Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Rational sums of inverse powers of fixed points of e
#10
The first one looks about right, meaning it looks familiar at a glance.

Hmm, going through Excel, the next few look correct, so at least we're on the same page there.

Now, to get the first sum, we'll sum the inverse 2nd powers. To start, square each of the values you listed:
Code:
-0.472565386708 - 0.238338175183*I
-0.013946445102 - 0.008184595884*I
-0.004613490799 - 0.001820881553*I
-0.002277041586 - 0.000693879494*I
-0.001352042857 - 0.000339668175*I
-0.000894117468 - 0.000192447243*I

And of course, we'll add the conjugates as well. Essentially then, just double the real parts and sum them.

The second sum is the sum of the inverse 3rd powers, so cube the values you listed and sum (including conjugates).
~ Jay Daniel Fox
Reply


Messages In This Thread
RE: Rational sums of inverse powers of fixed points of e - by jaydfox - 11/21/2007, 09:35 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  tetration from alternative fixed point sheldonison 22 30,564 12/24/2019, 06:26 AM
Last Post: Daniel
  Thoughts on hyper-operations of rational but non-integer orders? VSO 2 785 09/09/2019, 10:38 PM
Last Post: tommy1729
  Inverse Iteration Xorter 3 2,771 02/05/2019, 09:58 AM
Last Post: MrFrety
  Inverse super-composition Xorter 11 13,796 05/26/2018, 12:00 AM
Last Post: Xorter
  Are tetrations fixed points analytic? JmsNxn 2 3,173 12/14/2016, 08:50 PM
Last Post: JmsNxn
  the inverse ackerman functions JmsNxn 3 6,156 09/18/2016, 11:02 AM
Last Post: Xorter
  Rational operators (a {t} b); a,b > e solved JmsNxn 30 41,489 09/02/2016, 02:11 AM
Last Post: tommy1729
  Removing the branch points in the base: a uniqueness condition? fivexthethird 0 1,641 03/19/2016, 10:44 AM
Last Post: fivexthethird
  Inverse power tower functions tommy1729 0 1,963 01/04/2016, 12:03 PM
Last Post: tommy1729
  Derivative of exp^[1/2] at the fixed point? sheldonison 10 10,943 01/01/2016, 03:58 PM
Last Post: sheldonison



Users browsing this thread: 1 Guest(s)