  We consider in the complex field the differential equation $\displaystyle
\frac{d^2}{d x^2} \Phi(x) = \frac{P_m(x,\a)}{x^2}\Phi(x)$, where $P_m$ is a
monic polynomial function of order $m$ with coefficients $\a=(a_1, ..., a_m)$.
We investigate the asymptotic, resurgent, properties of the solutions at
infinity, focusing in particular on the analytic dependence on $\a$ of the
Stokes-Sibuya multipliers. Taking into account the non trivial monodromy at the
origin, we derive a set of functional equations for the Stokes-Sibuya
multipliers. We show how these functional relations can be used to compute the
Stokes multipliers for a class of polynomials $P_m$. In particular, we obtain
conditions for isomonodromic deformations when $m=3$.
