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Regular version of the site

Article

Painleve functions and conformal blocks

Constructive Approximation. 2014. Vol. 39. No. 1. P. 255-272.
Iorgov N., Lisovyy O., Tykhyy Y., A. Shchechkin.

We outline recent developments relating Painlev ́e equations and 2D conformal field theory. Generic tau functions of Painlev ́e VI and Painlev ́e III_3 are written as linear combinations of c= 1 conformal blocks and their irregular limits. This provides explicit combinatorial series representations of the tau functions, and helps to establish connection formula for the tau function in the Painlev ́e VI case.