FANDOM


This blog will be an analysis of more powerfull expressions in BHAN.If you want to see the previous analysis,you can check out my older blog post.

BHAN Approximation in FGH
\(//M_1[_1]^2_1a,b//\) \(f_{\psi(\chi(M^2))}(n)\)
\(//M_1[_1]^3_1a,b//\) \(f_{\psi(\chi(M^2 \omega))}(n)\)
\(//M_1[_1]^4_1a,b//\) \(f_{\psi(\chi(M^2 \Omega))}(n)\)
\(//M_1[_1]^5_1a,b//\) \(f_{\psi(\chi(M^2 \Omega 2))}(n)\)
\(//M_1[_1]^c_1a,b//\) \(f_{\psi(\chi(M^2 \Omega \omega))}(n)\)
\(//M_1[_1]^{[2]}_1a,b//\) \(f_{\psi(\chi(M^2 \Omega^2))}(n)\)
\(//M_1[_1]^{[c]}_1a,b//\) \(f_{\psi(\chi(M^2 \Omega^{\omega}))}(n)\)
\(//M_1[_1]^{[[{2}]]}_1a,b//\) \(f_{\psi(\chi(M^2 \Omega^{\Omega}))}(n)\)
\(//M_1[_1]^{[[[{2}]]]}_1a,b//\) \(f_{\psi(\chi(M^2 \Omega^{\Omega^2}))}(n)\)
\(//M_1[_1]^{[[[{c}]]]}_1a,b//\) \(f_{\psi(\chi(M^2 \Omega^{\Omega^{\omega}}))}(n)\)
\(//M_1[_1]^{_0[1]}_1a,b//\) \(f_{\psi(\chi(M^2 \varepsilon_{\Omega +1}))}(n)\)
\(//M_1[_1]^{_1[1]}_1a,b//\) \(f_{\psi(\chi(M^2 \varepsilon_{\varepsilon_{\Omega +1}}))}(n)\)
\(//M_1[_1]^{_c[1]}_1a,b//\) \(f_{\psi(\chi(M^2 \zeta_{\Omega +1}))}(n)\)
\(//M_1[_2]_1a,b//\) \(f_{\psi(\chi(M^2 \Omega_2))}(n)\)
\(//M_1[_c]_1a,b//\) \(f_{\psi(\chi(M^2 \Omega_{\omega}))}(n)\)
\(//M_1[_{//M_1[_c]_1a,b//}]_1a,b//\) \(f_{\psi(\chi(M^2 \Omega_{\psi(\chi(M^2 \Omega_{\omega}))}))}(n)\)
\(//M_1[_{[ ]}]_1a,b//\) \(f_{\psi(\chi(M^2 \Omega_{\Omega}))}(n)\)
\(//M_1[_{[_{[]}]}]_1a,b//\) \(f_{\psi(\chi(M^2 I))}(n)\)
\(//M_1[_{[_{[_{[]}]}]}]_1a,b//\) \(f_{\psi(\chi(M^2 \chi(M^2)))}(n)\)
\(//M_1[_{[_{[_{[_{[]}]}]}]}]_1a,b//\) \(f_{\psi(\chi(M^2 \chi(M^2 \chi(M^2))))}(n)\)
\(//M_1[_{[c-|1]}]_1a,b//\) \(f_{\psi(\chi(M^3))}(n)\)
\(//M_1[_{[[]-|1]}]_1a,b//\) \(f_{\psi(\chi(M^M))}(n)\)
\(//M_1[_{[[_{[]}]-|1}]_1a,b//\) \(f_{\psi(\chi(M^{M^2}))}(n)\)
\(//M_1[_{[[_{[_{[]}]}]-|1]}]_1a,b//\) \(f_{\psi(\chi(M^{M^3}))}(n)\)
\(//M_1[_{[c-|2]}]_1a,b//\) \(f_{\psi(\chi(M^{M^{\omega}}))}(n)\)
\(//M_1[_{[[]-|2]}]_1a,b//\) \(f_{\psi(\chi(M^{M^M}))}(n)\)
\(//M_1[_{[[_{[]}]-|2]}]_1a,b//\) \(f_{\psi(\chi(M^{M^{M^2}}))}(n)\)
\(//M_1[_{[[_{[_{[]}]}]-|2]}]_1a,b//\) \(f_{\psi(\chi(M^{M^{M^3}}))}(n)\)
