Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Rational operators (a {t} b); a,b > e solved
(06/06/2011, 08:47 AM)JmsNxn Wrote: I was sort of aware that there was no way I was gonna produce an analytic function over the whole complex domain, I'm happy with analytic in a few regions.
Well not on the whole complex plane, but on the real axis, wouldnt that be nice?
I anyway wonder whether thats possible at all.
As is not even differentiable at 1, I wonder whether f is. Did you compare the derivations from left and right?

Quote:Alright, from henceforth I shall refer to logarithmic semi operators with the following notation:

oh I thought }t{ was kinda the inverse in t. But as I see that it is not ... there are already conventions that we use on the forum, even ASCII capable:
a [1] b = a+ b
a [2] b = a*b
a [3] b = a^b

so the operator is [t] (one off from your {t}). But then for the inverse functions
b [t] x = y
y /[t] x = b
b [t]\ y = x

for example
x /[1] y = x - y
x [1]\ y = -x + y

x /[4] p is the p-th superroot (which is not equal to x [4] 1/p)
b [4]\ x is the superlogarithm to base b.

This is also in sync with the convention for quasigroups, i.e. groups with non-associative operation but with left- and right-inverse. There the left- and right inverse are written as / and \.


Messages In This Thread
RE: Rational operators (a {t} b); a,b > e solved - by bo198214 - 06/06/2011, 09:23 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Has anyone solved iterations of z+Γ(z)? Leo.W 5 700 01/07/2022, 08:15 AM
Last Post: JmsNxn
  [MSE-SOLVED] Subfunction is functorial!!!! MphLee 14 3,834 06/06/2021, 11:16 PM
Last Post: JmsNxn
  Thoughts on hyper-operations of rational but non-integer orders? VSO 2 3,875 09/09/2019, 10:38 PM
Last Post: tommy1729
  Hyper operators in computability theory JmsNxn 5 9,794 02/15/2017, 10:07 PM
Last Post: MphLee
  Recursive formula generating bounded hyper-operators JmsNxn 0 3,325 01/17/2017, 05:10 AM
Last Post: JmsNxn
  holomorphic binary operators over naturals; generalized hyper operators JmsNxn 15 28,845 08/22/2016, 12:19 AM
Last Post: JmsNxn
  The bounded analytic semiHyper-operators JmsNxn 2 6,961 05/27/2016, 04:03 AM
Last Post: JmsNxn
  Bounded Analytic Hyper operators JmsNxn 25 39,834 04/01/2015, 06:09 PM
Last Post: MphLee
  Incredible reduction for Hyper operators JmsNxn 0 3,973 02/13/2014, 06:20 PM
Last Post: JmsNxn
  interpolating the hyper operators JmsNxn 3 8,958 06/07/2013, 09:03 PM
Last Post: JmsNxn

Users browsing this thread: 1 Guest(s)