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