  Level-spacing distributions of the Gaussian Unitary Ensemble (GUE) of random
matrix theory are expressed in terms of solutions of coupled differential
equations. Series solutions up to order 50 in the level spacing are obtained,
thus providing a very good description of the small-spacing part of the
level-spacing distribution, which can be used to make comparisons with
experimental or numerical data. The level-spacing distributions can be obtained
by solving the system of differential equations numerically.
