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In this talk we discuss the relevance of dispersive methods and theirdifferent applications to obtain simple but rigorous parameterizations ofpion-pion and kaon-pion scattering. We show as an example our latest dispersiveanalysis of $\pi K$ scattering, where we provide simple parameterizations ofdata satisfying Forward Dispersion Relations up to 1.6 GeV.

Dispersive analysis tools for $\pi\pi$ and $\pi K$ scattering