09/15/2009, 08:01 PM
(09/15/2009, 06:32 PM)Ansus Wrote: How many iterations did you do?
Also note that the coefficient is not exactly f'(0) because the indefinite product implyes indefinite multiplyer. And the indefinite sum inplyes indefinite term. So the constant coefficient can be found only after completing all iterations. If you do these iterations and find that it grows with any iteration, simply normalize the last result according the requirement f(0)=1.
Hmm. Normalizing it after each iteration seems to stop it from growing up, but if I use, say, 28 terms,then after around 6 iterations it still break away from converging toward the tetration.
Also, how did you come up with that initial value for f'(0)? Did you grab it from someone else's proposed extension from tetration (Kounzetsov? Cauchy Integral?) And does this formula also generalize and work for other bases, incl. \( 0 < b < e^{-e} \)? Can you graph the (probably complex-valued, so 2 graphs) tetration of, say, b = 0.04?