FANDOM


My new notation (Boris's hyper array notation) seems to go quite far!

Links to it here.

BHAN

Approximation in FGH

\(//a,b//\) \(f_2(n)\)
\(//a,b,2//\) \(f_3(n)\)
\(//a,b,3//\) \(f_4(n)\)
\(//a,b,c//\) \(f_{\omega}(n)\)
\(//a,b,1,d//\) \(f_{\omega +1}(n)\)
\(//a,b,2,d//\) \(f_{\omega+2}(n)\)
\(//a,b,3,d//\) \(f_{\omega+3}(n)\)
\(//a,b,c,d//\) \(f_{\omega 2}(n)\)
\(//a,b,c,1,d//\) \(f_{\omega 2 +1}(n)\)
\(//a,b,c,2,2//\) \(f_{\omega 2 +2}(n)\)
\(//a,b,c,3,2//\) \(f_{\omega 2 +3}(n)\)
\(//a,b,c,d,2//\) \(f_{\omega 3}(n)\)
\(//a,b,c,2,3//\) \(f_{\omega 3 +1}(n)\)
\(//a,b,c,3,3//\) \(f_{\omega 3 +2}(n)\)
\(//a,b,c,4,3//\) \(f_{\omega 3 +3}(n)\)
\(//a,b,c,d,3//\) \(f_{\omega 4}(n)\)
\(//a,b,c,2,4//\) \(f_{\omega 4 +1}(n)\)
\(//a,b,1,c,d//\) \(f_{\omega^2}(n)\)
\(//a,b,c,d,e//\) \(f_{\omega^2}(n)\)


BHAN Approximation in  FGH 
\(//a,b,c,d,e,2//\) \(f_{\omega^2 2}(n)\)
\(//a,b,c,d,e,3//\) \(f_{\omega^2 3}(n)\)
\(//a,b,c,d,e,f//\) \(f_{\omega^3}(n)\)
\(//a,b,c,d,e,f,3//\) \(f_{\omega^3 2}(n)\)
\(//a,b,c,d,e,f,4//\) \(f_{\omega^3 3}(n)\)
\(//a,b,c,d,e,f,g//\) \(f_{\omega^4}(n)\)
\(//a,b,c,d,e,f,g,3//\) \(f_{\omega^4 2}(n)\)
\(//a,b,c,d,e,f,g,4//\) \(f_{\omega^4 3}(n)\)
\(//a,b,c,d,e,f,g,h//\) \(f_{\omega^5}(n)\)
\(//\underbrace{a,b,c,d,e,\ldots,x,y,z}_v//\) \(f_{\omega^{v-3}}(n)\)
\(//\underbrace{a,b,c,d,e,\ldots,x,y,z}_n//\) \(f_{\omega^{\omega}}(n)\)


BHAN Approximation in FGH
\(//a(1)b//\) \(f_{\omega^{\omega}}(n)\)
\(//a(2)b//\) \(f_{\omega^{\omega}+1}(n)\)
\(//a(3)b//\) \(f_{\omega^{\omega}+2}(n)\)
\(//a(c)b//\) \(f_{\omega^{\omega}+\omega}(n)\)
\(//a(c(e)d)b//\) \(f_{\omega^{\omega}+\omega^{\omega}}(n)\)
\(//a(c(e(g)f)d)b//\) \(f_{\omega^{\omega}3}(n)\)
\(//a\backslash^{1}_b//\) \(f_{\omega^{\omega +1}}(n)\)
\(//a\backslash^{2}_1//\) \(f_{\omega^{\omega +1}}(n)\)
\(//a\backslash^{2}_2//\) \(f_{\omega^{\omega +1}+1}(n)\)
\(//a\backslash^{2}_3//\) \(f_{\omega^{\omega +1}+2}(n)\)
\(//a\backslash^{2}_b//\) \(f_{\omega^{\omega +1}+\omega}(n)\)
\(//a\backslash^{3}_1//\) \(f_{\omega^{\omega +1}+\omega^{\omega +1}}(n)\)
\(//a\backslash^{4}_1//\) \(f_{\omega^{\omega +1}3}(n)\)
\(//a\backslash^{b}_1//\) \(f_{\omega^{\omega +2}}(n)\)


BHAN Approximation in FGH
\(//n\backslash^{a}_b\backslash^{c}_d//\) \(f_{\omega^{\omega^2}}(n)\)
\(//n\backslash^{a}_b\backslash^{c}_d\backslash^{e}_f//\) \(f_{\omega^{\omega^3}}(n)\)
\(//a\backslash \backslash^{b}_c//\) \(f_{\omega^{\omega^{b-1}c}}(a)\)
\(//a\backslash \backslash^{n}_n//\) \(f_{\omega^{\omega^{\omega}}}(n)\)
\(//a\backslash \backslash^{n}_1\backslash^{n}_1//\) \(f_{\omega^{\omega^{\omega +1}}}(n)\)
\(//a\backslash \backslash^{n}_1\backslash^{n}_1\backslash^{n}_1//\) \(f_{\omega^{\omega^{\omega +2}}}(n)\)
\(//a\backslash \backslash^{n}_1\backslash \backslash^{n}_1//\) \(f_{\omega^{\omega^{\omega 2}}}(n)\)

\(//a\backslash \backslash^n_1 \backslash \backslash^n_1 \backslash \backslash^n_1//\)                                          

