• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Conjectures jaydfox Long Time Fellow Posts: 440 Threads: 31 Joined: Aug 2007 12/04/2007, 12:23 AM (This post was last modified: 12/04/2007, 12:23 AM by jaydfox.) jaydfox Wrote:andydude Wrote:Super-logarithm Derivative From my approximations, $\text{slog}_e'(0) \approx 0.916$, and ${}^{i}{e} \approx 0.786 + i 0.916$. My first conjecture is that $\text{Im}({}^{i}{e}) = \text{slog}_e'(0)$, and my second conjecture is that $\text{slog}_e'(0) = 0.915965594177\cdots$ otherwise known as Catalan's constant.In computing the solutions (for base e) to moderately large systems with your proposed slog, I think the first derivative is closer to 0.9159460564995..., which puts Catalan's constant out of the running (or puts your slog out of the running?).Following up on the $\Im({}^{i}{e}) = \mathrm{slog}_e'(0)$ conjecture, my initial estimate puts $\Im({}^{i}{e})$ closer to 0.9163, give or take. It would have been very cool if it had been true. PS: Which looks better, $\text{Im}(z)$ or $\Im(z)$? ~ Jay Daniel Fox « Next Oldest | Next Newest »

 Messages In This Thread Conjectures - by andydude - 10/09/2007, 06:57 PM RE: Conjectures - by bo198214 - 10/09/2007, 09:23 PM RE: Conjectures - by jaydfox - 10/10/2007, 07:43 AM RE: Conjectures - by jaydfox - 12/04/2007, 12:23 AM RE: Conjectures - by jaydfox - 12/04/2007, 05:21 AM RE: Conjectures - by andydude - 12/04/2007, 10:35 PM RE: Conjectures - by andydude - 01/09/2008, 10:58 PM RE: Conjectures - by andydude - 10/13/2007, 04:51 PM RE: Conjectures - by andydude - 10/13/2007, 05:13 PM

 Possibly Related Threads... Thread Author Replies Views Last Post Generalized Bieberbach conjectures ? tommy1729 0 1,881 08/12/2013, 08:11 PM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)