The one-loop functional of chiral SU(2)

The one-loop functional for chiral SU(2) of Gasser and Leutwyler is extended to include up to three propagators. With this generating functional it is possible to calculated all amplitudes up to order phi^6 to next-to-leading order in the low-energy expansion. An external pion is of order phi and a vector gauge boson is of order phi^2. A check of the existing amplitudes for two photons into two pions is given. The one-loop amplitudes and the cross sections for four-pion production in e^+e^- annihilation are calculated.