\(f_{\omega^{\omega^{\omega 3}}}(n)\)
\(//a\backslash \backslash \backslash^{n}_n//\) \(f_{\omega^{\omega^{\omega^2}}}(n)\)
\(//a\backslash \backslash \backslash^{n}_1\backslash \backslash \backslash^{n}_1//\) \(f_{\omega^{\omega^{\omega^2 2}}}(n)\)
\(//a\backslash \backslash \backslash \backslash^{n}_n//\) \(f_{\omega^{\omega^{\omega^3}}}(n)\)
\(//a\backslash \backslash \backslash \backslash \backslash^n_1//\) \(f_{\omega^{\omega^{\omega^4}}}(n)\)
\(//a^+b//\) \(f_{\omega \uparrow \uparrow 4}(n)\)
\(//a^{+2}b//\) \(f_{\omega \uparrow \uparrow 4 +\omega}(n)\)
\(//a^{+3}b//\) \(f_{\omega \uparrow \uparrow 4 +\omega 2}(n)\)
\(//a^{+b}c//\) \(f_{\omega \uparrow \uparrow 4 +\omega^2}(n)\)
\(//a^{++}b//\) \(f_{\omega \uparrow \uparrow 4 +\omega^2}(n)\)
\(//a^{+++}b//\) \(f_{\omega \uparrow \uparrow 4 +\omega^3}(n)\)
\(//a^{\{b,+\}}c//\) \(f_{\omega \uparrow \uparrow 4 +\omega^{\omega}}(n)\)


BHAN Approximation in FGH
\(//M1,a//\) \(f_{\omega \uparrow \uparrow 4 +\omega^{\omega}}(n)\)
\(//M2,a//\) \(f_{\omega \uparrow \uparrow 4 +\omega^{\omega} +1}(n)\)
\(//M3,a//\) \(f_{\omega \uparrow \uparrow 4 +\omega^{\omega} +\omega}(n)\)
\(//M4,a//\) \(f_{\omega \uparrow \uparrow 4 +\omega^{\omega} +\omega^{\omega}}(n)\)
\(//M5,a//\) \( > f_{\omega \uparrow \uparrow 4 +\omega^{\omega^{\omega}}}(n)\)
\(//M6,a//\) \( > f_{(\omega \uparrow \uparrow 4)2}(n)\)
\(//M7,a//\) \( > f_{\omega \uparrow \uparrow 5}(n)\)
\(//Ma,b//\) \( > f_{\omega^{\lambda}}(n)\) ,where \(\lambda\) is the ordinal for \(//Ma-1,b//\)
\(//Ma,b//\) \(f_{\varepsilon_0}(n)\)
\(//M//Ma,b//,b//\) \(f^2_{\varepsilon_0}(n)\)
\(//M[2]a,b//\) \(f_{\varepsilon_0 +1}(n)\)
\(//M[2][2]a,b//\) \(f_{\varepsilon_0 +2}(n)\)
\(//M[2][3]a,b//\) \(f_{\varepsilon_0 +3}(n)\)
\(//M[2][c]a,b//\) \(f_{\varepsilon_0 +\omega}(n)\)
\(//M[2][ Ma,b ]a,b//\) \(f_{\varepsilon_0 2}(n)\)
\(//M[3]a,b//\) \(f_{\varepsilon_0 \omega}(n)\)
\(//M[3][c]a,b//\) \(f_{\varepsilon_0 \omega +\omega}(n)\)
\(//M[4]a,b//\) \(f_{\varepsilon_0 \omega^2}(n)\)
\(//M[c]a,b//\) \(f_{\varepsilon_0 \omega^{\omega}}(n)\)
\(//M[ Ma,b ]a,b//\) \(f_{\varepsilon_0^2}(n)\)
\(//M[1,2]a,b//\) \(f_{\varepsilon_0^{\omega}}(n)\)
\(//M[1,3]a,b//\) \(f_{\varepsilon_0^{\omega +1}}(n)\)
\(//M[1,c]a,b//\) \(f_{\varepsilon_0^{\omega 2}}(n)\)


BHAN Approximation in FGH
\(//M[1,Ma,b]a,b//\) \(f_{\varepsilon_0^{\varepsilon_0}}(n)\)
\(//M[1,M[1,Ma,b]a,b]a,b//\) \(f_{\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}}(n)\)
\(//M[2,2]a,b//\) \(f_{\varepsilon_1}(n)\)
\(//M[2,2][2]a,b//\) \(f_{\varepsilon_1 +1}(n)\)
\(//M[2,2][3]a,b//\) \(f_{\varepsilon_1 +2}(n)\)
\(//M[2,2][c]a,b//\) \(f_{\varepsilon_1 +\omega}(n)\)
\(//M[2,2][ Ma,b ]a,b//\) \(f_{\varepsilon_1 +\varepsilon_0}(n)\)
\(//M[2,2][ M[2,2]a,b ]//\) \(f_{\varepsilon_1 2}(n)\)
\(//M[2,3]a,b//\) \(f_{\varepsilon_1 \omega}(n)\)
\(//M[2,3][c]a,b//\) \(f_{\varepsilon_1 \omega +\omega}(n)\)
\(//M[2,3][ Ma,b ]a,b//\) \(f_{\varepsilon_1 \omega +\varepsilon_0}(n)\)
\(//M[2,3][ M[2,2]a,b ]a,b//\) \(f_{\varepsilon_1 (\omega +1)}(n)\)
\(//M[2,3][ M[2,3] a,b]a,b//\) \(f_{\varepsilon_1 (\omega 2)}(n)\)
\(//M[2,4]a,b//\) \(f_{\varepsilon_1 \omega^2}(n)\)
\(//M[2,c]a,b//\) \(f_{\varepsilon_1 \omega^{\omega}}(n)\)
\(//M[2,Ma,b]a,b//\) \(f_{\varepsilon_1 \times \varepsilon_0}(n)\)
\(//M[2,M[2,2]a,b]a,b//\) \(f_{\varepsilon_1^2}(n)\)
\(//M[3,2]a,b//\) \(f_{\varepsilon_1^{\omega}}(n)\)
\(//M[4,2]a,b//\) \(f_{\varepsilon_2}(n)\)


