Asymptotic representations of the running parameters in Yang-Mills theories

It is shown that a unique perturbative solution to the renormalization group (RG) equation for the running coupling constant (RCC) exists. The general representations of the running coupling constant and mass in the form of asymptotic expansions are explicity derived. A two-parameter ambiguity in these expansions which leaves invariant the full result is discovered. This feature is observed to be an attribute of the particular type of transcedental equations resulting from the differential RG equation for the RCC. 16 refs