User blog:Ynought/A pair of functions "Z and chi"

\(Z\) function
so like with every good function the start is a simple \(+\)

\(aZ(n)=n+a\)

\(aZ(n,0)=a+1Z(n)\)

\(aZ(0,n)=a+1Z(a,n-1)\)

\(C=a+1Z(b-1,c)\)

\(aZ^0(b_*,c)=a+1Z(\chi_{a+c}(a+c),c)\) \(\chi\) will be defined later

\(aZ^k(b_*,c)=a+1Z^{k-1}(a+1Z^{k-1}(...a+1Z^{k-1}(b_*,c),c)...)_*,c)\) a nests

\(aZ(b,c)=a+1Z^C(b_*,c-1)\)

\(\chi_0(c)=\chi(c)\)

\(\chi(0)=a\)

\(\chi(d)=\chi(d-1)+a\)

\(\chi_k(0)=\chi_{k-1}(a)\)

\(\chi_k(d)=\chi^a(\chi_k(d-1))\)

If you have any tips please tell me.Also growth rates are apreciated(if you have them).