BHAN Approximation in FGH
\(//M[5,2]a,b//\) \(f_{\varepsilon_2^{\omega}}(n)\)
\(//M[c,2]a,b//\) \(f_{\varepsilon_{{c} \over {2}}}(n)\),if \(c\) is even
\(//M[c,2]a,b//\) \(f_{\varepsilon_{{{c} \over {2}}-1}^{\omega}}(n)\) if \(c\) is odd
\(//M[ Ma,b,2]a,b//\) \(f_{\varepsilon_{\varepsilon_0}}(n)\)
\(//M[ M[ Ma,b,2 ]a,b ],2]a,b//\) \(f_{\varepsilon_{\varepsilon_{\varepsilon_0}}}(n)\)
\(//M[1,1,2]a,b//\) \(f_{\zeta_0}(n)\)
\(//M[1,1,2][c]a,b//\) \(f_{\zeta_0 + \omega}(n)\)
\(//M[1,1,2][ Ma,b ]a,b//\) \(f_{\zeta_0 + \varepsilon_0}(n)\)
\(//M[1,1,2][ M[1,1,2]a,b ]a,b]a,b//\) \(f_{\zeta_0 2}(n)\)
\(//M[1,1,3]a,b//\) \(f_{\zeta_0 \omega}(n)\)
\(//M[1,1,4]a,b//\) \(f_{\zeta_0 \omega^2}(n)\)
\(//M[1,1,c]a,b//\) \(f_{\zeta_0 \omega^{\omega}}(n)\)
\(//M[1,1,Ma,b]a,b//\) \(f_{\zeta_0 \times \varepsilon_0}(n)\)
\(//M[1,2,2]a,b//\) \(f_{\zeta_0^{\omega}}(n)\)

\(//M[1,2,2][ M[1,2,2]a,b ]a,b//\)

\(f_{\zeta_0^{\omega}2}(n)\)
\(//M[1,2,3]a,b//\) \(f_{\zeta_0^{\omega +1}}(n)\)
\(//M[1,2,c]a,b//\) \(f_{\zeta_0^{\omega 2}}(n)\)
\(//M[1,2,Ma,b]a,b//\) \(f_{\zeta_0^{\varepsilon_0}}(n)\)
\(//M[1,2,M[1,2,2]a,b]a,b//\) \(f_{\zeta_0^{\zeta_0}}(n)\)
\(//M[1,3,2]a,b//\) \(f_{\varepsilon_{\zeta_0 +1}}(n)\)
\(//M[1,4,2]a,b//\) \(f_{\varepsilon_{\varepsilon_{\zeta_0 +1}}}(n)\)
\(//M[1,c,2]a,b//\) \(f_{\zeta_1}(n)\)


BHAN Approximation in FGH
\(//M[1,Ma,b,2]a,b//\) \(f_{\varepsilon_{\zeta_1 +1}}(n)\)
\(//M[1,M[1,Ma,b,2]a,b,2]a,b//\) \(f_{\varepsilon_{\varepsilon_{\zeta_1 +1}}}(n)\)
\(//M[2,1,2]a,b//\) \(f_{\zeta_2}(n)\)
\(//M[c,1,2]a,b//\) \(f_{\zeta_{\omega}}(n)\)
\(//M[ Ma,b,1,2]a,b//\) \(f_{\zeta_{\varepsilon_0}}(n)\)
\(//M[ M[1,1,2]a,b ]a,b//,1,2]a,b//\) \(f_{\zeta_{\zeta_0}}(n)\)
\(//M[1,1,1,2]a,b//\) \(f_{\varphi(3,0)}(n)\)
\(//M[1,c,1,2]a,b//\) \(f_{\varphi(3,\omega)}(n)\)
\(//M[1,//M[1,1,1,2]//,1,2]a,b//\) \(f_{\varphi(3,\varphi(3,0))}(n)\)
\(//M[2,1,1,2]a,b//\) \(f_{\varphi(4,0)}(n)\)
\(//M[c,1,1,2]a,b//\) \(f_{\varphi(\omega,0)}(n)\)
\(//M[ M[c,1,1,2]a,b,1,1,2]a,b//\) \(f_{\varphi(\varphi(\omega,0),0)}(n)\)
\(//M[1,1,1,1,2]a,b//\) \(f_{\Gamma_0}(n)\)
\(//M \underbrace{[1,1,1,\ldots,1,1,2]}_n a,b//\) \(f_{\vartheta(\Omega^{\omega})}(n)\)
\(//M_0[1]a,b//\) \(f_{\vartheta(\Omega^{\omega})}(n)\)
\(//M_0[2]a,b//\) \(f_{\vartheta(\Omega^{\omega +1})}(n)\)
\(//M_0[c]a,b//\) \(f_{\vartheta(\Omega^{\omega 2})}(n)\)
\(//M_0[ //M_0[1]a,b// ]a,b//\) \(f_{\vartheta(\Omega^{\vartheta(\Omega^{\omega})})}(n)\)
\(//M_1[1]a,b//\) \(f_{\vartheta(\Omega^{\Omega})}(n)\)


