@Henryk
I just read your implementation for parabolic and hyperbolic iteration, and I recognize that you are using Jabotinsky's formula for the parabolic case, but for the hyperbolic case, you seem to be using a method I've never seen before. Embedded in your implementation is the implicit recurrence equation:
Where did you find this? Is this your own formula? Have you posted this before?
Andrew Robbins
I just read your implementation for parabolic and hyperbolic iteration, and I recognize that you are using Jabotinsky's formula for the parabolic case, but for the hyperbolic case, you seem to be using a method I've never seen before. Embedded in your implementation is the implicit recurrence equation:
\(
f^{\circ t}(x) = x f_1^t + \sum_{n=2}^{\infty} \frac{x^n}{n!} \sum_{k=1}^{n-1}
\frac{f^{(k)} ((f^{\circ t})^k)^{(n)} - (f^{\circ t})^{(k)}(f^k)^{(n)}}{(f_1^n - f_1)k!}
\)
f^{\circ t}(x) = x f_1^t + \sum_{n=2}^{\infty} \frac{x^n}{n!} \sum_{k=1}^{n-1}
\frac{f^{(k)} ((f^{\circ t})^k)^{(n)} - (f^{\circ t})^{(k)}(f^k)^{(n)}}{(f_1^n - f_1)k!}
\)
Where did you find this? Is this your own formula? Have you posted this before?
Andrew Robbins