  We start with the explicit solution, in terms of the Lambert W function, of
the renormalization group equation (RGE) for the gauge coupling in the
supersymmetric Yang-Mills theory described by the well-known beta function of
Novikov et al.(NSVZ). We then construct a class of beta functions for which the
RGE can be solved in terms of the Lambert W function. These beta functions are
expressed in terms of a function which is a truncated Laurent series in the
inverse of the gauge coupling. The parameters in the Laurent series can be
adjusted so that the first coefficients of the Taylor expansion of the beta
function in the gauge coupling reproduce the four-loop or five-loop QCD (or
SQCD) beta function.
