PADE APPROXIMATIONS FOR PAINLEVE I AND II TRANSCENDENTS

We use a version of the Fair-Luke algorithm to find the Pade approximate solutions of the Painleve I and II equations. We find the distributions of poles for the well-known Ablowitz-Segur and Hastings-McLeod solutions of the Painleve II equation. We show that the Boutroux tritronquee solution of the Painlee I equation has poles only in the critical sector of the complex plane. The algorithm allows checking other analytic properties of the Painleve transcendents, such as the asymptotic behavior at infinity in the complex plane.