Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
On the existence of rational operators
#13
I have a discovery that starts to legitimize logarithmic semi-operator calculus.

given:
q:d/dx f(x) = lim h->S(-q) [f(x{-q}h) }-q{ f(x)] }1-q{ h

I can prove that

q:d/dx e^x = e^x

or that if we lower the operators involved in the difference quotient by any value 0 <= q < 1; and change h's limit from zero (the additive identity) to S(-q) (the lowered additive identity), e^x is still it's own output.
Reply


Messages In This Thread
RE: On the existence of rational operators - by JmsNxn - 03/19/2011, 05:36 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Thoughts on hyper-operations of rational but non-integer orders? VSO 2 398 09/09/2019, 10:38 PM
Last Post: tommy1729
  Hyper operators in computability theory JmsNxn 5 3,819 02/15/2017, 10:07 PM
Last Post: MphLee
  Recursive formula generating bounded hyper-operators JmsNxn 0 1,451 01/17/2017, 05:10 AM
Last Post: JmsNxn
  Rational operators (a {t} b); a,b > e solved JmsNxn 30 37,506 09/02/2016, 02:11 AM
Last Post: tommy1729
  holomorphic binary operators over naturals; generalized hyper operators JmsNxn 15 15,953 08/22/2016, 12:19 AM
Last Post: JmsNxn
  The bounded analytic semiHyper-operators JmsNxn 2 3,464 05/27/2016, 04:03 AM
Last Post: JmsNxn
  Bounded Analytic Hyper operators JmsNxn 25 19,080 04/01/2015, 06:09 PM
Last Post: MphLee
  Incredible reduction for Hyper operators JmsNxn 0 2,208 02/13/2014, 06:20 PM
Last Post: JmsNxn
  interpolating the hyper operators JmsNxn 3 4,971 06/07/2013, 09:03 PM
Last Post: JmsNxn
  Number theory and hyper operators JmsNxn 7 7,618 05/29/2013, 09:24 PM
Last Post: MphLee



Users browsing this thread: 1 Guest(s)