  We consider formal power series defined through the functional q-equation of
the q-Lagrange inversion. Under some assumptions, we obtain the asymptotic
behavior of the coefficients of these power series. As a by-product, we show
that, via the 1/q-Borel transform, the q-Lagrange inversion formula provides an
interpolation between the usual Lagrange inversion (q=1) and the probabilistic
theory of renewal sequences (q tends to 0). We also discuss some new solutions
of the q-Lagrange inversion equation which do not vanish at 0.
