Migration of inflection points in y = b # x, for e^(1/e) < b < +oo
#8
I'd like to finish it even if it is wrong:

So we take :
dI/dp= p*(h((I/p)^(p-2I)/I* ln(I/e*p) - I/(p^2))

And put it =0 to find minimum:

We have 2 solutions : p=0 and

h((I/p)^(p-2I)/I* ln(I/e*p) - I/(p^2)=0

h(((I/p)^(p-2I)/I)*ln(I/e*p))= I/(p^2) we can make substitution p^2=q

Than from earlier, if h( function) = I/q then from another thread http://math.eretrandre.org/tetrationforu...hp?tid=110

function = (I/q)^(q/I)

so (((I/(q^(1/2))^(q^(1/2)-2I)/I))*ln(I/(e*(q^(1/2)))) = (I/q)^(q/I)

So we can find q and p, probably both complex numbers.

The idea was, this should give the minimum of Gottfrieds curve in the left upper corner , where Re ( imaginary zeroes of real x^1/x when x> e^1/e) <0 and since q is a square root, both conjugate minimums along imaginary axis.

May be not yet.
Reply


Messages In This Thread

Possibly Related Threads…
Thread Author Replies Views Last Post
  Down with fixed points! Daniel 1 3,120 04/29/2023, 11:02 PM
Last Post: tommy1729
  Iteration with two analytic fixed points bo198214 62 81,083 11/27/2022, 06:53 AM
Last Post: JmsNxn
Question The Different Fixed Points of Exponentials Catullus 22 27,767 07/24/2022, 12:22 PM
Last Post: bo198214
Question Two Attracting Fixed Points Catullus 4 7,497 07/04/2022, 01:04 PM
Last Post: tommy1729
  Are tetrations fixed points analytic? JmsNxn 2 11,908 12/14/2016, 08:50 PM
Last Post: JmsNxn
  Removing the branch points in the base: a uniqueness condition? fivexthethird 0 5,973 03/19/2016, 10:44 AM
Last Post: fivexthethird
  cyclic points tommy1729 3 11,846 04/07/2011, 07:57 PM
Last Post: JmsNxn
  Branch points of superlog mike3 0 6,134 02/03/2010, 11:00 PM
Last Post: mike3
  Complex fixed points of base-e tetration/tetralogarithm -> base-e pentation Base-Acid Tetration 19 77,920 10/24/2009, 04:12 AM
Last Post: andydude
  Iterating at fixed points of b^x bo198214 28 72,166 05/28/2008, 07:37 AM
Last Post: Kouznetsov



Users browsing this thread: 1 Guest(s)