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 10,385 02/23/2023, 12:56 PM
Last Post: tommy1729
Question Derivative of the Tetration Logarithm Catullus 1 4,164 07/03/2022, 07:23 AM
Last Post: JmsNxn
  On the first derivative of the n-th tetration of f(x) Luknik 5 10,750 10/28/2021, 11:53 AM
Last Post: tommy1729
  Trying to find a fast converging series of normalization constants; plus a recap JmsNxn 0 4,216 10/26/2021, 02:12 AM
Last Post: JmsNxn
  Semi-exp and the geometric derivative. A criterion. tommy1729 0 6,257 09/19/2017, 09:45 PM
Last Post: tommy1729
  A calculus proposition about sum and derivative tommy1729 1 8,262 08/19/2016, 12:24 PM
Last Post: tommy1729
  Tetration series for integer exponent. Can you find the pattern? marraco 20 62,027 02/21/2016, 03:27 PM
Last Post: marraco
  Derivative of exp^[1/2] at the fixed point? sheldonison 10 40,538 01/01/2016, 03:58 PM
Last Post: sheldonison
  Derivative of E tetra x Forehead 7 30,533 12/25/2015, 03:59 AM
Last Post: andydude
  A derivative conjecture matrix 3 15,401 10/25/2013, 11:33 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)