New transformations for Painlevé’s third transcendent

Witte, N.

doi:10.1090/S0002-9939-04-07087-X

New transformations for Painlevé’s third transcendent
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by N. S. Witte PDF

Proc. Amer. Math. Soc. 132 (2004), 1649-1658 Request permission

Abstract:

We present transformations relating the third transcendent of Painlevé 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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