Its interesting to see the discrete case. Let D_n be a difference operator like D_n(F) = F(x+n) - F(x) Solving by induction for the equation D_n(F)/D_n(x) = F

Its interesting to see the discrete case. Let D_n be a difference operator like D_n(F) = F(x+n) - F(x) Solving by induction for the equation D_n(F)/D_n(x) = F(x), F(0)=1, it gives (1+n)^(x/n). So now you have a "family" of functions that when "derived" by its difference, gives the same constant ^ x. Euler is the case when n→0. This aplies for every n, including complex numbers.