05/05/2009, 11:21 AM

(05/03/2009, 10:20 PM)tommy1729 Wrote: ???I agree that the base conversion problem is very interesting, and needs more attention.

how does change of base formula for tetration and exp(z) -1 relate ???

i would recommend -- in case this is important and proved -- that more attention is given to it on the forum and/or FAQ

Here's another way to write the change of base equation, converting from base a to base b.

In this equation, converges to n plus the base conversion constant. This base conversion will have a small 1-cyclic periodic wobble, , when compared to Dimitrii's solution.

Convergence for real values of x is easy to show, and emperically the derivatives appear continuous, but behavior for complex values is a more difficult problem. I would also like to characterize the sinusoid, and find out whether or not it is c-oo, and whether the sexp_b(z) shows the singularities in the complex plane predicted by Dimitrii Kouznetsov. My thoughts started before I read Jay's post, but you can see them here, http://math.eretrandre.org/tetrationforu...hp?tid=236.