On solutions to the second Painlevé equation of higher order (Q2761385)

The authors discuss a method for deriving a representation of the meromorphic solutions to differential equations with the Painlevé property. Using this tool, one can derive a representation of solutions to the Painlevé equations and the Painlevé equations of higher order. It is well known that the Painlevé equations possess hierarchies of rational solutions and one-parameter families of solutions expressible in terms of the classical spacial functions for some values of parameters. The same approach is used to obtain the rational solutions and some value distribution properties of solutions to the first equation from the list of the second Painlevé equations of higher order.