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 NSVZ β-function. We then construct a class of β-functions for which the RGE can be solved in terms of the Lambert W function. These β-functions are expressed in terms of a function which is a truncated Laurent series in the inverse μ of the gauge coupling α ≡ α/π. The parameters in the Laurent series can be adjusted so that the first coefficients of the Taylor expansion of the β-function in the gauge coupling a reproduce the four-loop or five-loop QCD (or SQCD) β-function. © SISSA 2011.