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arXiv · 1011.1641

A tau-function solution to the sixth Painleve transcendent

Yurii V. Brezhnev
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Abstract

We represent and analyze the general solution of the sixth Painleve transcendent in the Picard-Hitchin-Okamoto class in the Painleve form as the logarithmic derivative of the ratio of certain $\tau$-functions. These functions are expressible explicitly in terms of the elliptic Legendre integrals and Jacobi $\theta$-functions, for which we write the general differentiation rules. We also establish a relation between the P6-equation and the uniformization of algebraic curves and present examples.

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Yurii V. Brezhnev. 2010-11-07. A tau-function solution to the sixth Painleve transcendent. https://arxiv.org/abs/1011.1641

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