  The Airy process A(t), introduced by Pr\"ahofer and Spohn, is the limiting
stationary process for a polynuclear growth model. Adler and van Moerbeke found
a PDE in the variables s_1, s_2, and t for the probability that A(0)<s_1 and
A(t)<s_2. Using this they were able, assuming the truth of a certain conjecture
and appropriate uniformity, to obtain the first few terms of an asymptotic
expansion for this probability as t->infinity, with fixed s_1 and s_2. We shall
show that the expansion can be obtained by using the Fredholm determinant
representation for the probability. The main ingredients are formulas obtained
by the author and C. A. Tracy in the derivation of the Painlev\'e II
representation for the distribution function F_2 plus a few others obtained in
the same way.
