User blog comment:Wythagoras/Catching function in normal ordinals/@comment-11227630-20140203095754/@comment-68.111.90.23-20140625142528

You can continue the C function into higher uncountable cardinals in the same way as for the standard ordinal notations.

So C(Ω2) will be C(εΩ+1) or C(ΓΩ+1), depending on the precise definition used.