Special function solutions of the discrete Painlevé equations
A review of special solutions of discrete (difference) and \(q\)-discrete Painlevé equations in terms of discrete special functions is given. It is shown that these solutions exist if the parameters of the Painlevé equation satisfy a particular constraint. The discrete special functions belong to the hypergeometric family, although in some cases they seem to go beyond the known discrete and \(q\)-discrete hypergeometric functions.
scientific article; zbMATH DE number 1755277
scientific article