[en] We report on the analysis of the rare decay K_L→μ⁺μ^-γ the 1997 data from the KTeV experiment at Fermilab. A total of 9327 candidate events are observed with 2.4% background, representing a factor of 40 increase in statistics over the current world sample. We find that B(K_L→μ⁺μ^-γ)=(3.62±0.04_stat±0.08_syst) x 10^-7. The form factor parameter α_K^* is measured to be α_K^*=-0.160^+0.026_-0.028. In addition, we make the first measurement of the parameter α from the D'Ambrosio-Isidori-Portoles form factor, finding α=-1.54±0.10. In that model, this α measurement limits the Cabibbo-Kobayashi-Maskawa parameter ρ>-0.2