Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Actual formulas for tetration and its derivative
#13
Well, unfortunately, no magic at all. Formulas 1 and 2 can be easily obtained, taking into account the hyperoperational properties of tetration, e.g..:
e#(x-1) = ln(e#x)
as well as the definition of the product logarithm:
if x . e^x = z then: x = ProductLog[z].

However, it is interesting to remind that the product logarithm is a complex function, with two real branches. I shall come back to it.

Please see the attached short pdf comment. I am too lazy to insert it in this text.

GFR


Attached Files
.pdf   No magic.pdf (Size: 5.96 KB / Downloads: 397)
Reply


Messages In This Thread
RE: Actual formulas for tetration and its derivative - by GFR - 08/31/2007, 10:21 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  from formulas to pari implementations Xorter 0 6 Yesterday, 11:22 PM
Last Post: Xorter
  Semi-exp and the geometric derivative. A criterion. tommy1729 0 1,503 09/19/2017, 09:45 PM
Last Post: tommy1729
  How to find the first negative derivative ? tommy1729 0 1,611 02/13/2017, 01:30 PM
Last Post: tommy1729
  A calculus proposition about sum and derivative tommy1729 1 2,178 08/19/2016, 12:24 PM
Last Post: tommy1729
  Derivative of exp^[1/2] at the fixed point? sheldonison 10 11,372 01/01/2016, 03:58 PM
Last Post: sheldonison
  Derivative of E tetra x Forehead 7 10,000 12/25/2015, 03:59 AM
Last Post: andydude
  A derivative conjecture matrix 3 4,845 10/25/2013, 11:33 PM
Last Post: tommy1729
  Non-recursive coefficient formulas. Can the Riemann mapping be constructed? mike3 0 2,387 06/04/2011, 12:17 AM
Last Post: mike3



Users browsing this thread: 1 Guest(s)