  We study a model-independent parameterization of the vector pion form factor
that arises from the constraints of analyticity and unitarity. Our description
should be suitable up to sqrt(s) ~ 1.2 GeV and allows a model-independent
determination of the mass of the rho(770) resonance, M(rho) = (775.1 +- 0.5)
MeV. We analyse the experimental data on tau(-) -> pion(-) pion(0)
neutrino(tau), in this framework, and its consequences on the low-energy
observables worked out by chiral perturbation theory. An evaluation of the
two-pion contribution to the anomalous magnetic moment of the muon, a_muon, and
to the fine structure constant, alpha(M(Z)^2), is also performed.
