The radial diffusion equation with synchrotron lossess is solved by the Laplace transform method for near equatorially mirroring relativistic electrons. The evolution of a power law distribution function is found, and the characteristics of synchrotron burn-off are stated in terms of explicit parameters for an arbitrary diffusion coefficient of the form DLL=D0L&agr;. The peaking of the 10.4-cm volume emissivity from Jupiter at L?1.8 provides an estimte D0?9¿10-11 in the radiation belts; this value is suggested as the appropriate modification for an equatorial field strenght of 4.2 G of the Birmingham et al.(1974) result. Nonsynchrotron losses are included phenomenologically, and from the phase space densities reported by McIlwain and Fillius (1975) the particle lifetime is estimated as &tgr;~6¿108L2-&agr; s. Asymptotic forms for the distribution in the strong synchrotron loss regime are provided.