Bell formula for iterated exponentiation bo198214 Administrator Posts: 1,616 Threads: 102 Joined: Aug 2007 08/26/2007, 10:28 AM Gottfried Wrote:m=arbitrary, integer>0: $\hspace{24} T^{\tiny(m)}_s(x)= \sum_{ k_m...k_1 =0..\infty \\ k_1+k_2+...+k_m=n } x^{k_m} * \left( k_{m-1}^{k_m} \dots k_2^{k_3} k_1^{k_2} \right) * \begin{pmatrix} n \\ k_2,k_3,...,k_m \end{pmatrix} * \frac{ log(s)^n}{n!}$ (hope I didn't make an index-error). This formula can also be found in E.T.BELL ,"The iterated Exponential Integers", Annals of Mathematics (193 p539-557Are you sure Gottfried? I didnt find it in the mentioned article. Gottfried Ultimate Fellow Posts: 898 Threads: 130 Joined: Aug 2007 08/26/2007, 12:27 PM bo198214 Wrote:Are you sure Gottfried? I didnt find it in the mentioned article. Too bad. I don't know, where my brain was... I had just skimmed through some articles and meant to have caught the source correctly. I'll seek, where I've actually have seen it, maybe in Abramowitsch/Stegun... Anyway, it is easy to derive it with pen & paper. I'll be back in the evening, going for a walk today - Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest »

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