meromorphic function

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11: 13.2 Definitions and Basic Properties
$M\left(a,b,z\right)$ is entire in $z$ and $a$, and is a meromorphic function of $b$. …
12: 23.15 Definitions
A modular function $f(\tau)$ is a function of $\tau$ that is meromorphic in the half-plane $\Im\tau>0$, and has the property that for all $\mathcal{A}\in\mbox{SL}(2,\mathbb{Z})$, or for all $\mathcal{A}$ belonging to a subgroup of SL$(2,\mathbb{Z})$, …
13: 25.15 Dirichlet $L$-functions
The notation $L\left(s,\chi\right)$ was introduced by Dirichlet (1837) for the meromorphic continuation of the function defined by the series …
14: 29.12 Definitions
In consequence they are doubly-periodic meromorphic functions of $z$. …
15: 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). …
16: 8.2 Definitions and Basic Properties
When $z\neq 0$, $\Gamma\left(a,z\right)$ is an entire function of $a$, and $\gamma\left(a,z\right)$ is meromorphic with simple poles at $a=-n$, $n=0,1,2,\dots$, with residue $(-1)^{n}/n!$. …
17: 22.2 Definitions
§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 $z$. … … The Jacobian functions are related in the following way. … In terms of Neville’s theta functions20.1) …
If $f$ is meromorphic, with poles near the saddle point, then the foregoing method can be modified. …
$\zeta\left(s,a\right)$ has a meromorphic continuation in the $s$-plane, its only singularity in $\mathbb{C}$ being a simple pole at $s=1$ with residue $1$. …The Riemann zeta function is a special case: …
As functions of $g_{2}$ and $g_{3}$, $\wp\left(z;g_{2},g_{3}\right)$ and $\zeta\left(z;g_{2},g_{3}\right)$ are meromorphic and $\sigma\left(z;g_{2},g_{3}\right)$ is entire. …