Generating Function Associated with the Determinant Formula for the   Solutions of the Painleve' II Equation
  In this paper we consider a Hankel determinant formula for generic solutions of the Painleve' II equation. We show that the generating functions for the entries of the Hankel determinants are related to the asymptotic solution at infinity of the linear problem of which the Painleve' II equation describes the isomonodromic deformations. 
Nalini Joshi, Kenji Kajiwara, Marta Mazzocco