We have obtained the following results. The p.d.f. for the
infinite GUE is given in
terms of a Fredholm determinant by
where is the integral operator on with kernel
( denotes the Bessel function) and b=1. Furthermore
(here the mean eigenvalue spacing is ), where satisfies
the non-linear equation
with b=1, subject to the boundary condition
with b=1 (the parameter b is included above for later convenience).
Note that with b=0 (2.7) reduces to (2.2).