User blog comment:LittlePeng9/Fast growing hierarchy of analytic functions/@comment-30754445-20170617192307/@comment-30754445-20170617200859

I meant "smooth" in the intuitive googological sense.

I don't particularly care whether the function is technically differentiable. I'm far more interested in whether these function can serve as a sensible "scale" of large numbers. It's a practical issue rather than a theoretical one, and it has very little to do with ordinary differentiability.

Of-course, given the incredibly strong properties of analytic functions, it may well be that "being analytic" is indeed sufficient for the kind of smoothness I seek. This is exactly the reason I'm so interested in trying this out.