Generalized Umemura polynomials

Anatol N. Kirillov, Makoto Taneda

We introduce and study generalized Umemura polynomials $U_{n,m}^{(k)}(z,w;a,b)$ which are a natural generalization of the Umemura polynomials $U_n(z,w;a,b)$ related to Painlevé $VI…