Running my tetration code I was reminded that my results for \[^x a \textrm{, where } 1<a<1.444\] have their range on the real line. Do other extensions of tetration work in a similar fashion?
Daniel
Range of complex tetration as real

Running my tetration code I was reminded that my results for \[^x a \textrm{, where } 1<a<1.444\] have their range on the real line. Do other extensions of tetration work in a similar fashion?
Daniel
10/14/2022, 06:47 PM
(10/13/2022, 05:11 AM)Daniel Wrote: Running my tetration code I was reminded that my results for \[^x a \textrm{, where } 1<a<1.444\] have their range on the real line. Do other extensions of tetration work in a similar fashion? As far as I remember the Paulsen continuation has a super small imaginary part on the real axis for those bases. But for those bases there are not much different from regular tetrations out there. The interesting bases are surely \[b>e^{1/e}\] and there is much more variety with different methods.
10/22/2022, 08:08 PM
(10/13/2022, 05:11 AM)Daniel Wrote: Running my tetration code I was reminded that my results for \[^x a \textrm{, where } 1<a<1.444\] have their range on the real line. Do other extensions of tetration work in a similar fashion? With my extention, as long as you're not doing any tetration towards 2 or less, it always gives real outputs with real heights, ONLY if the base is higher than 1. Otherwise my extension do gives complex results. 
« Next Oldest  Next Newest »

Possibly Related Threads…  
Thread  Author  Replies  Views  Last Post  
Behaviour of tetration into the real negatives  Shanghai46  1  865 
10/12/2023, 11:01 PM Last Post: leon 

Real tetration as a limit of complex tetration  Daniel  6  2,521 
10/10/2023, 03:23 PM Last Post: leon 

Real and complex tetration  Daniel  13  6,269 
04/04/2023, 10:25 AM Last Post: JmsNxn 

Evaluating Arithmetic Functions In The Complex Plane  Caleb  6  3,034 
02/20/2023, 12:16 AM Last Post: tommy1729 

From complex to real tetration  Daniel  3  2,277 
10/21/2022, 07:55 PM Last Post: Daniel 

Cost of real tetration  Daniel  1  1,481 
09/30/2022, 04:41 PM Last Post: bo198214 

Real Multivalued/Parametrized Iteration Groups  bo198214  11  6,255 
09/10/2022, 11:56 AM Last Post: tommy1729 

Constructive real tetration  Daniel  1  1,390 
09/01/2022, 05:41 AM Last Post: JmsNxn 

What are the types of complex iteration and tetration?  Daniel  5  3,406 
08/17/2022, 02:40 AM Last Post: JmsNxn 

Complex to real tetration  Daniel  1  1,362 
08/14/2022, 04:18 AM Last Post: JmsNxn 