So as to put our calculation of
in context, we first note that the expression (1.3) for has
been made more explicit by Jimbo et al. , who proved that
where satisfies the form of the Painlevé V equation:
subject to the boundary condition
Subsequent derivations of this result have been given by Its et al. ,
Mehta  and Tracy and Widom . Our expression for is given in
terms of the solution of a non-linear equation which generalizes (2.2).