\(//M_1[_{[c-|3]}]_1a,b//\) \(f_{\psi(\chi(M^{M^{M^M}}))}(n)\)
\(//M_1[_{[c-|4]}]_1a,b//\) \(f_{\psi(\chi(M^{M^{M^{M^M}}}))}(n)\)
\(//M_1[_{[c-|d]}]_1a,b//\) \(f_{\psi(\chi(\varepsilon_{M+1}))}(n)\)
\(//M_1[_{[c-|[]]}]_1a,b//\) \(f_{\psi(\chi(\varepsilon_{M 2}))}(n)\)
\(//M_1[_{[c-|\{0,d\}]}]_1a,b//\) \(f_{\psi(\chi(\zeta_{M+1}))}(n)\)
\(//M_1[_{[c-|\{1,0\}]}]_1a,b//\) \(f_{\psi(\chi(\eta_{M+1}))}(n)\)
\(//M_1[_{[c-|\{1,1\}]}]_1a,b//\) \(f_{\psi(\chi(\eta_{\eta_{M+1}}))}(n)\)
\(//M_1[_{[c-|\{1,2\}]}]_1a,b//\) \(f_{\psi(\chi(\eta_{\eta_{\eta_{M+1}}}))}(n)\)
\(//M_1[_{[c-|\{1,d\}]}]_1a,b//\) \(f_{\psi(\chi(\varphi(4,{M+1})))}(n)\)
\(//M_1[_{[c-|\{1,[]\}]}]_1a,b//\) \(f_{\psi(\chi(\Omega_{M+1}))}(n)\)
\(//M_1[_{[c-|\{1,[_{[]}]\}]}]_1a,b//\) \(f_{\psi(\chi(\Omega_{\Omega_{M+1}}))}(n)\)
\(//M_1[_{[c-|\{1,d-|1\}]}]_1a,b//\) \(f_{\psi(\chi(I_{M+1}))}(n)\)
\(//M_1[_{[c-|\{1,[]-|1\}]}]_1a,b//\) \(f_{\psi(\chi(M_2))}(n)\)
\(//M_1[_{[c-|\{1,[_{[]}]-|1\}]}]_1a,b//\) \(f_{\psi(\chi(M_3))}(n)\)
\(//M_1[_{[c-|\{1,d-|2\}]}]_1a,b//\) \(f_{\psi(\chi(M_{\omega}))}(n)\)
\(//M_1[_{[c-|\{1,[]-|2\}]}]_1a,b//\) \(f_{\psi(\chi(M_M))}(n)\)
\(//M_1[_{[c-|\{1,[_{[]}]-|2\}]}]_1a,b//\) \(f_{\psi(\chi(M_{M_M}))}(n)\)
\(//M_1[_{[c-|\{1,d-|3\}]}]_1a,b//\) \(f_{\psi(\chi(M(1,0)))}(n)\)
\(//M_1[_{[c-|\{1,d-|e\}]}]_1a,b//\) \(f_{\Psi_{\Xi(3,0)}(2,\Xi(3,0) \omega)}(n)\)
\(//M_1[_{[c-|\{1,\{0,d\}\}]}]_1a,b//\) \(f_{\Psi_{\Xi(3,0)}(2,\Xi(3,0)^2)}(n)\)
\(//M_1[_{[c-|\{1,\{1,0\}\}]}]_1a,b//\) \(f_{\Psi_{\Xi(3,0)}(2,\Xi(3,0)^3)}(n)\)
\(//M_1[_{[c-|\{1,\{1,\{1,0\}\}\}]}]_1a,b//\) \(f_{\Psi_{\Xi(3,0)}(2,\Xi(3,0)^4)}(n)\)
\(//M_1[_{[c-|\{2,0\}]}]_1a,b//\) \(f_{\Psi_{\Xi(3,0)}(2,\Xi(3,0)^{\omega})}(n)\)
\(//M_1[_{[c-|\{2,1\}]}]_1a,b//\) \(f_{\Psi_{\Xi(3,0)}(2,\Xi(3,0)^{\omega +1})}(n)\)
\(//M_1[_{[c-|\{3,0\}]}]_1a,b//\) \(f_{\Psi_{\Xi(3,0)}(2,\Xi(3,0)\uparrow\uparrow 2)}(n)\)
\(//M_1[_{[c-|\{4,0\}]}]_1a,b//\) \(f_{\Psi_{\Xi(3,0)}(2,\Xi(3,0)\uparrow\uparrow 3)}(n)\)
\(//M_1[_{[c-|\{d,0\}]}]_1a,b//\) \(f_{\Psi_{\Xi(3,0)}(2,\varepsilon_{\Xi(3,0) +1})}(n)\)
\(//M_1[_{[c-|\{[],0\}]}]_1a,b//\) \(f_{\Psi_{\Xi(3,0)}(2,\Omega_{\Xi(3,0) +1})}(n)\)

