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. [
4
], 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. [
5
], Mehta [
6
] and Tracy and Widom [
7
]. Our expression for
is given in terms of the solution of a non-linear equation which generalizes (2.2).
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