Forward analysis of πN scattering with an expansion method

The $\pi$N forward scattering data are analyzed using an expansion method, where the invariant amplitudes are represented by expansions satisfying the forward dispersion relations. The experimental errors of the data are taken into account through the covariance matrix of the coefficients of the expansions in a careful error analysis. From the results, some coefficients, $c_{n0}^\pm$, of the subthreshold expansions have been calculated with proper error bars.