  The Lempert function for several poles $a_0, ..., a_N$ in a domain $\Omega$
of $\mathbb C^n$ is defined at the point $z \in \Omega$ as the infimum of
$\sum^N_{j=0} \log|\zeta_j|$ over all the choices of points $\zeta_j$ in the
unit disk so that one can find a holomorphic mapping from the disk to the
domain $\Omega$ sending 0 to $z$. This is always larger than the pluricomplex
Green function for the same set of poles, and in general different.
  Here we look at the asymptotic behavior of the Lempert function for three
poles in the bidisk (the origin and one on each axis) as they all tend to the
origin. The limit of the Lempert functions (if it exists) exhibits the
following behavior: along all complex lines going through the origin, it
decreases like $(3/2) \log |z|$, except along three exceptional directions,
where it decreases like $2 \log |z|$. The (possible) limit of the corresponding
Green functions is not known, and this gives an upper bound for it.
