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We consider several classes of analytic parametrisations of hadronicscattering amplitudes, and compare their predictions to all available forwarddata (p p, pbar p, pi p, K p, gamma p, gamma gamma, Sigma p). Although theseparametrisations are very close for sqrt(s) > 9 GeV, it turns out that theydiffer markedly at low energy, where a universal pomeron term ~log^2(s) enablesone to extend the fit down to sqrt(s)=4 GeV.Comment: 33 pages. Notations revised, clarified and corrected, appendix added  with the formulae used, one reference added, typos correcte

Hadronic scattering amplitudes: Medium-energy constraints on asymptotic behavior