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

2005/12/16 by Joshi, Nalini, Kajiwara, Kenji, Mazzocco, Marta
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences

paper · doi:10.48550/arxiv.nlin/0512041

Abstract

We consider a Hankel determinant formula for generic solutions of the Painlevé 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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