Posts: 626
Threads: 22
Joined: Oct 2008
06/15/2015, 01:00 AM
(This post was last modified: 06/15/2015, 03:07 AM by sheldonison.)
(06/11/2015, 10:27 AM)sheldonison Wrote: ....
}\left[\pi\sqrt{\frac{2\eta\cdot n}{e}} + \text{slog}_e(\frac{n}{e}-1) + C + \mathcal{O}(\theta) \right] -n = 0\;\;\;\;C \approx -2 - \text{slog}_e(388.7874/e-1))
}\left[\pi\sqrt{\frac{2\eta\cdot n}{e}} -2 \right] \approx 388.7874)
I was about to post a closely related question about Pi in the Mandelbrot set; it takes about
iterations to escape near the parabolic cusp at c=0.25. Then I found this paper about the occurrence of Pi in the Mandelbrot set; although I haven't finished reading their paper, but I am sure the same mechanisms can be used to justify the result, that it takes
iterations to "escape" for sexp_{eta+1/n}, and for iterating
-1+\frac{1}{n})
, it takes
iterations.
http://www.doc.ic.ac.uk/~jb/teaching/jmc...elbrot.pdf
- Sheldon
