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
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