# entire

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## 1—10 of 48 matching pages

##### 1: 21.10 Methods of Computation

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##### 2: 4.14 Definitions and Periodicity

##### 3: 10.2 Definitions

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►When $\nu =n$
$(\in \mathbb{Z})$, ${J}_{\nu}\left(z\right)$ is entire in $z$.
►For fixed $z$
$(\ne 0)$ each branch of ${J}_{\nu}\left(z\right)$ is entire in $\nu $.
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►For fixed $z$
$(\ne 0)$ each branch of ${Y}_{\nu}\left(z\right)$ is entire in $\nu $.
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►For fixed $z$
$(\ne 0)$ each branch of ${H}_{\nu}^{(1)}\left(z\right)$ and ${H}_{\nu}^{(2)}\left(z\right)$ is entire in $\nu $.
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##### 4: 19.32 Conformal Map onto a Rectangle

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►As $p$ proceeds along the entire real axis with the upper half-plane on the right, $z$ describes the rectangle in the clockwise direction; hence $z({x}_{3})$ is negative imaginary.
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##### 5: 7.2 Definitions

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$\mathrm{erf}z$, $\mathrm{erfc}z$, and $w\left(z\right)$ are entire functions of $z$, as is $F\left(z\right)$ in the next subsection.
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$\mathcal{F}\left(z\right)$, $C\left(z\right)$, and $S\left(z\right)$ are entire functions of $z$, as are $\mathrm{f}\left(z\right)$ and $\mathrm{g}\left(z\right)$ in the next subsection.
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##### 6: 18.24 Hahn Class: Asymptotic Approximations

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►When the parameters $\alpha $ and $\beta $ are fixed and the ratio $n/N=c$ is a constant in the interval (0,1), uniform asymptotic formulas (as $n\to \mathrm{\infty}$ ) of the Hahn polynomials ${Q}_{n}(z;\alpha ,\beta ,N)$ can be found in Lin and Wong (2013) for $z$ in three overlapping regions, which together cover the entire complex plane.
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##### 7: 6.2 Definitions and Interrelations

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►It is entire.
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$\mathrm{Si}\left(z\right)$ is an odd entire function.
…$\mathrm{Cin}\left(z\right)$ is an even entire function.
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##### 8: 1.9 Calculus of a Complex Variable

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###### Analyticity

… ►A function analytic at every point of $\u2102$ is said to be*entire*. … ►###### Liouville’s Theorem

►Any bounded entire function is a constant. …##### 9: 2.10 Sums and Sequences

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