BHAN Approximation in FGH
\(//M_1[c]a,b//\) \(f_{\vartheta(\Omega^{\Omega \omega})}(n)\)
\(//M_1[ //M_1[1]a,b// ]a,b//\) \(f_{\vartheta(\Omega^{\Omega^2})}(n)\)
\(//M_2[1]a,b//\) \(f_{\vartheta(\Omega^{\Omega^{\omega}})}(n)\)
\(//M_2[2]a,b//\) \(f_{\vartheta(\Omega^{\Omega^{\omega 2}})}(n)\)
\(//M_2[c]a,b//\) \(f_{\vartheta(\Omega^{\Omega^{\omega^2}})}(n)\)
\(//M_2[ //M_2[1]a,b// ]//\) \(f_{\vartheta(\Omega^{\Omega^{\vartheta(\Omega^{\Omega})}})}(n)\)
\(//M_3[1]a,b//\) \(f_{\vartheta(\Omega^{\Omega^{\Omega}})}(n)\)
\(//M_c[d]a,b//\) \(f_{\vartheta(\varepsilon_{\Omega +1})}(n)\)
\(//M[c]_1a,b//\) \(f_{\vartheta(\varepsilon_{\Omega +\omega^4})}(n)\)
\(//M[ //M[c]_1a,b// ]_1a,b//\) \(f_{\vartheta(\varepsilon_{\Omega +1} 2)}(n)\)
\(//M[c]_2a,b//\) \(f_{\vartheta(\varepsilon_{\Omega +1} \omega)}(n)\)
\(//M[ //M[c]_2a,b// ]_2a,b//\) \(f_{\vartheta(\varepsilon_{\Omega +1}^2)}(n)\)
\(//M[c]_3a,b//\) \(f_{\vartheta(\varepsilon_{\Omega +1}^{\omega})}(n)\)
\(//M[c]_4a,b//\) \(f_{\vartheta(\varepsilon_{\Omega +2})}(n)\)
\(//M[c]_da,b//\) \(f_{\vartheta(\varepsilon_{\Omega +\omega})}(n)\)
\(//M[c]_{ //M[c]_1a,b// }a,b//\) \(f_{\vartheta(\varepsilon_{\Omega +\vartheta(\varepsilon_{\Omega})})}(n)\)
\(//M[c]_{[1]}a,b//\) \(f_{\vartheta(\varepsilon_{\Omega +\vartheta(\varepsilon_{\Omega})})}(n)\)
\(//M[c]_{[2]}a,b//\) \(f_{\vartheta(\varepsilon_{\Omega 2})}(n)\)
\(//M[c]_{[d]}a,b//\) \(f_{\vartheta(\varepsilon_{\Omega \omega})}(n)\)


BHAN Approximation in FGH
\(//M[c]_{[{[1]}]}a,b//\) \(f_{\vartheta(\varepsilon_{\Omega \omega})}(n)\)
\(//M[c]_{[{[2]}]}a,b//\) \(f_{\vartheta(\varepsilon_{\Omega (\omega +1)})}(n)\)
\(//M[c]_{[{[d]}]}a,b//\) \(f_{\vartheta(\varepsilon_{\Omega \omega 2})}(n)\)
\(//M[c]_{[[ //M[c]_{ 1 }a,b// ]]}a,b//\) \(f_{\vartheta(\varepsilon_{\Omega \vartheta(\varepsilon_{\Omega \omega})})}(n)\)
\(//M[c]_{[[[1]]]}a,b//\) \(f_{\vartheta(\varepsilon_{\Omega \omega 2})}(n)\)
\(//M[c]_{[[[2]]]}a,b//\) \(f_{\vartheta(\varepsilon_{\Omega^2})}(n)\)
\(//M[c]_{[[[3]]]}a,b//\) \(f_{\vartheta(\varepsilon_{\Omega^{\omega}})}(n)\)
\(//M[c]_{[[[4]]]}a,b//\) \(f_{\vartheta(\varepsilon_{\varepsilon_{\Omega +1}})}(n)\)
\(//M[c]_{[[[5]]]}a,b//\) \(f_{\vartheta(\zeta_{\Omega +1})}(n)\)
\(//M[c]_{[[[d]]]}a,b//\) \(f_{\vartheta(\varphi(\omega,\Omega +1))}(n)\)
\(//M{[c]}_{[[[{[1]}]]]}a,b//\) \(f_{\vartheta(\varphi(\omega,\Omega +1))}(n)\)
\(//M{[c]}_{[[[{[2]}]]]}a,b//\) \(f_{\vartheta(\varphi(1,0,\Omega +1))}(n)\)
\(//M{[c]}_{[[[{[3]}]]]}a,b//\) \(f_{\vartheta(\varphi(2,0,\Omega +1))}(n)\)
\(//M[c]_{[[[{[d]}]]]}a,b//\) \(f_{\vartheta(\varphi(\omega,0,\Omega +1))}(n)\)
\(//M[c]_{[[[{[{[2]}]}]]]]}a,b//\) \(f_{\vartheta(\varphi(1,0,0,\Omega +1))}(n)\)
\(//M[c]_{_0[1]}a,b//\) \(f_{\vartheta(\vartheta(\Omega^{\omega} (\Omega +1)))}(n)\)
\(//M_0[_0[c]]a,b//\) \(f_{\vartheta(\Omega_2)}(n)\)
\(//M_0[_0[_0[c]]]a,b//\) \(f_{\vartheta(\Omega_3)}(n)\)
\(//M_1[_0[c]]a,b//\) \(f_{\vartheta(\Omega_{\omega})}(n)\)


BHAN Approximation in FGH
\(//M_1[_1[c]]a,b//\) \(f_{\vartheta(\Omega_{\vartheta(\Omega_{\omega})})}(n)\)
\(//M_2[_0[c]]a,b//\) \(f_{\vartheta(\Omega_{\Omega})}(n)\)
\(//M_2[_0[_0[c]]]a,b//\) \(f_{\vartheta(\Omega_{\Omega +1})}(n)\)
\(//M_2[_1[c]]a,b//\) \(f_{\vartheta(\Omega_{\Omega +\omega})}(n)\)
\(//M_2[_1[_1[c]]]a,b//\) \(f_{\vartheta(\Omega_{\Omega +\vartheta(\Omega_{\Omega +\omega})})}(n)\)
\(//M_2[_2[c]]a,b//\) \(f_{\vartheta(\Omega_{\Omega 2})}(n)\)
\(//M_2[_2[_2[c]]]a,b//\) \(f_{\vartheta(\Omega_{\Omega 3})}(n)\)
\(//M_3[_0[c]]a,b//\) \(f_{\vartheta(\Omega_{\Omega \omega})}(n)\)
\(//M_3[_3[c]]a,b//\) \(f_{\vartheta(\Omega_{\Omega \vartheta(\Omega_{\Omega \omega})})}(n)\)
\(//M_4[_0[c]]a,b//\) \(f_{\vartheta(\Omega_{\Omega^2})}(n)\)
\(//M_4[_4[c]]a,b//\) \(f_{\vartheta(\Omega_{\Omega^3})}(n)\)
\(//M_4[_4[_4[c]]]a,b//\) \(f_{\vartheta(\Omega_{\Omega^4})}(n)\)
\(//M_5[_0[c]]a,b//\) \(f_{\vartheta(\Omega_{\Omega^{\omega}})}(n)\)
\(//M_5[_4[c]]a,b//\) \(f_{\vartheta(\Omega_{\Omega^{\omega +1}})}(n)\)
\(//M_5[_5[c]]a,b//\) \(f_{\vartheta(\Omega_{\Omega^{\omega 2}})}(n)\)
\(//M_6[_0[c]]a,b//\) \(f_{\vartheta(\Omega_{\Omega^{\omega^2}})}(n)\)
\(//M_7[_0[c]]a,b//\) \(f_{\vartheta(\Omega_{\Omega^{\omega^3}})}(n)\)
\(//M_d[_0[c]]a,b//\) \(f_{\vartheta(\Omega_{\Omega^{\omega^{d-4}}})}(n)\)
\(//M_d[_0[c]]a,b//\) \(f_{\vartheta(\Omega_{\Omega^{\omega^{\omega}}})}(n)\)


