♦ 3 matching pages ♦
3 matching pages
… ►Lastly, if for infinitely many negative , then is an isolated essential singularity. … ► … ►If the poles are infinite in number, then the point at infinity is called an essential singularity: it is the limit point of the poles. … ►In any neighborhood of an isolated essential singularity, however small, an analytic function assumes every value in with at most one exception. …
… ►An equation is said to have the Painlevé property if all its solutions are free from movable branch points; the solutions may have movable poles or movable isolated essential singularities (§1.10(iii)), however. …
Essential singularity of the Painlevé function of the second kind and the nonlinear Stokes phenomenon.
Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov.
(LOMI) 187, pp. 139–170 (Russian).