Generating Function Associated with the Determinant Formula for the Solutions of the Painleve' II Equation

Details Generating Function Associated with the Determinant Formula for the Solutions of the Painleve' II Equation Generating Function Associated with the Determinant Formula for the Solutions of the Painleve' II Equation

2004-06-17

arxiv.org/abs/nlin/0406035v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

9 pages, dedicated to Jean Pierre Ramis. A comment on summability is added

Scientific paper

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.

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