Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Interesting commutative hyperoperators ?
#1
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 ).
Reply


Messages In This Thread
Interesting commutative hyperoperators ? - by tommy1729 - 02/17/2020, 11:07 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  All Maps Have Flows & All Hyperoperators Operate on Matrices Daniel 0 176 03/14/2020, 06:22 AM
Last Post: Daniel
  Very interesting topic Ansus 0 593 10/01/2019, 08:14 PM
Last Post: Ansus
  Logic hyperoperators hixidom 0 1,600 10/14/2015, 08:26 PM
Last Post: hixidom
  Theorem in fractional calculus needed for hyperoperators JmsNxn 5 7,092 07/07/2014, 06:47 PM
Last Post: MphLee
  regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 Gottfried 7 10,103 06/25/2013, 01:37 PM
Last Post: sheldonison
  Proof Ackermann function extended to reals cannot be commutative/associative JmsNxn 1 3,290 06/15/2013, 08:02 PM
Last Post: MphLee
  (MSE): Comparision of powertowers -.Possibly interesting thread in MSE Gottfried 0 2,062 05/22/2013, 07:02 AM
Last Post: Gottfried
  Hyperoperators [n] basics for large n dyitto 9 9,580 03/12/2011, 10:19 PM
Last Post: dyitto
  Continuum sums -- a big problem and some interesting observations mike3 17 21,270 10/12/2010, 10:41 AM
Last Post: Ansus
  Something interesting about Taylor series Ztolk 3 6,879 06/29/2010, 06:32 AM
Last Post: bo198214



Users browsing this thread: 1 Guest(s)