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Abstract We provide global parameterizations of $$\pi \pi \rightarrow \pi \pi $$ ππ→ππ scattering S0 and P partial waves up to roughly 2 GeV for phenomenological use. These parameterizations describe the output and uncertainties of previous partial-wave dispersive analyses of $$\pi \pi \rightarrow \pi \pi $$ ππ→ππ , both in the real axis up to 1.12 $${\mathrm {\,GeV}}$$ GeV and in the complex plane within their applicability region, while also fulfilling forward dispersion relations up to 1.43 $${\mathrm {\,GeV}}$$ GeV . Above that energy we just describe the available experimental data. Moreover, the analytic continuations of these global parameterizations also describe accurately the dispersive determinations of the $$\sigma /f_0(500)$$ σ/f0(500) , $$f_0(980)$$ f0(980) and $$\rho (770)$$ ρ(770) pole parameters.