BHAN Approximation in FGH
\(//M_{[1]}[_0[c]]a,b//\) \(f_{\vartheta(\Omega_{\Omega^{\omega^{\omega}}})}(n)\)
\(//M_{[2]}[_0[c]]a,b//\) \(f_{\vartheta(\Omega_{\Omega^{\Omega}})}(n)\)
\(//M_{[3]}[_0[c]]a,b//\) \(f_{\vartheta(\Omega_{\Omega^{\Omega^2}})}(n)\)
\(//M_{[d]}[_0[c]]a,b//\) \(f_{\vartheta(\Omega_{\Omega^{\Omega^{\omega}}})}(n)\)
\(//M_{[{[1]}]}[_0[c]]a,b//\) \(f_{\vartheta(\Omega_{\Omega^{\Omega^{\omega}}})}(n)\)
\(//M_{[{[2]}]}[_0[c]]a,b//\) \(f_{\vartheta(\Omega_{\Omega^{\Omega^{\Omega}}})}(n)\)
\(//M_{[{[3]}]}[_0[c]]a,b//\) \(f_{\vartheta(\Omega_{\Omega^{\Omega^{\Omega^2}}})}(n)\)
\(//M_{[{[d]}]}[_0[c]]a,b//\) \(f_{\vartheta(\Omega_{\Omega^{\Omega^{\Omega^{\omega}}}})}(n)\)
\(//M_{[{[{[1]}]}]}[_0[c]]a,b//\) \(f_{\vartheta(\Omega_{\Omega^{\Omega^{\Omega^{\omega}}}})}(n)\)
\(//M[_0[c]]_1a,b//\) \(f_{\vartheta(\Omega_{\varepsilon_{\Omega +1}})}(n)\)
\(//M[[c]_1]_1a,b//\) \(f_{\vartheta(\Omega_{\vartheta(\Omega_{\varepsilon_{\Omega +1}} (\Omega))})}(n)\)
\(//M[[[c]_1]_1]_1a,b//\) \(f_{\vartheta(\Omega_{\vartheta(\Omega_{\vartheta(\varepsilon_{\Omega +1}(\Omega))}(\Omega))})}(n)\)
\(//M[_0[c]]_2a,b//\) \(f_{\vartheta(\Omega_{\Omega_2})}(n)\)
\(//M[_0[c]_2]_2a,b//\) \(f_{\vartheta(\Omega_{\Omega_2 2})}(n)\)
\(//M[_0[c]]_3a,b//\) \(f_{\vartheta(\Omega_{\Omega_2 \omega})}(n)\)
\(//M[[c]_3]_3a,b//\) \(f_{\vartheta(\Omega_{\Omega_2^2 \omega})}(n)\)
\(//M[_0[c]]_4a,b//\) \(f_{\vartheta(\Omega_{\Omega_2^{\omega}})}(n)\)
\(//M[_0[c]]_5a,b//\) \(f_{\vartheta(\Omega_{\Omega_2^{\omega^2}})}(n)\)
\(//M[_0[c]]_da,b//\) \(f_{\vartheta(\Omega_{\Omega_2^{\omega^{\omega}}})}(n)\)
\(//M[_0[c]]_{[1]}a,b//\) \(f_{\vartheta(\Omega_{\Omega_2^{\omega^{\omega}}})}(n)\)
\(//M[_0[c]]_{[2]}a,b//\) \(f_{\vartheta(\Omega_{\Omega_2^{\Omega}})}(n)\)
\(//M[_0[c]]_{[3]}a,b//\) \(f_{\vartheta(\Omega_{\Omega_2^{\Omega^{\Omega}}})}(n)\)
\(//M[_0[c]]_{[d]}a,b//\) \(f_{\vartheta(\Omega_{\Omega_2^{\varepsilon_{\Omega}}})}(n)\)
\(//M[_0[c]]_{[{[1]}]}a,b//\) \(f_{\vartheta(\Omega_{\Omega_2^{\varepsilon_{\Omega}}})}(n)\)
\(//M[_0[c]]_{[{[2]}]}a,b//\) \(f_{\vartheta(\Omega_{\Omega_2^{\zeta_{\Omega}}})}(n)\)
\(//M[_0[c]]_{[{[d]}]}a,b//\) \(f_{\vartheta(\Omega_{\Omega_2^{\varphi(\omega,\Omega)}})}(n)\)
\(//M[_0[c]]_{[{[{[2]}]}]}a,b//\) \(f_{\vartheta(\Omega_{\Omega_2^{\varphi(1,0,\Omega)}})}(n)\)
\(//M[_0[c]]_{[{[{[d]}]}]}a,b//\) \(f_{\vartheta(\Omega_{\Omega_2^{\vartheta(\Omega^{\omega}(\Omega))}})}(n)\)
\(//M[_0[c]]_{_0[d]}a,b//\) \(f_{\vartheta(\Omega_{\Omega_2^{\vartheta(\varepsilon_{\Omega} (\Omega))}})}(n)\)
\(//M_0[_0[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\Omega_2^{\Omega_2}})}(n)\)
\(//M_0[_0[_0[c]]_1]a,b//\) \(f_{\vartheta(\Omega_{\Omega_2\uparrow\uparrow 3})}(n)\)
\(//M_1[_0[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\Omega_2 \uparrow\uparrow \omega})}(n)\)
\(//M_1[_0[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\varepsilon_{\Omega_2 +1}}}(n)\)
\(//M_1[_0[_0[c]]_1]a,b//\) \(f_{\vartheta(\Omega_{\zeta_{\Omega_2 +1}})}(n)\)
\(//M_1[_0[_0[_0[c]]]_1]a,b//\) \(f_{\vartheta(\Omega_{\varphi(3,\Omega_2 +1)})}(n)\)
\(//M_1[_1[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\varphi(\omega,\Omega_2 +1)})}(n)\)
\(//M_1[_1[_0[c]]_1]a,b//\) \(f_{\vartheta(\Omega_{\varphi(\varphi(\omega,0),\Omega_2 +1)})}(n)\)
\(//M_1[_1[_1[c]]_1]a,b//\) \(f_{\vartheta(\Omega_{\Gamma_{\Omega_2 +1}})}(n)\)
\(//M_2[[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\vartheta(\Omega^{\omega} (\Omega_2))})}(n)\)
