Iterated compositions - 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: Iterated compositions (/showthread.php?tid=1089) Iterated compositions - Xorter - 08/20/2016 There are two really important operators: + (addition) and o (composition) If we iterate +, we get Hyper-operators, like this: Hyper(A;n;B) = A[n-1]B E. g.: A[0]B = A+B A[1]B = A*B A[2]B = A^B A[3]B = A^^B (tetration) ... But if we iterate o, we get Hot-operators, like this Hot(F;n;G) E. g.: Hot(f;1;c) = f(x) o c = f( c) Hot(f;2;n) = ☉ f(x) ☥^n = f(x) o f(x) o ... o f(x) (steinix-ankh operator) Hot(f;3;n) = ☉ f(x) ☥^(☉ f(x) ☥^...) (super-steinix-ankh operator) ... For example: Hot(2+x;1;2) = 4 Hot(2+x;2;2) = 4+x Hot(2+x;3;2) = 4+3x Hot(2+x;4;2) = 4*2^x+(4*2^x - 1)*x The question is what Hot(f;n;g) gives if n is real or complex?