  The notion of generating functions of Poisson structures was first studied in
math.SG/0312380.They are special functions which induce, on open subsets of
$\R^d$, a Poisson structure together with the local symplectic groupoid
integrating it. A universal generating function was provided in terms of a
formal power series coming from Kontsevich star product. The present article
proves that this universal generating function converges for analytical Poisson
structures and compares the induced local symplectic groupoid with the phase
space of Karasev--Maslov.
