# essential singularity

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## 3 matching pages

##### 1: 1.10 Functions of a Complex Variable

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►Lastly, if ${a}_{n}\ne 0$ 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 $\u2102$ with at most one exception. …##### 2: 32.2 Differential Equations

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►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. …##### 3: Bibliography K

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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).
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