09/17/2009, 11:03 AM

(09/17/2009, 08:01 AM)bo198214 Wrote:(09/14/2009, 09:43 PM)mike3 Wrote: Is there any way in which this could be done with something other than the matrix operator? For example, could a limit formula be used like that for , for this base () even if convergence is dog slow?

Hm actually, I am not aware of such a limit formula. I only know and but there should be also a formula somewhere for your case of (or generally for for some , here ). If I have some time I will look through some books.

The powerseries development of the regular slog/sexp probably anyway has zero convergence radius.

One can get a limit formula for as the behavior at large values of the tower is somewhat like (x = tower). And the bases have exponential behavior (exponential-like convergence to their fixed point) at large towers. But what sort of behavior does have at large values of the tower? It's not exponential and it's also not a simple rational function either (as it was for ).