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Recently, we introduced several dispersive representations for the vector$K\pi$ form factor and fitted them to the Belle spectrum of $\tau \to K \pi\nu_\tau$. Here, we briefly present the model and discuss the results for theslope and curvature of $F_+(s)$ arising from the best fit. Furthermore, wecompare the pole position of the charged $K^*(892)$ computed from our modelwith other results in the literature. Finally, we discuss the prospects of asimultaneous fit to $\tau \to K \pi \nu_\tau$ and $K_{e3}$ spectra.

Dispersive representation of the K pi vector form factor and fits to tau -> K pi nu(tau) and Ke3 data