  The probability that an interval $I$ is free of eigenvalues in a matrix
ensemble with unitary symmetry is given by a Fredholm determinant. When the
weight function in the matrix ensemble is a classical weight function, and the
interval $I$ includes an endpoint of the support, Tracy and Widom have given a
formalism which gives coupled differential equations for the required
probability and some auxilary quantities. We summarize and extend earlier work
by expressing the probability and some of the auxilary quantities in terms of
Painlev\'e transcendents.
