# meromorphic

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## 1—10 of 22 matching pages

##### 1: 21.8 Abelian Functions

##### 2: 13.5 Continued Fractions

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►This continued fraction converges to the meromorphic function of $z$ on the left-hand side everywhere in $\u2102$.
For more details on how a continued fraction converges to a meromorphic function see Jones and Thron (1980).
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►This continued fraction converges to the meromorphic function of $z$ on the left-hand side throughout the sector $$.
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##### 3: 13.17 Continued Fractions

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►This continued fraction converges to the meromorphic function of $z$ on the left-hand side for all $z\in \u2102$.
For more details on how a continued fraction converges to a meromorphic function see Jones and Thron (1980).
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►This continued fraction converges to the meromorphic function of $z$ on the left-hand side throughout the sector $$.
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##### 4: 5.2 Definitions

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►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 $z=-n$.
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##### 5: 4.14 Definitions and Periodicity

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►The functions $\mathrm{tan}z$, $\mathrm{csc}z$, $\mathrm{sec}z$, and $\mathrm{cot}z$ are meromorphic, and the locations of their zeros and poles follow from (4.14.4) to (4.14.7).
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##### 6: 22.17 Moduli Outside the Interval [0,1]

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►When $z$ is fixed each of the twelve Jacobian elliptic functions is a meromorphic function of ${k}^{2}$.
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##### 7: 23.2 Definitions and Periodic Properties

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$\mathrm{\wp}\left(z\right)$ and $\zeta \left(z\right)$ are meromorphic functions with poles at the lattice points.
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►Hence $\mathrm{\wp}\left(z\right)$ is an

*elliptic function*, that is, $\mathrm{\wp}\left(z\right)$ is meromorphic and periodic on a lattice; equivalently, $\mathrm{\wp}\left(z\right)$ is meromorphic and has two periods whose ratio is not real. …##### 8: 22.2 Definitions

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►Each is meromorphic in $z$ for fixed $k$, with simple poles and simple zeros, and each is meromorphic in $k$ for fixed $z$.
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##### 9: 25.2 Definition and Expansions

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►It is a meromorphic function whose only singularity in $\u2102$ is a simple pole at $s=1$, with residue 1.
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25.2.4
$$\zeta \left(s\right)=\frac{1}{s-1}+\sum _{n=0}^{\mathrm{\infty}}\frac{{(-1)}^{n}}{n!}{\gamma}_{n}{(s-1)}^{n},$$

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##### 10: 1.10 Functions of a Complex Variable

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►A function whose only singularities, other than the point at infinity, are poles is called a

*meromorphic function*. … …