# removable singularity

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## 7 matching pages

##### 1: 1.10 Functions of a Complex Variable
This singularity is removable if $a_{n}=0$ for all $n<0$, and in this case the Laurent series becomes the Taylor series. …Lastly, if $a_{n}\not=0$ 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 $(\sin z)/z$ at $z=0$. …
##### 2: 8.12 Uniform Asymptotic Expansions for Large Parameter
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 … A different type of uniform expansion with coefficients that do not possess a removable singularity at $z=a$ is given by …
##### 3: 1.4 Calculus of One Variable
A removable singularity of $f(x)$ at $x=c$ occurs when $f(c+)=f(c-)$ but $f(c)$ is undefined. … …
##### 4: 14.3 Definitions and Hypergeometric Representations
From (15.9.15) it follows that $1-2\mu=0,-1,-2,\dots$ and $\nu+\mu+1=0,-1,-2,\dots$ are removable singularities of the right-hand sides of (14.3.21) and (14.3.22).
##### 5: 21.7 Riemann Surfaces
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.
##### 6: Errata
• Subsection 14.3(iv)

A sentence was added at the end of this subsection indicating that from (15.9.15), it follows that $1-2\mu=0,-1,-2,\dots$ and $\nu+\mu+1=0,-1,-2,\dots$ are removable singularities.

• ##### 7: 25.2 Definition and Expansions
It is a meromorphic function whose only singularity in $\mathbb{C}$ is a simple pole at $s=1$, with residue 1. …
25.2.4 $\zeta\left(s\right)=\frac{1}{s-1}+\sum_{n=0}^{\infty}\frac{(-1)^{n}}{n!}\gamma% _{n}(s-1)^{n},$