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essential singularity


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1: 1.10 Functions of a Complex Variable
Lastly, if a n 0 for infinitely many negative n , then z 0 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. …
2: 32.2 Differential Equations
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 singularities1.10(iii)), however. …
3: Bibliography K
  • A. A. Kapaev (1991) 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).