# removable singularity

♦
7 matching pages ♦

(0.002 seconds)

## 7 matching pages

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

…
►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

…
►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 $1-2\mu =0,-1,-2,\mathrm{\dots}$ and $\nu +\mu +1=0,-1,-2,\mathrm{\dots}$ 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 $1-2\mu =0,-1,-2,\mathrm{\dots}$ and $\nu +\mu +1=0,-1,-2,\mathrm{\dots}$ are removable singularities.