Generating functions related to the Okamoto polynomials for the Painlevé IV equation Academic Article uri icon

abstract

  • We construct generating functions for the entries of Hankel determinant formula for the Okamoto polynomials which characterise a class of rational solutions to the Painlevé IV equation. Generating functions are characterised as asymptotic expansions of log derivative of Ai and Bi, which are solutions of the Airy equation.

publication date

  • June 2005