question about differential equation for a[4]x - 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: question about differential equation for a[4]x (/showthread.php?tid=296) question about differential equation for a[4]x - Base-Acid Tetration - 05/26/2009 $(\operatorname{sexp}_a(x))' = \operatorname{sexp}'_a(0) (\ln a)^{x} \exp_a \sum_{n=1}^{\infty} \frac{f^{(n-1)} (0)}{n!} (B_n(x)-B_n))$ what is the function f in this differential equation? and how do you prove this as a characteristic of the tetrational?