Wow! I can't believe I gave that away for free! I would pay hundreds to get my hands on this code! Good thing I didn't have to... I just found the asymptotes of pentation, hexation, heptation, octation, and beyond! And they're fascinating:

where the box is GFR's box notation for hyperops, and a is sufficiently close to e, because thats the number I used.

I suppose you could see this from the integer versions of these operators, but I think the continuous (or if not continuous, mostly real-valued) versions make it easier to see.

[update]These limits are false, the true value for the first limit is closer to -1.85, not -2... sorry about that.[/update]

where the box is GFR's box notation for hyperops, and a is sufficiently close to e, because thats the number I used.

I suppose you could see this from the integer versions of these operators, but I think the continuous (or if not continuous, mostly real-valued) versions make it easier to see.

[update]These limits are false, the true value for the first limit is closer to -1.85, not -2... sorry about that.[/update]