The conventional definition of the running coupling
<i>alpha<sub>MS</sub>(mu)</i> in quantum chromodynamics is based on a
solution to the renormalization group equations which treats quarks as
either completely massless at a renormalization scale <i>mu</i> above their
thresholds or infinitely massive at a scale below them. The coupling
is thus nonanalytic at these thresholds. In this paper we present an
analytic extension of <i>alpha<sub>MS</sub>(mu)</i> which incorporates
the finite-mass quark threshold effects into the running of the
coupling. This is achieved by using a commensurate scale relation to
connect <i>alpha<sub>MS</sub>(mu)</i> to the physical
<i>alpha<sub>V</sub></i> scheme at specific scales, thus naturally
including finite quark masses. The analytic-extension inherits the
exact analyticity of the <i>alpha<sub>V</sub></i> scheme and matches
the conventional MS scheme far above and below mass
thresholds. Furthermore just as in <i>alpha<sub>V</sub></i> scheme,
there is no renormalization scale ambiguity, since the position of the
physical mass thresholds is unambiguous.