Generating functions related to the Okamoto polynomials for the Painlevé IV equation

Hiromichi Goto, Kenji Kajiwara
2005 Bulletin of the Australian Mathematical Society  
We construct generating functions for the entries of Hankel determinant formula for the Okamoto polynomials which characterise a class of rational solutions to the Painleve IV equation. Generating functions are characterised as asymptotic expansions of log derivative of Ai and Bi, which are solutions of the Airy equation.
doi:10.1017/s0004972700038521 fatcat:den4xv423rfw3eyjpupsb5es5m