Series for x-tetra-x - Printable Version +- Tetration Forum ( https://math.eretrandre.org/tetrationforum)+-- Forum: Tetration and Related Topics ( https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1)+--- Forum: Mathematical and General Discussion ( https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3)+--- Thread: Series for x-tetra-x ( /showthread.php?tid=276) |

Series for x-tetra-x - andydude - 04/27/2009
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 |