[en] The observables at short distance in quantum chromodynamics defined through scaling violations in the moments of the deep inelastic structure functions are determined here in terms of the single parameter Λ = Λ(g², μ) to all orders in the loop expansion in the form Msub(i)sup(n) = [log(Q²/Λ²)]sup(asub(n))Σsub(k=0) Σsub(j=0)sup(k)Csub(k,j)sup(n,i)[log(Q²/Λ²)]sup(-k) [log(log(Q²/Λ²))]sup(j). The constants Csub(k,j)sup(n,i) in terms of the renormalization group functions and the coefficient functions define a set of observables and thus are invariant under such changes of renormalization conditions that induce, for example, the recently discussed mappings g → g of the coupling constant plane. The general procedure for deriving these coefficients to all orders is presented and their implications on the study of the g-plane mappings and on practical high order calculations of scaling violations at high Q² are briefly discussed. (Auth.)