• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Rational sums of inverse powers of fixed points of e jaydfox Long Time Fellow Posts: 440 Threads: 31 Joined: Aug 2007 11/20/2007, 09:31 PM Aha! $\ln\left(1-\frac{-z}{\hspace{5} e^{-z} \hspace{5}}\right)$ $\ln\left(1-\left(-ze^{z}\right)\right)$ $\ln\left(1+ze^{z}\right)$ So this is related to my previous findings! When z is the additive inverse of a fixed point, we get: $ \begin{eqnarray} 1+ze^{z}|_{\small z=-c_k} & = & -c_k e^{-c_k} \\ & = & 1+\frac{-c_k}{c_k} \\ & = & 1-1 \\ & = & 0 \end{eqnarray}$ Therefore, at the additive inverses of the fixed points, we'll get logarithmic singularities. I'm not sure about the bases though, and there are a few other oddities I need to figure out, but it's cool to see even this level of relationship. ~ Jay Daniel Fox « Next Oldest | Next Newest »

 Messages In This Thread Rational sums of inverse powers of fixed points of e - by jaydfox - 11/20/2007, 07:55 PM RE: Rational sums of inverse powers of fixed points of e - by jaydfox - 11/20/2007, 08:11 PM RE: Rational sums of inverse powers of fixed points of e - by Gottfried - 11/20/2007, 08:14 PM RE: Rational sums of inverse powers of fixed points of e - by jaydfox - 11/20/2007, 08:31 PM RE: Rational sums of inverse powers of fixed points of e - by jaydfox - 11/20/2007, 08:43 PM RE: Rational sums of inverse powers of fixed points of e - by jaydfox - 11/20/2007, 09:31 PM RE: Rational sums of inverse powers of fixed points of e - by jaydfox - 11/21/2007, 01:15 AM RE: Rational sums of inverse powers of fixed points of e - by jaydfox - 11/21/2007, 08:14 AM RE: Rational sums of inverse powers of fixed points of e - by Gottfried - 11/21/2007, 08:50 AM RE: Rational sums of inverse powers of fixed points of e - by jaydfox - 11/21/2007, 09:35 AM RE: Rational sums of inverse powers of fixed points of e - by Gottfried - 11/21/2007, 12:52 PM RE: Rational sums of inverse powers of fixed points of e - by jaydfox - 11/21/2007, 06:20 PM RE: Rational sums of inverse powers of fixed points of e - by Gottfried - 11/22/2007, 06:25 PM RE: Rational sums of inverse powers of fixed points of e - by jaydfox - 11/22/2007, 08:32 PM

 Possibly Related Threads... Thread Author Replies Views Last Post tetration from alternative fixed point sheldonison 22 30,621 12/24/2019, 06:26 AM Last Post: Daniel Thoughts on hyper-operations of rational but non-integer orders? VSO 2 791 09/09/2019, 10:38 PM Last Post: tommy1729 Inverse Iteration Xorter 3 2,775 02/05/2019, 09:58 AM Last Post: MrFrety Inverse super-composition Xorter 11 13,806 05/26/2018, 12:00 AM Last Post: Xorter Are tetrations fixed points analytic? JmsNxn 2 3,174 12/14/2016, 08:50 PM Last Post: JmsNxn the inverse ackerman functions JmsNxn 3 6,162 09/18/2016, 11:02 AM Last Post: Xorter Rational operators (a {t} b); a,b > e solved JmsNxn 30 41,511 09/02/2016, 02:11 AM Last Post: tommy1729 Removing the branch points in the base: a uniqueness condition? fivexthethird 0 1,642 03/19/2016, 10:44 AM Last Post: fivexthethird Inverse power tower functions tommy1729 0 1,964 01/04/2016, 12:03 PM Last Post: tommy1729 Derivative of exp^[1/2] at the fixed point? sheldonison 10 10,947 01/01/2016, 03:58 PM Last Post: sheldonison

Users browsing this thread: 1 Guest(s)