Right © 2015 EMS Publishing House. Type Journal Article

On WKB theoretic transformations for Painleve transcendents on degenerate Stokes segments by Kohei Iwaki* The WKB theoretic transformation theorem established in [KT2] implies that the rst Painleve equation gives a normal form of Painleve equations with a large parameter near a simple P-turning point. In this paper we extend this result and show that the second Painleve equation (PII) and the third Painleve equation (PIII0(D7)) of type D7 give a normal form of Painleve equations on a degenerate P-Stokes segments connecting two dierent simple P-turning points and on a degenerate P-Stokes segment of loop-type, respectively. That is, any 2-parameter formal solution of a Painleve equation is reduced to a 2-parameter formal solution of (PII) or (PIII0(D7)) on these degenerate P-Stokes segments by our transformation