Zeration

[marraco]

the natural zeration would be
\( a \,\circ_{\small{0}}^{\small{e}}\, b \)
or
\( a \,\circ_{\small{0}}^{\small{2}}\, b \)

If we take this definition for zeration, then this may be a link between zeration and tetration. If we represent iterated zeration symbol this way:

\( (\circ_{\small{0}}^{\small{a}})^n1 \,=\, \circ_{\small{n}}\circ_{\small{n-1}}...\circ_{\small{1}} 1 \)

then
\( (\circ_{\small{0}}^{\small{a}})^n1 \,=\,\circ^n\,1 \,=\, ^{-n}a \)

which is valid if tetration to negative integer exponents is taken as
\( ^{-n}a \,=\, ln_{a_n}(ln_{a_{n-1}}(ln_{a_{n-2}}(...ln_{a_0}(1=e^{i2m\pi})...)))) \)

as explained here
http://math.eretrandre.org/tetrationforu...66#pid7666