06/29/2014, 04:07 AM
So we can represent the tetration via
\( G(z) = \sum_{n=-\infty}^{\infty} a_n \left(\frac{1 + z}{1 - z}\right)^n \).
where \( a_n \) are the coefficients of the Fourier series for the wrapped unit circle, and the fraction is just the inverse Moebius mapping taking the imaginary axis to the circle. That is, the choice of basis functions for the HAM is given by
\( b_n(z) = \left(\frac{1 + z}{1 - z}\right)^n \).
100 coefficients then gives 32 places accuracy.
\( G(z) = \sum_{n=-\infty}^{\infty} a_n \left(\frac{1 + z}{1 - z}\right)^n \).
where \( a_n \) are the coefficients of the Fourier series for the wrapped unit circle, and the fraction is just the inverse Moebius mapping taking the imaginary axis to the circle. That is, the choice of basis functions for the HAM is given by
\( b_n(z) = \left(\frac{1 + z}{1 - z}\right)^n \).
100 coefficients then gives 32 places accuracy.