# isolated

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4 matching pages ♦

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## 4 matching pages

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

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►Then $z={z}_{0}$ is an

*isolated singularity*of $f(z)$. …Lastly, if ${a}_{n}\ne 0$ for infinitely many negative $n$, then ${z}_{0}$ is an*isolated essential singularity*. … ► … ► … ►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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►be a nonlinear second-order differential equation in which $F$ is a rational function of $w$ and $dw/dz$, and is

*locally analytic*in $z$, that is, analytic except for isolated singularities in $\u2102$. …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: 1.4 Calculus of One Variable

##### 4: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

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►Often circumstances allow rather stronger statements, such as uniform convergence, or pointwise convergence at points where $f(x)$ is continuous, with convergence to $(f({x}_{0}-)+f({x}_{0}+))/2$ if ${x}_{0}$ is an isolated point of discontinuity.
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