  We present direct representations of the scaling functions of the 3d O(4)
model which are relevant for comparisons to other models, in particular QCD.
This is done in terms of expansions in the scaling variable
z=t/h^{1/\beta\delta}. The expansions around z=0 and the corresponding
asymptotic ones for z --> +/- infty, overlap such that no interpolation is
needed. We explicitly present the expansion coefficients which have been
determined numerically from data of a previous high statistics simulation of
the O(4) model on a three-dimensional lattice of linear extension L=120. This
allows to derive smooth representations of the first three derivatives of the
scaling function of the free energy density, which determine universal
properties of up to sixth order cumulants of net charge fluctuations in QCD.
