From trihomographic to elliptic Painleve equations

摘要

We use the trihomographic representation of discrete Painleve equations in order to derive a new, factorised form for equations associated with the affine Weyl group E-8((1)). Introducing an ancillary dependent variable we are able to obtain factorised forms for the general additive, multiplicative and elliptic discrete E-8((1)) related Painleve equations. The advantage of these factorised forms is that they make the singularity analysis of the E-8((1)) straightforward in par with the situation for equations associated with lower affine Weyl groups.