Bell formula for iterated exponentiation - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- Thread: Bell formula for iterated exponentiation (/showthread.php?tid=40) Bell formula for iterated exponentiation - bo198214 - 08/26/2007 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. RE: Bell formula for iterated exponentiation - Gottfried - 08/26/2007 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