\(//M_3[_1[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\vartheta(\Omega^{\Omega} (\Omega_2))})}(n)\)
\(//M_3[_2[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\vartheta(\Omega^{\Omega^{\omega}} (\Omega_2))})}(n)\)
\(//M_3[_3[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\vartheta(\Omega^{\Omega^{\Omega}} (\Omega_2))})}(n)\)
\(//M_4[_0[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\vartheta(\varepsilon_{\Omega +1} (\Omega_2))})}(n)\)
\(//M_5[_0[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\vartheta(\varepsilon_{\Omega +2} (\Omega_2))})}(n)\)
\(//M_d[_0[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\vartheta(\varepsilon_{\Omega +\omega} (\Omega_2))})}(n)\)
\(//M_{[2]}[_0[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\vartheta(\varepsilon_{\Omega 2} (\Omega_2))})}(n)\)
\(//M_{[3]}[_0[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\vartheta(\varepsilon_{\Omega \omega} (\Omega_2))})}(n)\)
\(//M_{[4]}[_0[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\vartheta(\varepsilon_{\Omega^2} (\Omega_2))})}(n)\)
\(//M_{[5]}[_0[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\vartheta(\varepsilon_{\Omega^{\omega}} (\Omega_2))})}(n)\)
\(//M_{[6]}[_0[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\vartheta(\varepsilon_{\Omega^{\Omega}} (\Omega_2))})}(n)\)
\(//M_{[d]}[_0[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\vartheta(\varepsilon_{\varepsilon_{\Omega +1}} (\Omega_2))})}(n)\)
\(//M_{[{[1]}]}[_0[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\vartheta(\varepsilon_{\varepsilon_{\Omega +1}} (\Omega_2))})}(n)\)
\(//M_{[{[2]}]}[_0[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\vartheta(\zeta_{\Omega +1} (\Omega_2))})}(n)\)
\(//M_{[{[d]}]}[_0[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\vartheta({\varphi(\omega,\Omega_2 +1)})})}(n)\)
\(//M_{[[{[1]}]]}[_0[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\vartheta({\varphi(\omega,\Omega_2 +1)})})}(n)\)
\(//M_{[[{[2]}]]}[_0[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\vartheta({\varphi(1,0,\Omega_2 +1)})})}(n)\)
\(//M_{[[{[d]}]]}[_0[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\vartheta({\varphi(\omega,0,\Omega_2 +1)})})}(n)\)
\(//M_{_0[1]}[_0[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\vartheta(\vartheta(\Omega^{\omega} (\Omega_2)) (\Omega_2))})}(n)\)
\(//M_{_1[1]}[_0[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\Omega_3})}(n)\)
\(//M_{_d[1]}[_0[c]_1]a,b//\) \(f_{\vartheta(\Omega_{\Omega_{\omega}})}(n)\)
\(//M_0[_0[_0[c]_1]_1]a,b//\) \(f_{\vartheta(\Omega_{\Omega_{\vartheta(\Omega_{\Omega_{\omega}})}})}(n)\)
\(//M_1[[{2}]]_1a,b//\) \(f_{\vartheta(\Omega_{\Omega_{\Omega}})}(n)\)
\(//M_1[[{3}]]_1a,b//\) \(f_{\vartheta(\Omega_{\Omega_{\Omega_{\vartheta(\Omega_{\Omega_{\Omega}})}}})}(n)\)
\(//M_1[[{c}]]_1a,b//\) \(f_{\vartheta(\Omega_{\Omega_{\Omega_{\Omega}}})}(n)\)
\(//M_1[[_1[[{c}]]_1]]_1a,b//\) \(f_{\vartheta(\Omega_{\Omega_{\Omega_{\Omega_2}}})}(n)\)
\(//M_1[[[2]]]_1a,b//\) \(f_{\vartheta(\Omega_{\Omega_{\Omega_{\Omega_{\omega}}}})}(n)\)
\(//M_1[[[3]]]_1a,b//\) \(f_{\vartheta(\Omega_{\Omega_{\Omega_{\Omega_{\omega 2}}}})}(n)\)
\(//M_1[[[c]]]_1a,b//\) \(f_{\vartheta(\Omega_{\Omega_{\Omega_{\Omega_{\omega^2}}}})}(n)\)
\(//M_1[[[[{2}]]]]_1a,b//\) \(f_{\vartheta(\Omega_{\Omega_{\Omega_{\Omega_{\Omega}}}})}(n)\)
\(//M_1[[[[{3}]]]]_1a,b//\)

