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The $K\pi$ vector form factor, $F_+^{K\pi}$, used to reproduce the Bellespectrum of $\tauKpi$ decays is described by means of a three-times subtracteddispersion relation also incorporating constraints from $K_{l3}$ decays. Theslope and curvature of $F_+^{K\pi}$ are fitted to the data yielding$\lambda_+'=(25.49 \pm 0.31) \times 10^{-3}$ and $\lambda_+"= (12.22 \pm 0.14)\times 10^{-4}$. The pole parameters of the $K^*(892)^\pm$ are found to be$m_{K^*(892)^\pm}= 892.0\pm 0.5$ MeV and $\Gamma_{K^*(892)^\pm}= 46.5 \pm1.1$MeV. The phase-space integrals relevant for $K_{l3}$ analyses and the $P$-waveisospin-1/2 $K\pi$ phase-shift threshold parameters are also calculated.

Improving the Kpi vector form factor through Kl3 constraints