# removable singularity

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5 matching pages ♦

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## 5 matching pages

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

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►This singularity is

*removable*if ${a}_{n}=0$ for all $$, and in this case the Laurent series becomes the Taylor series. …Lastly, if ${a}_{n}\ne 0$ for infinitely many negative $n$, then ${z}_{0}$ is an*isolated essential singularity*. … ►An isolated singularity ${z}_{0}$ is always removable when ${lim}_{z\to {z}_{0}}f(z)$ exists, for example $(\mathrm{sin}z)/z$ at $z=0$. …##### 2: 8.12 Uniform Asymptotic Expansions for Large Parameter

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►The right-hand sides of equations (8.12.9), (8.12.10) have removable singularities at $\eta =0$, and the Maclaurin series expansion of ${c}_{k}(\eta )$ is given by
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►A different type of uniform expansion with coefficients that do not possess a removable singularity at $z=a$ is given by
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##### 3: 1.4 Calculus of One Variable

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►A

*removable singularity*of $f(x)$ at $x=c$ occurs when $f(c+)=f(c-)$ but $f(c)$ is undefined. … …##### 4: 21.7 Riemann Surfaces

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►Removing the singularities of this curve gives rise to a two-dimensional connected manifold with a complex-analytic structure, that is, a

*Riemann surface. All compact Riemann surfaces can be obtained this way.*…