* Institute for Theoretical Physics, State University of New York at Stony Brook, Stony Brook, New York 11794, USA
Abstract:
We continue our study of those Painlevé V equations which admit a one-parameter family of solutions analytic at the origin and solve the global problem of connecting the 2-parameter expansion about t = 0 with the 2-parameter expansion valid for t → ± i∞. A special case of our results is applied to the study of the one-particle reduced density matrix of the one-dimensional gas of impenetrable bosons. We also use our results to obtain a 2-parameter connection formula for a class of Painlevé III functions.