User blog comment:Edwin Shade/There is No Limit To Googology/@comment-80.98.179.160-20171123100714

I have already a function hiearchy, $$E$$, defined so:

$$E(a,b)$$ is the largest number expressible in a symbols in b-th order oodle theory. (E is shorthand for E0)

$$E(a)=E^a(a,a)$$, with recursion of 2-argument functions being fed inside itself as both arguments.

$$E_{\alpha+1}(a)$$ is $$E_\alpha^{E_\alpha^{E_\alpha(a)}(a)}(a)}(a)$$.

$$E_\alpha(n)$$ is $$E_{\alpha[E_{\alpha[n]}(n)}(n)$$ iff α is a limit ordinal