Means and intermediate operations (was: Rational operators (a {t} b); a,b > e solved)

[bo198214]

I just want to add the observation that:
\( M^1 \) and \( M^2 \) satisfy the modified property
\( M(r_1^c,\dots,r_n^c)=M(r_1,\dots,r_n)^c \).

And if we define
\( x (t) y = \exp^{\circ t}(\log^{\circ t}(x)+\log^{\circ t}(y)) \)

then we have for integers (and even non-integers) s=t and s=t-1:

\( M^s(r_1 (t) c, \dots, r_n (t) c) = M^s(r_1,\dots,r_n) (t) c \)