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VOL. 76 | 2018 Remarks on $\tau$-functions for the difference Painlevé equations of type $E_8$
Masatoshi Noumi

Editor(s) Hitoshi Konno, Hidetaka Sakai, Junichi Shiraishi, Takao Suzuki, Yasuhiko Yamada

## Abstract

We investigate the structure of $\tau$-functions for the elliptic difference Painlevé equation of type $E_8$. Introducing the notion of ORG $\tau$-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 $\tau$-functions associated with the configuration of generic nine points in the projective plane.

## Information

Published: 1 January 2018
First available in Project Euclid: 21 September 2018

zbMATH: 07039299

Digital Object Identifier: 10.2969/aspm/07610001

Subjects:
Primary: 39A20
Secondary: 33D70, 33E17