Thread Rating:
• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Continuum sum - a new hope mike3 Long Time Fellow Posts: 368 Threads: 44 Joined: Sep 2009 06/12/2010, 11:10 AM (This post was last modified: 06/12/2010, 11:12 AM by mike3.) (06/12/2010, 04:42 AM)bo198214 Wrote: I am referring to the regular Abel function at the primary fixed point. The inverse function (regular superfunction) is entire. But the Abel function has singularities on the real line at $\exp^{[n]}(0)$, $n\in \mathbb{N}$. Does this mean that there are no values of $z$ such that $\mathrm{reg}_F\left[\exp^z\right](u) = {}^n e = \exp^n(1) = \exp^{n+1}(0)$ for $n = 0, 1, 2, ...$? (here $F$ is the fixpoint, $u$ is the starting point, and $reg$ means regular iteration) I.e. the regular iteration super-function does not contain the sequence of integer-height tetrations of e? That makes no sense, since an entire function must take on every complex value with at most one exception. Or are these singularities only on some "branches" of the Abel function, so there's other branches in which there are no singularities there, thus yielding values for where the integer-height tetration sequence occurs? (which would make more sense) « Next Oldest | Next Newest »

 Messages In This Thread Continuum sum - a new hope - by kobi_78 - 04/24/2010, 09:01 PM RE: Continuum sum - a new hope - by kobi_78 - 04/25/2010, 05:48 AM RE: Continuum sum - a new hope - by bo198214 - 04/25/2010, 10:41 AM RE: Continuum sum - a new hope - by kobi_78 - 05/03/2010, 09:27 PM RE: Continuum sum - a new hope - by bo198214 - 05/09/2010, 11:35 AM RE: Continuum sum - a new hope - by sheldonison - 06/11/2010, 12:34 AM RE: Continuum sum - a new hope - by bo198214 - 06/12/2010, 04:42 AM RE: Continuum sum - a new hope - by mike3 - 06/12/2010, 11:10 AM RE: Continuum sum - a new hope - by bo198214 - 06/13/2010, 06:49 AM RE: Continuum sum - a new hope - by sheldonison - 06/13/2010, 11:23 PM

 Possibly Related Threads... Thread Author Replies Views Last Post 2015 Continuum sum conjecture tommy1729 3 3,576 05/26/2015, 12:24 PM Last Post: tommy1729 Another way to continuum sum! JmsNxn 6 6,817 06/06/2014, 05:09 PM Last Post: MphLee Continuum sum = Continuum product tommy1729 1 2,782 08/22/2013, 04:01 PM Last Post: JmsNxn applying continuum sum to interpolate any sequence. JmsNxn 1 2,996 08/18/2013, 08:55 PM Last Post: tommy1729 Powerful way to perform continuum sum JmsNxn 7 8,238 08/12/2013, 07:17 PM Last Post: JmsNxn sexp by continuum product ? tommy1729 6 8,998 06/30/2011, 10:07 PM Last Post: tommy1729 continuum sum again tommy1729 0 2,360 02/10/2011, 01:25 PM Last Post: tommy1729 Continuum sums -- a big problem and some interesting observations mike3 17 20,693 10/12/2010, 10:41 AM Last Post: Ansus New tetration method based on continuum sum and exp-series mike3 16 22,270 05/02/2010, 09:58 AM Last Post: andydude Borel summation and other continuation/summability methods for continuum sums mike3 2 5,362 12/30/2009, 09:51 PM Last Post: mike3

Users browsing this thread: 1 Guest(s)