User blog comment:Deedlit11/Ordinal Notations V: Up to a weakly Mahlo cardinal/@comment-24509095-20140509071457/@comment-5150073-20140509134023

$$\chi(\alpha)_{\beta} = \chi(\alpha,\beta)$$ (we use binary function instead of subscripts)

So $$\chi(\alpha,\beta+1) = \chi(\alpha[n],\chi(\alpha,\beta)+1)$$, like in the standard phi function.