• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 [2014] composition of 3 functions. tommy1729 Ultimate Fellow Posts: 1,493 Threads: 356 Joined: Feb 2009 08/25/2014, 12:08 AM I want to consider composition of 3 nonlinear analytic functions. Lets require that composition is noncommutative. Denote composition with & and the functions with A,B,C. A & B & C = B & C & A = C & A & B = T1 A & C & B = C & B & A = B & A & C = T2 T1 =/= T2. This reminds me of quaternions and related stuff. However we are considering functions here instead of numbers. It seems like a natural continuation of algebra and dynamics. Well this or a weaker set of equations. An intresting weaker set of equations is A & B & C = B & C & A = C & A & B = T1 {A & C & B , C & B & A , B & A & C }= T2 T1 is not equal to any member of the set T2. I was inspired by being bored with f^[a+b] = f^[a](f^[b]) = f^[b](f^[a]) or chebyshev type polynomials. The commutative property started to feel like a prison for my mind. We want more functions and concepts than just commutative. regards tommy1729 « Next Oldest | Next Newest »

 Possibly Related Threads... Thread Author Replies Views Last Post Using a family of asymptotic tetration functions... JmsNxn 15 4,597 08/06/2021, 01:47 AM Last Post: JmsNxn Improved infinite composition method tommy1729 5 1,542 07/10/2021, 04:07 AM Last Post: JmsNxn Composition, bullet notation and the general role of categories MphLee 8 3,211 05/19/2021, 12:25 AM Last Post: MphLee Inverse super-composition Xorter 11 25,069 05/26/2018, 12:00 AM Last Post: Xorter The AB functions ! tommy1729 0 3,211 04/04/2017, 11:00 PM Last Post: tommy1729 the inverse ackerman functions JmsNxn 3 9,846 09/18/2016, 11:02 AM Last Post: Xorter Uniterated composition Xorter 2 5,942 09/15/2016, 05:17 PM Last Post: MphLee Look-alike functions. tommy1729 1 4,204 03/08/2016, 07:10 PM Last Post: hixidom Inverse power tower functions tommy1729 0 3,441 01/04/2016, 12:03 PM Last Post: tommy1729 [2014] Beyond Gamma and Barnes-G tommy1729 1 4,410 12/28/2014, 05:48 PM Last Post: MphLee

Users browsing this thread: 1 Guest(s)