This paper is a continuation of our analysis, begun in arXiv:1310.2276, ofthe rational solutions of the inhomogeneous Painleve-II equation and associatedrational solutions of the homogeneous coupled Painleve-II system in the limitof large degree. In this paper we establish asymptotic formulae valid near acertain curvilinear triangle in the complex plane that was previously shown toseparate two distinct types of asymptotic behavior. Our results display both atrigonometric degeneration of the rational Painleve-II functions and also adegeneration to the tritronquee solution of the Painleve-I equation. Ourrigorous analysis is based on the steepest descent method applied to aRiemann-Hilbert representation of the rational Painleve-II functions, andsupplies leading-order formulae as well as error estimates.
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