\(f_{\vartheta(\Omega_{\Omega_{\Omega_{\Omega_{\Omega_{\Omega}}}}})}(n)\)

\(//M_1[[[[{c}]]]]_1a,b//\) \(f_{\psi(\psi_I(0))}(n)\)
\(//M_1[[[[[{1}]]]]]_1a,b//\) \(f_{\psi(\psi_I(0))}(n)\)
\(//M_1[[[[[{2}]]]]]_1a,b//\) \(f_{\psi(\psi_I(\omega))}(n)\)
\(//M_1[[[[[{3}]]]]]_1a,b//\) \(f_{\psi(\psi_I(\omega 2))}(n)\)
\(//M_1[[[[[{c}]]]]]_1a,b//\) \(f_{\psi(\psi_I(\omega^2))}(n)\)
\(//M_1[[[[[[{1}]]]]]]_1a,b//\) \(f_{\psi(\psi_I(\omega^2))}(n)\)
\(//M_1[[[[[[[_1[[[[[[{1}]]]]]]_1]]]]]]]a,b//\) \(f_{\psi(\psi_I(\psi(\psi_I(0)))}(n)\)
\(//M_1[[[[[[{2}]]]]]]_1a,b//\) \(f_{\psi(\psi_I(\Omega))}(n)\)
\(//M_1[[[[[[{3}]]]]]]]_1a,b//\) \(f_{\psi(\psi_I(\Omega 2))}(n)\)
\(//M_1[[[[[[{c}]]]]]]_1a,b//\) \(f_{\psi(\psi_I(\Omega \omega))}(n)\)
\(//M_1[[[[[[[{2}]]]]]]]_1a,b//\) \(f_{\psi(\psi_I(\Omega^2))}(n)\)
\(//M_1[[[[[[[{c}]]]]]]]_1a,b//\) \(f_{\psi(\psi_I(\Omega^{\omega}))}(n)\)

\(//M_1[[[[[[[[{2}]]]]]]]]_1a,b//\)

