Remarks on $τ$-functions for the difference Painlevé equations of type $E_8$

Masatoshi Noumi

paper

Remarks on $τ$ -functions for the difference Painlevé equations of type $E_{8}$

arXiv:1604.06869

Abstract

We investigate the structure of $τ$ -functions for the elliptic difference Painlevé equation of type $E_{8}$ . Introducing the notion of ORG $τ$ -functions for the $E_{8}$ lattice, we construct some particular solutions which are expressed in terms of elliptic hypergeometric integrals. Also, we discuss how this construction is related to the framework of lattice $τ$ -functions associated with the configuration of generic nine points in the projective plane.

55 pages

Remarks on τ-functions for the difference Painlevé equations of type E8​

Abstract

Remarks on $τ$ -functions for the difference Painlevé equations of type $E_{8}$