We analyze the energy scale dependence of fragmentation functions from e + -e − collisions using conventional momentum measures x p and ξ p and rapidity y. We find that replotting fragmentation functions on normalized rapidity u 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 small Q in order to describe fragment distributions at low transverse momentum p t in heavy ion collisions at RHIC.