  The vector form factor f_+(t) of the semileptonic decay D -> K l nu, measured
recently with a high accuracy, can be used to determine the strong coupling
constant g_{D_s^* D K}. The latter is related to the normalised coupling
\hat{g} releveant in heavy-meson chiral perturbation theory. This determination
relies on the estimation of the residue of the form factor at the D_s^* pole
and thus on an extrapolation of the form factor in the unphysical region
(m_D-m_K)^2<t<(m_D+m_K)^2. We test this extrapolation for several
parametrisations of the form factors by determining the value of \hat{g}, whose
value can be compared to other (experimental and theoretical) estimates.
Several unsophisticated parametrisations, differing by the amount of physical
information that they embed, are shown to pass this test. An apparently more
elaborated parametrisation of form factors, the so-called z-expansion, is at
variance with the other models, and we point out some significant shortcomings
of this parametrisation for the problem under consideration.
