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 9,295 02/23/2023, 12:56 PM
Last Post: tommy1729
Question Derivative of the Tetration Logarithm Catullus 1 3,867 07/03/2022, 07:23 AM
Last Post: JmsNxn
  On the first derivative of the n-th tetration of f(x) Luknik 5 10,013 10/28/2021, 11:53 AM
Last Post: tommy1729
  Trying to find a fast converging series of normalization constants; plus a recap JmsNxn 0 3,979 10/26/2021, 02:12 AM
Last Post: JmsNxn
  Semi-exp and the geometric derivative. A criterion. tommy1729 0 6,054 09/19/2017, 09:45 PM
Last Post: tommy1729
  A calculus proposition about sum and derivative tommy1729 1 7,965 08/19/2016, 12:24 PM
Last Post: tommy1729
  Tetration series for integer exponent. Can you find the pattern? marraco 20 60,032 02/21/2016, 03:27 PM
Last Post: marraco
  Derivative of exp^[1/2] at the fixed point? sheldonison 10 39,156 01/01/2016, 03:58 PM
Last Post: sheldonison
  Derivative of E tetra x Forehead 7 29,187 12/25/2015, 03:59 AM
Last Post: andydude
  A derivative conjecture matrix 3 14,834 10/25/2013, 11:33 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)