User blog comment:Googology Noob/Ordinal FGH, with an actual definition!/@comment-25337554-20151219053025/@comment-27173506-20151219073507

In that case we first need to find the normal limit (that is, with finite applications) of the nestings, that is omega times nested. Then we take the resulting ordinal, and plug it into the function to its normal limit, which is omega2 times nested. Then we take the resulting ordinal, and plug it into the function to its normal limit, which is omega3 times nested. The limit of the repeated nestings (omega, omega2, omega3...) would be omega*omega = omega^2 nestings.

Or slightly more formally:

f_alphaw(beta) = lim{f_alpha(beta), f_alpha(f_alpha(beta)), f_alpha(f_alpha(f_alpha(beta)))...} = lambda (random choice of ordinal)

f_alphaw2(beta) = lim{f_alpha(lambda), f_alpha(f_alpha(lambda)), f_alpha(f_alpha(f_alpha(lambda)))...} = gamma (random choice of ordinal

f_alphaw3(beta) = lim{f_alpha(gamma), f_alpha(f_alpha(gamma)), f_alpha(f_alpha(f_alpha(gamma)))...} = delta

f_alphaw^2(beta) = lim{f_alphaw(beta), f_alphaw2(beta), f_alphaw3(beta)...}

Is that helpful?