 Functional power - 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: Functional power (/showthread.php?tid=1158) Functional power - Xorter - 03/11/2017 Let f and g be total functions (so e. g. C -> C) and N and M be complexes. Then (f o g)(x) and f o a = f(a) are so-called functional multiplications. But the interesting thing is the following: functional power: When N is an integer, it is trivial, just look: ... We have rules for it, like these ones: But for instance: (Also functional tetration exists.) My theory is that if we can get an explicit formula for with x and N, then N is extendable to any total function. For example: And in the same way, theoritacelly you could do the same with all the functions. But how? My concept is that by Carleman matrices.