  In this paper, we study Hankel determinants generated from a perturbed
Laguerre weight function, Under the double scaling scheme, we give the uniform
asymptotic approximations of Hankel determinants in terms of a solution of a
third-order nonlinear differential equation, which is equivalent to a
particular Painleve V equation. In fact, this Painleve V equation is equivalent
to the general Painleve III equation. The asymptotic approximations of the
leading coefficients and the recurrence coefficients for the corresponding
orthogonal polynomials also involve the painleve V equation. The asymptotic
analysis is based on our earlier results by using the Deift-Zhou nonlinear
steepest descent method.
