User blog:Ynought/The degree function

My first serious attempt at a really fast growing function.here is the definition:

this is solved from left to right

\(f(n)=k^3\)

\(A\) is the leftmost entry 

\(B+n\) means adding n to every upper value (the a in (a)_b) 

This takes the form of \(k°(a)_b,(c)_d…,(e)_f\) now for arrays 
 * 1) if there is nothing besides \([k]\) the expression equals \(f(k)\)
 * 2) any \((n)_0)\) and \((0)_n\) gets removed and \(B+k+n\) and \(f(n)\)
 * 3) otherwise find the number at the level of \(A\) and place that many entries with the level decreased by one and the \(a+k\) at the left side and \(B+k\) and \(f(k)\) 
 * 4) when the system is reduced to one entry and b=0 then it equalls \(f(a+k)\)
 * 5) when the system is reduced to one entry and b>0 then \(b-1\) and place \(a\) new entrys like the one left on the right and \(f(k)\)

\(C_n\) is the \(n\)-th element in \(A\)  

\(D\) is the number of elements in \(A\)

\(E_n\) is the \(n\)-th element in level of \(A\) 

\(F\) is the number of elements in the level of \(A\) 

you also solve the main members first

additional rules (for the main entry(the \((a)\) in \((a)_b\)): additional rules for the levels:  If anyone has any tips for making it better please tell me
 * 1) any 0 gets removed while adding k to every first entry in any cell in the whole system and \(f(k)\)
 * 2) otherwise reduce \(C_D\) by one and replace every other \(C_i\) with the whole system with \(C_i\) reduced by one and every other \(C_j\) increased by \(k\) and \(f(k)\) while adding \(k\) to every level if the level is an array then you ad \(k\) to every member
 * 1) any 0 gets removed while adding k to every first entry in any level in the whole system and \(f(k)\)
 * 2) otherwise reduce \(E_F\) by one and replace every other \(E_i\) with the whole system with \(E_i\) reduced by one and every other \(E_j\) increased by \(k\) and \(f(k)\) while adding \(k\) to every main member