Study of the Three-Body Leptonic Decay Modes of theK+Meson

${K_{e3\mathrm{}}}^{+}$ and ${K_{\mu 3}}^{+}$ decay spectra are studied. The results strongly favor vector coupling even if the form factors are allowed arbitrary energy dependence. The relative amplitudes of scalar and tensor couplings are less than 0.3 with the most probable value around 0. The muon and electron couplings are found to be the same within the 14% error quoted. All energy dependences of the form factors are found to be small. If $f_V=A(1+\frac{\lambda q^2}{{M_{\pi }}^2})$ and $g_V=B$, where $q^2={(p^K-p^{\pi })}^2$, then $\lambda =-0.020\mathrm{}\pm 0.027$, $\frac{B}{A}=-0.54\mathrm{}\pm 0.35$.