Conjectures

[andydude]

Sorry, I just read the "more info" part. I developed two approximations to f(b) based on the numerical data of finding when slog(f(b) + I) = slog(f(b)), and they're basically the same except for accuracy. The less accurate one is:

\( f(x) \approx \exp{(2-x)} \)

and the more accurate approximation to f(b) is:

\( f(x) \approx \exp{\left\[2-x + 2(G(4) - G(x))\right\]} \)

where

\( G(x) = \left(\frac{ex}{e-1} - 1\right)^{\frac{e-1}{e(x-1)+1}} \)

Andrew Robbins