\(//M_1[_{[c-|\{[_{[]}],0\}]}]_1a,b//\)

\(f_{\Psi_{\Xi(3,0)}(2,I_{\Xi(3,0) +1})}(n)\)
\(//M_1[_{[c-|\{d-|1,0\}]}]_1a,b//\) \(f_{\Psi_{\Xi(3,0)}(2,\Xi(4,0))}(n)\)
\(//M_1[_{[c-|\{[]-|1,0\}]}]_1a,b//\) \(f_{\Psi_{\Xi(3,0)}(2,\Xi(\omega,0))}(n)\)
\(//M_1[_{[c-|\{[_{[]}]-|,0\}]}]_1a,b//\) \(f_{\Psi_{\Xi(3,0)}(2,\Xi(1,0,0))}(n)\)
\(//M_1[_{[c-|\{d-|2,0\}]}]_1a,b//\) \(f_{\Psi_{\Xi(3,0)}(2,\Xi(1,0,0,0))}(n)\)
\(//M_1[_{[c-|\{d-|e,0\}]}]_1a,b//\) \(f_{\Psi_{\Xi(4,0)}(3,\Xi(4,0)^{\omega})}(n)\)
\(//M_1[_{[c-|\{d-|[],0\}]}]_1a,b//\) \(f_{\Psi_{\Xi(4,0)}(3,\Xi(4,0)^{\Xi(4,0)})}(n)\)
\(//M_1[_{[c-|\{d-|e-|1,0\}]}]_1a,b//\) \(f_{\Psi_{\Xi(4,0)}(3,\varepsilon_{\Xi(4,0)})}(n)\)
\(//M_1[_{[c-|\{\{0,d\},0\}]}]_1a,b//\) \(f_{\Psi_{\Xi(4,0)}(3,\Omega_{\Xi(4,0)})}(n)\)
\(//M_1[_{[c-|\{\{0,[]\},0\}]}]_1a,b//\) \(f_{\Psi_{\Xi(4,0)}(3,I_{\Xi(4,0)})}(n)\)
\(//M_1[_{[c-|\{\{0,d-|1\},0\}]}]_1a,b//\) \(f_{\Psi_{\Xi(4,0)}(3,\Xi(\omega,0))}(n)\)
\(//M_1[_{[c-|\{\{1,0\},0\}]}]_1a,b//\) \(f_{\Psi_{\Xi(4,0)}(3,\Xi(1,0,0))}(n)\)
\(//M_1[_{[c-|\{1,0,0\}]}]_1a,b//\) \(f_{\Psi_{\Xi(4,0)}(3,\Xi(1,0,0,0))}(n)\)
\(//M_1[_{[c-|\{1,0,0,0\}]}]_1a,b//\) \(f_{\Psi_{\Xi(4,0)}(3,\Xi(1,0,0,0,0))}(n)\)
\(//M_1[_{[c-|\{1,0,0,0,0\}]}]_1a,b//\) \(f_{\Psi_{\Xi(4,0)}(3,\Xi(1,0,0,0,0,0))}(n)\)

Limit of h-neBHAN

\(f_{\Psi_{\Xi(5,0)}(4,\Xi(5,0)^{\omega})}(n)\)

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