# removable

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## 1—10 of 32 matching pages

##### 1: Viewing DLMF Interactive 3D Graphics

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►Any installed VRML or X3D browser should be removed before installing a new one.
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##### 2: 5.10 Continued Fractions

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##### 3: 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 $z=0$. … ►A*cut domain*is one from which the points on finitely many nonintersecting simple contours (§1.9(iii)) have been removed. … ►Branches of $F(z)$ can be defined, for example, in the cut plane $D$ obtained from $\u2102$ by removing the real axis from $1$ to $\mathrm{\infty}$ and from $-1$ to $-\mathrm{\infty}$; see Figure 1.10.1. …##### 4: 25.14 Lerch’s Transcendent

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25.14.1
$$\mathrm{\Phi}(z,s,a)\equiv \sum _{n=0}^{\mathrm{\infty}}\frac{{z}^{n}}{{(a+n)}^{s}},$$
$$; $\mathrm{\Re}s>1,|z|=1$.

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##### 5: 26.15 Permutations: Matrix Notation

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►For $(j,k)\in B$, $B\setminus [j,k]$ denotes $B$ after removal of all elements of the form $(j,t)$ or $(t,k)$, $t=1,2,\mathrm{\dots},n$.
$B\setminus (j,k)$ denotes $B$ with the element $(j,k)$
removed.
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##### 6: 23.18 Modular Transformations

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23.18.7
$$s(d,c)=\sum _{r=1}^{c-1}\frac{r}{c}\left(\frac{dr}{c}-\lfloor \frac{dr}{c}\rfloor -\frac{1}{2}\right),$$
$c>0$.

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##### 7: 5.6 Inequalities

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##### 8: 5.17 Barnes’ $G$-Function (Double Gamma Function)

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##### 9: 8.18 Asymptotic Expansions of ${I}_{x}(a,b)$

##### 10: 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. … …