi_1(\Omega_\omega+\psi_1(0)))\\&f_{\psi(\Omega_\omega[n]+\psi(\Omega_\omega[n]))}(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega+\psi_1(\Omega_\omega+\psi_1(\Omega_\omega)))\\&f_{\psi(\Omega_\omega[n]+\Omega)[n]}(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega+\Omega_2)\\&f_{\psi(\Omega_\omega[n]+\Omega)[n\times2]}(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega+\Omega_2\times2)\\&f_{\psi(\Omega_\omega[n]+\Omega)}^n(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega+\Omega_2\times\Omega)\\&f_{\psi(\Omega_\omega[n]+\Omega^2)}^n(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega+\Omega_2^2\times\Omega)\\&f_{\psi(\Omega_\omega[n]+\psi_1(0))}^n(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega+\psi_2(\Omega))\\&f_{\psi(\Omega_\omega[n]+\psi_1(\Omega_\omega[n]))}(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega+\psi_2(\Omega_\omega))\\&f_{\psi(\Omega_\omega[n]+\psi_2(\Omega_\omega[n]))}(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega+\psi_3(\Omega_\omega))\\&f_{\psi(\Omega_\omega[n]\times2)}(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega\times2)\\&f_{\psi(\Omega_\omega[n]\times3)}(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega\times3)\\&f_{\psi(\Omega_\omega[n]\times\omega)}^n(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega\times\Omega)\\&f_{\psi(\Omega_\omega[n]\times\psi(0))}^n(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega\times\psi_1(\Omega))\\&f_{\psi(\Omega_\omega[n]\times\psi(\Omega_\omega[n]))}(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega\times\psi_1(\Omega_\omega))\\&f_{\psi(\Omega_\omega[n]\times\psi_1(\Omega_\omega[n]))}(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega\times\psi_2(\Omega_\omega))\\&f_{\psi(\Omega_\omega[n]^2)}(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega^2)\\&f_{\psi(\Omega_\omega[n]^{\Omega_\omega[n]})}(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_\omega^{\Omega_\omega})\\&f_{\psi(\psi_n(0))}(f_{\psi(\Omega_\omega)}(n))\sim\psi(\psi_\omega(0))\\&f_{\psi(\Omega_\omega)[n+1]}(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_{\omega+1})\\&f_{\psi(\Omega_\omega)[n+2]}(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_{\omega+2})\\&f_{\psi(\Omega_\omega)[n\times2]}(f_{\psi(\Omega_\omega)}(n))\sim\psi(\Omega_{\omega\times2})\\&f_{\psi(\Omega_\omega)}^2(n)\sim\psi(\Omega_{\psi(\Omega_\omega)})\\&f_{\psi(\Omega_\omega)[f_{\psi(\Omega_\omega)}(n)+1]}(f_{\psi(\Omega_\omega)}^2(n))\sim\psi(\Omega_{\psi(\Omega_\omega)+1})\\&f_{\psi(\Omega_\omega)}^3(n)\sim\psi(\Omega_{\psi(\Omega_{\psi(\Omega_\omega)})})\\&f_{\psi(\Omega_\omega)+1}(n)\sim\psi(\Omega_\Omega)\end{align}