Differential equations and dispersion relations for the sunrise amplitudes

The study of the imaginary part and of the corresponding dispersion relations of Feynman graph amplitudes within the differential equations method can provide a powerful tool for the solution of the equations, especially in the massive case. We illustrate the main features of the approach by applying it to the case of two-loop massive sunrise graph and to the two-loop kite integral with three internal massive propagators. We will then show how to derive compact analytical results for the first two non-trivial orders of their ϵ = (4-d)/2 expansion and to continue them analytically for all physical values of the incoming momentum.