12/15/2009, 01:48 AM
(12/15/2009, 01:40 AM)bo198214 Wrote: Actually you rediscovered the Kœnigs formula (2.24 in the (unfinished) overview paper).
\( f^{[w]}(z)=\lim_{k\to\infty}
f^{[-k]}\left((1-\lambda^{w})\cdot p+\lambda^{w}\cdot f^{[k]}(z)\right) \)
for \( f(x)=b^x \). \( \lambda \) is the derivative at the fixed point \( p={^\infty b} \), which is \( \lambda=\ln(p)=\ln(b^p)=p\ln(b)=\ln(b){^\infty b} \).
Good work!
ahh I knew it was something like that I had just never seen it before
