• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Should tetration be a multivalued function? tommy1729 Ultimate Fellow Posts: 1,374 Threads: 337 Joined: Feb 2009 01/10/2016, 03:37 AM (This post was last modified: 01/10/2016, 03:38 AM by tommy1729.) Hold on we can do a bit better. For base sqrt(2) = a using sheldon's y and z. a^^0 is defined by a^^0 ^ a^^0 = 2^4 = 4^2 = 16. ( 2 and 4 are a^^oo or the fixpoints ) So a^^0 = ssqrt(16). From sheldon we then get a^(y z) = 16. subst a = sqrt(2) [ for example , this idea works for other bases too ] => y z = 8. Now notice r = -(r+1) for r = -1/2. So a^^(-1/2) ^ 2 = 8. So a^^(-1/2) = sqrt( 8 ) = 2 sqrt(2). Since we have a^^0 and a^^(-1/2) we actually have a^^(K/2) for all integer K. Maybe this idea can be extended to a unique analytic solution ... ¯\_(ツ)_/¯ Regards tommy1729 The master « Next Oldest | Next Newest »

 Messages In This Thread Should tetration be a multivalued function? - by marraco - 01/03/2016, 11:24 PM RE: Should tetration be a multivalued function? - by marraco - 01/03/2016, 11:32 PM RE: Should tetration be a multivalued function? - by andydude - 01/03/2016, 11:55 PM RE: Should tetration be a multivalued function? - by andydude - 01/04/2016, 12:01 AM RE: Should tetration be a multivalued function? - by marraco - 01/04/2016, 12:08 AM RE: Should tetration be a multivalued function? - by andydude - 01/04/2016, 12:35 AM RE: Should tetration be a multivalued function? - by marraco - 01/04/2016, 03:57 AM RE: Should tetration be a multivalued function? - by marraco - 01/08/2016, 06:26 PM RE: Should tetration be a multivalued function? - by marraco - 01/08/2016, 11:05 PM RE: Should tetration be a multivalued function? - by sheldonison - 01/09/2016, 06:20 AM RE: Should tetration be a multivalued function? - by marraco - 01/09/2016, 05:56 PM RE: Should tetration be a multivalued function? - by marraco - 01/14/2016, 04:24 AM RE: Should tetration be a multivalued function? - by tommy1729 - 01/10/2016, 03:37 AM RE: Should tetration be a multivalued function? - by marraco - 01/11/2016, 09:28 PM RE: Should tetration be a multivalued function? - by andydude - 01/13/2016, 08:24 AM RE: Should tetration be a multivalued function? - by sheldonison - 01/13/2016, 01:37 PM

 Possibly Related Threads... Thread Author Replies Views Last Post New mathematical object - hyperanalytic function arybnikov 4 3,613 01/02/2020, 01:38 AM Last Post: arybnikov Is there a function space for tetration? Chenjesu 0 1,337 06/23/2019, 08:24 PM Last Post: Chenjesu Degamma function Xorter 0 1,762 10/22/2018, 11:29 AM Last Post: Xorter Introducing new special function : Lambert_t(z,r) tommy1729 2 5,401 01/10/2016, 06:14 PM Last Post: tommy1729 Tommy-Mandelbrot function tommy1729 0 2,804 04/21/2015, 01:02 PM Last Post: tommy1729 The inverse gamma function. tommy1729 3 9,981 05/13/2014, 02:18 PM Last Post: JmsNxn entire function close to sexp ?? tommy1729 8 13,445 04/30/2014, 03:49 PM Last Post: JmsNxn Problem with infinite product of a function: exp(x) = x * f(x)*f(f(x))*... Gottfried 5 9,669 07/17/2013, 09:46 AM Last Post: Gottfried Proof Ackermann function extended to reals cannot be commutative/associative JmsNxn 1 4,190 06/15/2013, 08:02 PM Last Post: MphLee Hyperzeta function Balarka Sen 7 11,344 05/08/2013, 01:36 PM Last Post: Balarka Sen

Users browsing this thread: 4 Guest(s)