  In the absence of CMB precision measurements, a Taylor expansion has often
been invoked to parametrize the Hubble flow function during inflation. The
standard "horizon flow" procedure implicitly relies on this assumption.
However, the recent Planck results indicate a strong preference for plateau
inflation, which suggests the use of Pad\'e approximants instead. We propose a
novel method that provides analytic solutions of the flow equations for a given
parametrization of the Hubble function. This method is illustrated in the
Taylor and Pad\'e cases, for low order expansions. We then present the results
of a full numerical treatment scanning larger order expansions, and compare
these parametrizations in terms of convergence, prior dependence, predictivity
and compatibility with the data. Finally, we highlight the implications for
potential reconstruction methods.
