New Transformations for Painlevé's Third Transcendent

Details New Transformations for Painlevé's Third Transcendent New Transformations for Painlevé's Third Transcendent

2002-10-02

arxiv.org/abs/math/0210019v1

Mathematics

Classical Analysis and ODEs

AMSLatex with Proc. Amer. Math. Soc. macros

Scientific paper

We present transformations relating the third transcendent of Painlev\'e with parameter sets located at the corners of the Weyl chamber for the symmetry group of the system, the affine Weyl group of the root system $ B^{(1)}_2 $, to those at the origin. This transformation entails a scaling of the independent variable, and implies additive identities for the canonical Hamiltonians and product identities for the $\tau$-functions with these parameter sets.

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