Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Series for x-tetra-x
#1
I just found a nice "power series" for . It's based on regular iteration, and I took the regular iteration power series for and evaluated it at (z=1), then substituted (y=x) to obtain a power series for . At this point, I noticed there were lots of logarithms, or in other words, it seemed to be of the form which is nice, but not very interesting. It was when I noticed that the power series expansion of about 0 also produces this kind of series that I thought the two could be combined to make a new kind of series. So I tried doing some linear algebra change-of-basis stuff but I forgot how, so I used "undetermined coefficients" instead.

I want to discuss this more, but it will have to wait until this weekend. Here is the power series.


[update]Fixed some coefficient signs[/update]

Andrew Robbins
Reply


Possibly Related Threads...
Thread Author Replies Views Last Post
  Perhaps a new series for log^0.5(x) Gottfried 3 4,010 03/21/2020, 08:28 AM
Last Post: Daniel
Question Taylor series of i[x] Xorter 12 21,917 02/20/2018, 09:55 PM
Last Post: Xorter
  An explicit series for the tetration of a complex height Vladimir Reshetnikov 13 22,953 01/14/2017, 09:09 PM
Last Post: Vladimir Reshetnikov
  Complaining about MSE ; attitude against tetration and iteration series ! tommy1729 0 3,104 12/26/2016, 03:01 AM
Last Post: tommy1729
  2 fixpoints , 1 period --> method of iteration series tommy1729 0 3,157 12/21/2016, 01:27 PM
Last Post: tommy1729
  Taylor series of cheta Xorter 13 23,906 08/28/2016, 08:52 PM
Last Post: sheldonison
  Tetration series for integer exponent. Can you find the pattern? marraco 20 28,465 02/21/2016, 03:27 PM
Last Post: marraco
  Derivative of E tetra x Forehead 7 14,451 12/25/2015, 03:59 AM
Last Post: andydude
  [AIS] (alternating) Iteration series: Half-iterate using the AIS? Gottfried 33 63,023 03/27/2015, 11:28 PM
Last Post: tommy1729
  [integral] How to integrate a fourier series ? tommy1729 1 4,536 05/04/2014, 03:19 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)