Algoritmization of parametric derivation - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Computation (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=8) +--- Thread: Algoritmization of parametric derivation (/showthread.php?tid=1165) Algoritmization of parametric derivation - Xorter - 04/12/2017 I have a really strange f function (that I would like to take into Carleman matrices) so I need the derivative of its powers. We have just know about the function that: $\int f dx = F$ ${dF \over dx} = f$ ${df \over dx} = a/F$ where a is a constant. I am interested in the following expression: ${d^N \over dx^N} f^M = ?$ A recursive formula is not the best, but really enough. Not to be in PARI/gp is not the best, but enough. (It is important for me to invastigate the infinite Taylor series with argument infinity.)