exponential polynomial interpolation

[andydude]

There is a recurrence equation for hyperbolic iteration that Henryk describes here, and I later noticed here and since this is a "finite" recurrence equation, everything is eventually defined in terms of \( f_1^t \), which is equivalent to your \( u^h \) in the case \( f(x) = e^{ux} - 1 \). I have also noticed that you can better describe hyperbolic iteration as a polynomial in \( f_1^t \), but I have yet to find any patterns of note. Henryk's recurrence equation for hyperbolic iteration seems to be a great resource for explaining how and why it works the way it does.

Andrew Robbins