General representation of physical quantities in scheme-invariant perturbation theory and its optimization

Solution of the complete renormalization group equation for a dimensionless physical quantity in the renormalization scheme-invariant perturbation theory is given. On its basis we obtain the improved power-series expansions of this quantity in powers of its two-loop approximant and a certain function introduced in the paper. General and optimized representations of moments of nonsinglet structure functions are derived.