Generating Function Associated with the Hankel Determinant Formula for the Solutions of the Painlevé IV Equation

Details Generating Function Associated with the Hankel Determinant Formula for the Solutions of the Painlevé IV Equation Generating Function Associated with the Hankel Determinant Formula for the Solutions of the Painlevé IV Equation

2005-12-16

arxiv.org/abs/nlin/0512041v3

Nonlinear Sciences

Exactly Solvable and Integrable Systems

17 pages; Corrected some errors

Scientific paper

We consider a Hankel determinant formula for generic solutions of the
Painlev\'e IV equation. We show that the generating functions for the entries
of the Hankel determinants are related to the asymptotic solution at infinity
of the isomonodromic problem. Summability of these generating functions are
also discussed.

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