(04/20/2010, 10:40 AM)bo198214 Wrote:

So we have a double exponential series instead of a single series, but nevertheless you again can apply your exponential summation. Though I in the moment have not the time to carry it out myself (so either you do it or I do it later).

Eh. I'm not sure if this method is going to work. Take what happens when . Then we have coefficients multiplying for integer . But this does not continuum-sum under the given method: we get , but the denominator is 0 when . This gives a division by zero. There is no joy trying to use a limit (of, say, as approaches ) -- this singularity explodes to infinity.

Yet it seems we can continuum-sum the tetrational regardless, by using the periodic-approximation method.) What's going on here?

(And as an aside, what did you think of the graph of the tetration of a complex base outside the Shell-Thron Region?)