  We derive an analytic expression for the O(alpha) radiative correction to the
anti-nu_e (nu_e) spectrum in allowed beta-decay. The m -> 0 limit is convergent
and leads to a very simple result (m is the electron mass). This is in sharp
contrast to the correction to the e^- (e^+) spectrum, that diverges as m -> 0,
an important difference that we explain on theoretical grounds. After
discussing some of their general properties, we use the corrections to the
anti-nu_e and e^- spectra to derive the corresponding correction to the e^- ->
anti-nu_e conversion, a relation that is of considerable interest for reactor
studies of neutrino oscillations.
