Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Conjectures
#1
I have several open questions that I have evidence to believe, and yet have no proof. I'm lumping these together because they don't seem to go anywhere else. I've selected four such open questions that I think would be nice to know:
  • Exponential factorial at 0
  • Superlog derivative at 0
  • Superlog derivative at 0 and E-tetra-I
  • Superlog equilibrium

Exponential Factorial
A common way to define the exponential factorial is EF(0) = 0, and , however, if you define EF(1) = 1, then the solution for EF(x) by assuming it is a C^n function (solving the system formed by differentiating repeatedly at x=1) gives .

My conjecture is that , the Euler-Mascheroni constant.

Super-logarithm Derivative
From my approximations, , and .

My first conjecture is that , and my second conjecture is that otherwise known as Catalan's constant.

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:


Other Open Questions
  • What is the boundary of period 2 (or period 3) behavior in b^x?
  • Is there a recurrence equation for the coefficients for super-roots?
  • Is there a Nelson-like continued fraction that makes a continuous super-log?

Is there an obvious answer to any of these? Do the values depend on which method one uses? Is there any way of knowing?

Andrew Robbins
Reply


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 1,628 08/12/2013, 08:11 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)