(04/21/2015, 08:23 AM)sheldonison Wrote: and sexp(10) is a humongous number. The largest number pari-gp can represent is aboutThat was my dumb mistake. I didn't needed sexp(10), but sexp(I*10).

¿Do you think that the tiny spirals at the end of the lines ͥ·ˣa (as x→∞) are accurate, or just a numerical artifact?

¿Did you attempted to find the base for which the lines turn into an "ellipse" (or something close)?. I guess a=e^(e^-1); that would "explain" the change of state.

Now, if the basesreally turn into ellipses, then it should be easy to find an algebraic expression for tetration to real exponents, or at least an important insight for

The base seems to match an ellipse with center near c=2.65599203615835 (Don't take that precision as accurate. I got it from Excel), relation of axis b=a, and radius , or

I have the result, but I do not yet know how to get it.