# meromorphic

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## 1—10 of 22 matching pages

##### 1: 21.8 Abelian Functions
An Abelian function is a $2g$-fold periodic, meromorphic function of $g$ complex variables. …
##### 2: 13.5 Continued Fractions
This continued fraction converges to the meromorphic function of $z$ on the left-hand side everywhere in $\mathbb{C}$. For more details on how a continued fraction converges to a meromorphic function see Jones and Thron (1980). … This continued fraction converges to the meromorphic function of $z$ on the left-hand side throughout the sector $|\operatorname{ph}{z}|<\pi$. …
##### 3: 13.17 Continued Fractions
This continued fraction converges to the meromorphic function of $z$ on the left-hand side for all $z\in\mathbb{C}$. For more details on how a continued fraction converges to a meromorphic function see Jones and Thron (1980). … This continued fraction converges to the meromorphic function of $z$ on the left-hand side throughout the sector $|\operatorname{ph}{z}|<\pi$. …
##### 4: 5.2 Definitions
It is a meromorphic function with no zeros, and with simple poles of residue $(-1)^{n}/n!$ at $z=-n$. …$\psi\left(z\right)$ is meromorphic with simple poles of residue $-1$ at $z=-n$. …
##### 5: 4.14 Definitions and Periodicity
The functions $\tan z$, $\csc z$, $\sec z$, and $\cot z$ are meromorphic, and the locations of their zeros and poles follow from (4.14.4) to (4.14.7). …
##### 6: 22.17 Moduli Outside the Interval [0,1]
When $z$ is fixed each of the twelve Jacobian elliptic functions is a meromorphic function of $k^{2}$. …
##### 7: 23.2 Definitions and Periodic Properties
$\wp\left(z\right)$ and $\zeta\left(z\right)$ are meromorphic functions with poles at the lattice points. … Hence $\wp\left(z\right)$ is an elliptic function, that is, $\wp\left(z\right)$ is meromorphic and periodic on a lattice; equivalently, $\wp\left(z\right)$ is meromorphic and has two periods whose ratio is not real. …
##### 8: 22.2 Definitions
Each is meromorphic in $z$ for fixed $k$, with simple poles and simple zeros, and each is meromorphic in $k$ for fixed $z$. …
##### 9: 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 $\zeta\left(s\right)=\frac{1}{s-1}+\sum_{n=0}^{\infty}\frac{(-1)^{n}}{n!}\gamma% _{n}(s-1)^{n},$
##### 10: 1.10 Functions of a Complex Variable
A function whose only singularities, other than the point at infinity, are poles is called a meromorphic function. … …