08/11/2014, 04:51 PM

(08/09/2014, 10:51 PM)jaydfox Wrote:(08/09/2014, 07:02 PM)jaydfox Wrote: I'm also working on a second-order approximation. This would consist of two parts. The first is to fix oscillations in the error term (1/1.083...)*f(k)-A(k). These oscillations follow approximately a scaled version of f(-x). Remember the zeroes on the negative real line?

First of all, in thinking about it, the oscillations actually seem to follow something along the lines of G(f(-c x^2)), where G(x) is some scaling function (similar to x^p for some 0 < p < 1, or perhaps similar to asinh?), and c is a constant. It's not exact of course, but I think it gets me in the right ballpark. I'll show pictures later to demonstrate the similarities that I'm working with.

Nice post. What is the most accurate version of the scaling constant that you know of? Earlier, you posted, "1.083063".

- Sheldon