\(f_{\psi(\psi_I(\Omega^{\Omega}))}(n)\)
\(//M_1^0[1]_1a,b//\) \(f_{\psi(\psi_I(\varepsilon_{\Omega +1}))}(n)\)
\(//M_1^1[1]_1a,b//\) \(f_{\psi(\psi_I(\varepsilon_{\Omega +\omega^4}))}(n)\)
\(//M_1^2[1]_1a,b//\) \(f_{\psi(\psi_I(\varepsilon_{\Omega +\varepsilon_{\Omega +\omega^4}}))}(n)\)
\(//M_1^d[1]_1a,b//\) \(f_{\psi(\psi_I(\varepsilon_{\Omega 2}))}(n)\)
\(//M_1^{[1]}[1]_1a,b//\) \(f_{\psi(\psi_I(\varepsilon_{\Omega 2}))}(n)\)
\(//M_1^{[2]}[1]_1a,b//\) \(f_{\psi(\psi_I(\varepsilon_{\Omega^2}))}(n)\)
\(//M_1^{[3]}[1]_1a,b//\) \(f_{\psi(\psi_I(\varepsilon_{\Omega^{\omega}}))}(n)\)
\(//M_1^{[4]}[1]_1a,b//\) \(f_{\psi(\psi_I(\varepsilon_{\Omega^{\Omega}}))}(n)\)
\(//M_1^{[c]}[1]_1a,b//\) \(f_{\psi(\psi_I(\varepsilon_{\varepsilon_{\Omega +1}}))}(n)\)
\(//M_1^{[{2}]}[1]_1a,b//\) \(f_{\psi(\psi_I(\zeta_{\Omega +1}))}(n)\)
\(//M_1^{[{3}]}[1]_1a,b//\) \(f_{\psi(\psi_I(\zeta_{\Omega +2}))}(n)\)
\(//M_1^{[{c}]}[1]_1a,b//\) \(f_{\psi(\psi_I(\zeta_{\Omega +\omega}))}(n)\)
\(//M_1^{[[{2}]]}[1]_1a,b//\) \(f_{\psi(\psi_I(\zeta_{\Omega 2}))}(n)\)
\(//M_1^{[[{c}]]}[1]_1a,b//\) \(f_{\psi(\psi_I(\zeta_{\Omega \omega}))}(n)\)
\(//M_1^{[[[{2}]]]}[1]_1a,b//\) \(f_{\psi(\psi_I(\zeta_{\Omega^2}))}(n)\)
\(//M_1^{[[[{3}]]]}[1]_1a,b//\) \(f_{\psi(\psi_I(\zeta_{\Omega^{\omega}}))}(n)\)
\(//M_1^{[[[{4}]]]}[1]_1a,b//\) \(f_{\psi(\psi_I(\zeta_{\Omega^{\Omega}}))}(n)\)
\(//M_1^{[[[{c}]]]}[1]_1a,b//\) \(f_{\psi(\psi_I(\zeta_{\varepsilon_{\Omega +1}}))}(n)\)
\(//M_1^{_0[1]}[1]_1a,b//\) \(f_{\psi(\psi_I(\eta_{\Omega +1}))}(n)\)
\(//M_1[1]^1_1a,b//\) \(f_{\psi(\psi_I(\eta_{\Omega +1}))}(n)\)
\(//M_1[1]^2_1a,b//\) \(f_{\psi(\psi_I(\varphi(\omega,\Omega +1)))}(n)\)
\(//M_1[1]^3_1a,b//\) \(f_{\psi(\psi_I(\varphi(1,0,\Omega +1)))}(n)\)
\(//M_1[1]^c_1a,b//\) \(f_{\psi(\psi_I(\varphi(\omega,0,\Omega +1)))}(n)\)
\(//M_1[1]^{[2]}_1a,b//\) \(f_{\psi(\psi_I(\varphi(1,0,0,\Omega +1)))}(n)\)
\(//M_1[1]^{_0[1]}_1a,b//\) \(f_{\psi(\psi_I(\vartheta(\Omega^{\omega}(\Omega +1))))}(n)\)
\(//M_1[1]^{_1[1]}_1a,b//\) \(f_{\psi(\psi_I(\vartheta(\varepsilon_{\Omega +1}(\Omega +1))))}(n)\)
\(//M_1[1]^{_c[1]}_1a,b//\) \(f_{\psi(\psi_I(\Omega_2))}(n)\)
\(//M_1[1]^{_0[_0[1]]}_1a,b//\) \(f_{\psi(\psi_I(\Omega_{\omega}))}(n)\)
\(//M_1[1]^{_0[_0[_0[1]]]}_1a,b//\) \(f_{\psi(\psi_I(\Omega_{\psi(\psi_I(\Omega_{\omega}))})}(n)\)
\(//M_1[1]^{_1[_0[1]]}_1a,b//\) \(f_{\psi(\psi_I(\Omega_{\Omega}))}(n)\)
\(//M_1[1]^{_2[_0[1]]}_1a,b//\) \(f_{\psi(\psi_I(\psi_I(0)))}(n)\)
\(//M_1[1]^{_3[_0[1]]}_1a,b//\) \(f_{\psi(\psi_I(I))}(n)\)
\(//M_1[1]^{_3[_2[1]]}_1a,b//\) \(f_{\psi(\psi_I(\psi_I(I) +1))}(n)\)
\(//M_1[1]^{_3[_3[1]]}_1a,b//\) \(f_{\psi(\psi_I(I 2))}(n)\)
\(//M_1[1]^{_4[_0[1]]}_1a,b//\) \(f_{\psi(\psi_I(I \omega))}(n)\)
\(//M_1[1]^{_c[_0[1]]}_1a,b//\) \(f_{\psi(\psi_I(I \omega^{\omega}))}(n)\)
\(//M_1[1]^{//M_1[1]^{_3[_0[1]]}_1a,b//}_1a,b//\) \(f_{\psi(\psi_I(I^2))}(n)\)
\(//M_1[_1]_1a,b//\) \(f_{\psi(\psi_I(I^{\omega}))}(n)\)
\(//M_2[_1]_1a,b//\) \(f_{\psi(\psi_I(I^{\Omega}))}(n)\)
\(//M_1[_1]_2a,b//\) \(f_{\psi(\psi_I(I^I))}(n)\)
\(//M_1[_1]_ca,b//\) \(f_{\psi(\psi_I(\varepsilon_{I+1}))}(n)\)
\(//M_1^1[_1]_1a,b//\) \(f_{\psi(\psi_I(\zeta_{I +1}))}(n)\)
\(//M_1^2[_1]_1a,b//\) \(f_{\psi(\psi_I(\varphi(\omega,I +1)))}(n)\)
\(//M_1^3[_1]_1a,b//\) \(f_{\psi(\psi_I(\varphi(1,0,I +1)))}(n)\)
\(//M_1^c[_1]_1a,b//\) \(f_{\psi(\psi_I(\varphi(\omega,0,I +1))}(n)\)
\(//M_1^{[2]}[_1]_1a,b//\) \(f_{\psi(\psi_I(\varphi(1,0,0,I +1))}(n)\)
\(//M_1^{[c]}[_1]_1a,b//\) \(f_{\psi(\psi_I(\vartheta(\Omega^{\omega}(I +1)))}(n)\)
\(//M_1^{[[{2}]]}[_1]_1a,b//\) \(f_{\psi(\psi_I(\vartheta(\Omega^{\Omega}(I+1))))}(n)\)
\(//M_1^{[[{c}]]}[_1]_1a,b//\) \(f_{\psi(\psi_I(\vartheta(\varepsilon_{\Omega +1}(I +1))))}(n)\)
\(//M_1^{[[[{2}]]]}[_1]_1a,b//\) \(f_{\psi(\psi_I(\vartheta(\Omega_{I +1})))}(n)\)
\(//M_1^{[[[{3}]]]}[_1]_1a,b//\) \(f_{\psi(\psi_I(\vartheta(\Omega_{\Omega_{I +1}})))}(n)\)
\(//M_1^{[[[{c}]]]}[_1]_1a,b//\) \(f_{\psi(\psi_I(I_2)}(n)\)
\(//M_1^{[[[[{2}]]]]}[_1]_1a,b//\) \(f_{\psi(\psi_I(I_{\Omega}))}(n)\)
\(//M_1^{[[[[{3}]]]]}[_1]_1a,b//\) \(f_{\psi(\psi_I(I_{\Omega_2}))}(n)\)
\(//M_1^{[[[[{c}]]]]}[_1]_1a,b//\) \(f_{\psi(\psi_I(I_{\Omega_{\omega}}))}(n)\)
\(//M_1^{[[[[[{2}]]]]]}[_1]_1a,b//\) \(f_{\psi(\psi_I(I_{\Omega_{\Omega}}))}(n)\)
\(//M_1^{[[[[[{3}]]]]]}[_1]_1a,b//\) \(f_{\psi(\psi_I(I_{\Omega_{\Omega_2}}))}(n)\)
\(//M_1^{[[[[[[{1}]]]]]]}[_1]_1a,b//\) \(f_{\psi(\psi_I(I_{\Omega_{\Omega_{\omega}}}))}(n)\)
\(//M_1^{[[[[[[{2}]]]]]]}[_1]_1a,b//\) \(f_{\psi(\psi_I(I_{\Omega_{\Omega_{\Omega}}}))}(n)\)
\(//M_1^{[[[[[[{c}]]]]]]}[_1]_1a,b//\) \(f_{\psi(\psi_I(I_{\Omega_{\Omega_{\Omega_{\omega}}}}))}(n)\)
\(//M_1^{_0[1]}[_1]_1a,b//\) \(f_{\psi(\psi_I(I_I))}(n)\)
\(//M_1[_1]^1_1a,b//\) \(f_{\psi(\psi_I(I_{I_I}))}(n)\)
\(//M_1[_1]^2_1a,b//\) \(f_{\psi(\psi_I(\psi_M(0)))}(n)\)

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