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andydude Wrote:Super-logarithm Derivative
From my approximations, , and .

My first conjecture is that , and my second conjecture is that 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?).

Quote:Super-logarithm Equilibrium
My experiments with the super-logarithm have shown that there is a line in which the real part of the complex-valued superlog do not depend on the imaginary part of the input, in other words, my conjecture is that there exist functions f(b) and g(a, b) such that:

Could you provide a bit more info on this one? Again using calculations based on your solution with base e, I've seen a line near z=0.5 (somewhere between 0.45 and 0.5), running almost a unit's length "up" and "down" in the imaginary direction, for which the slog has nearly fixed real part. But it's not quite exact, and as z approaches either primary fixed singularity, the slog eventually gets "sucked in". But maybe you had something else in mind?
~ Jay Daniel Fox

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

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