• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Interesting commutative hyperoperators ? tommy1729 Ultimate Fellow Posts: 1,645 Threads: 369 Joined: Feb 2009 02/17/2020, 11:07 PM Consider the following post made by my follower, who recycled some of my ideas : https://math.stackexchange.com/questions...eroperator In case that link dies or the topic gets closed I copy the text : —- After reading about Ackermann functions , tetration and similar, I considered the commutative following hyperoperator ?  $$F(0,a,b) = a + b$$ $$F(n,c,0) = F(n,0,c) = c$$ $$F(n,a,b) = F(n-1,F(n,a-1,b),F(n,a,b-1))$$ I have not seen this one before in any official papers. Why is this not considered ? Does it grow to slow ? Or to fast ? It seems faster than Ackermann or am I wrong ? Even faster is The similar  $$T(0,a,b) = a + b$$ $$T(n,c,0) = T(n,0,c) = n + c$$ $$T(n,a,b) = T(n-1,T(n,a-1,b),T(n,a,b-1))$$ which I got from a friend. Notice if $nab = 0$ then $T(n,a,b) = n + a + b$. One possible idea to extend these 2 functions to real values , is to extend those “ zero rules “ to negative ones.  So for instance for the case $F$ : $$F(- n,a,b) = a + b$$ $$F(n,-a,b) = -a + b$$ $$F(n,a,-b) = a - b$$ The downside is this is not analytic in $n$. Any references or suggestions ?? ———- What do you guys think ? Regards Tommy1729 Btw im thinking about extending fake function theory to include negative numbers too, but without singularities( still entire ). « Next Oldest | Next Newest »

 Possibly Related Threads… Thread Author Replies Views Last Post All Maps Have Flows & All Hyperoperators Operate on Matrices Daniel 0 2,214 03/14/2020, 06:22 AM Last Post: Daniel Logic hyperoperators hixidom 0 3,176 10/14/2015, 08:26 PM Last Post: hixidom Theorem in fractional calculus needed for hyperoperators JmsNxn 5 13,047 07/07/2014, 06:47 PM Last Post: MphLee Proof Ackermann function extended to reals cannot be commutative/associative JmsNxn 1 5,688 06/15/2013, 08:02 PM Last Post: MphLee Hyperoperators [n] basics for large n dyitto 9 17,190 03/12/2011, 10:19 PM Last Post: dyitto Hyperoperators Mr. Pig 4 10,050 06/20/2010, 12:26 PM Last Post: bo198214 interesting pattern in hyper-operations Base-Acid Tetration 8 19,991 05/04/2009, 09:15 PM Last Post: BenStandeven

Users browsing this thread: 1 Guest(s)