NigerianPidgin's Greek Notation

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This is a notation created by NigerianPidgin The definition provided is quite lengthy:

Αn = 10^n

ΑΑn = 10^10^n

Α^m(n) = (10^)^m n

Βn = 10^^^n

ΒΒn = 10^^^10^^^n

Β^m(n) = (10^^^)^m n

Γn = 10{n+5}10

ΓΓn = 10{10{n+5}10}10

Γ^m(n) = (10{)^m n+5 (}10)^m

Δn = 10{{n+1}}10

ΔΔn = 10{{10{{n+1}}10}}10

Δ^m(n) = (10{{)^m n+5 (}}10)^m

Εn = 10{{{n+1}}}10

ΕΕn = 10{{{10{{{n+2}}}10}}}10

Ε^m(n) = (10{{{)^m n+5 (}}}10)^m

Ζn = {10, 10, 10, n+3}

ΖΖn = {10, 10, 10, {10, 10, 10, n-3}}

Analysis

Analysis by TheInfinitySeeker:

1. An = 10^n = En#1
2. A^n(1) = 10^^n = E1#n
3. Bn = 10^^^n = E1#1#n
4. B^n(1) = 10^^^^n = E1#1#1#n
5. Gamma n = 10{n+5}10 (growth rate omega)
6. Gamma^n(1) > 10{{1}}n+1 (growth rate omega+1)
7. Delta n = 10{{n+1}}10 (growth rate 2*omega)
8. Delta^n(1) > 10{{{1}}}n+1 (growth rate 2*omega+1)
9. E n = 10{{{n+1}}}10 (growth rate 3*omega)
10. E^n(1) > 10{{{{1}}}}n+1 (growth rate 3*omega+1)
11. Zn = {10,10,10,n+3} (growth rate omega^2)
12. Z^n(1) > {10,n+1,1,1,2} (growth rate 1+omega^2)

A10 = 10^10

A^10(1) = 10^^10

B10 = 10^^^10

B^10(1) = 10^^^^10

Gamma 0 = 10^^^^^10

Gamma 1 = 10^^^^^^10

...

Delta 1 = {10,10,2,2}

etc