How to find the first negative derivative ?
#1
Sign theory

Consider f(x) = 0 + A1 x + A2 x^2 + ...

Where f is entire and all n th derivatives are positive.
Also f(x) > x for x > 0 and the fixpoint at 0 is hyperbolic.
Also there are no there are no other fixpoints within or on the unit radius.

Now use the usual method to find the half iteration g(x).

How to efficiently find the first n th derivative ( Of g(x) at x = 0 ) < 0 ??

Regards

Tommy1729
Reply


Possibly Related Threads…
Thread Author Replies Views Last Post
  CONCLUSION 1 : conditions for nice tetration : second derivative !! tommy1729 6 783 02/23/2023, 12:56 PM
Last Post: tommy1729
Question Derivative of the Tetration Logarithm Catullus 1 797 07/03/2022, 07:23 AM
Last Post: JmsNxn
  On the first derivative of the n-th tetration of f(x) Luknik 5 2,520 10/28/2021, 11:53 AM
Last Post: tommy1729
  Trying to find a fast converging series of normalization constants; plus a recap JmsNxn 0 1,012 10/26/2021, 02:12 AM
Last Post: JmsNxn
  Semi-exp and the geometric derivative. A criterion. tommy1729 0 3,729 09/19/2017, 09:45 PM
Last Post: tommy1729
  A calculus proposition about sum and derivative tommy1729 1 5,070 08/19/2016, 12:24 PM
Last Post: tommy1729
  Tetration series for integer exponent. Can you find the pattern? marraco 20 37,438 02/21/2016, 03:27 PM
Last Post: marraco
  Derivative of exp^[1/2] at the fixed point? sheldonison 10 25,261 01/01/2016, 03:58 PM
Last Post: sheldonison
  Derivative of E tetra x Forehead 7 18,287 12/25/2015, 03:59 AM
Last Post: andydude
  A derivative conjecture matrix 3 9,709 10/25/2013, 11:33 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)