  We analyze the energy scale dependence of fragmentation functions from
$e^+$-$e^-$ collisions using conventional momentum measures $x_p$ and $\xi_p$
and rapidity $y$. We find that replotting fragmentation functions on a
normalized rapidity variable results in a compact form precisely represented by
the beta distribution, its two parameters varying slowly and simply with parton
energy scale $Q$. The resulting parameterization enables extrapolation of
fragmentation functions to low $Q$ in order to describe fragment distributions
at low transverse momentum $p_t$ in heavy ion collisions at RHIC.
