• 2 Vote(s) - 3 Average
• 1
• 2
• 3
• 4
• 5
 The "cheta" function sheldonison Long Time Fellow Posts: 626 Threads: 22 Joined: Oct 2008 08/12/2009, 04:13 AM (08/11/2009, 04:30 PM)jaydfox Wrote: I'm not sure if the limit exists in the normal sense (i.e., it's well-defined for real numbers, but as you say, not for non-real numbers). However, rather than two distinct points x and x+d*i (where d goes to 0), consider a line segment L defined between those two points. As exp_b(x) is entire, the image exp_b(L) will be continuous, as will be exp_b(exp_b(L)), etc. Thus, no matter how many times this curve wraps around the origin in some bizarre fractal nature, there is always a well-defined "path" back to the real line. We can then iteratively perform the logarithm log_a(x), which has branches. We start at the real endpoint of exp_b^[ok](L) as we're performing the logarithms, so that when we wrap around the origin, we will always "know" which branch of the logarithm to use. When all is said and done, we will arrive at the correct location, with no ambiguity.... Agreed, for each value of "k", there is one and only one unambiguous solution, and that helps a lot... I'm working on some ideas, and calculations, as well as formalizing my thoughts on the limit equations, as k increases, in the complex plane. - Shel « Next Oldest | Next Newest »

 Possibly Related Threads... Thread Author Replies Views Last Post Is there a function space for tetration? Chenjesu 0 189 06/23/2019, 08:24 PM Last Post: Chenjesu Degamma function Xorter 0 668 10/22/2018, 11:29 AM Last Post: Xorter Taylor series of cheta Xorter 13 10,957 08/28/2016, 08:52 PM Last Post: sheldonison Should tetration be a multivalued function? marraco 17 14,911 01/14/2016, 04:24 AM Last Post: marraco Introducing new special function : Lambert_t(z,r) tommy1729 2 3,234 01/10/2016, 06:14 PM Last Post: tommy1729 Tommy-Mandelbrot function tommy1729 0 1,774 04/21/2015, 01:02 PM Last Post: tommy1729 The inverse gamma function. tommy1729 3 7,119 05/13/2014, 02:18 PM Last Post: JmsNxn entire function close to sexp ?? tommy1729 8 8,674 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 6,356 07/17/2013, 09:46 AM Last Post: Gottfried Proof Ackermann function extended to reals cannot be commutative/associative JmsNxn 1 2,831 06/15/2013, 08:02 PM Last Post: MphLee

Users browsing this thread: 2 Guest(s)