# entire

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##### 2: 4.14 Definitions and Periodicity
The functions $\sin z$ and $\cos z$ are entire. …
##### 3: 10.2 Definitions
When $\nu=n$ $(\in\mathbb{Z})$, $J_{\nu}\left(z\right)$ is entire in $z$. For fixed $z$ $(\neq 0)$ each branch of $J_{\nu}\left(z\right)$ is entire in $\nu$. … For fixed $z$ $(\neq 0)$ each branch of $Y_{\nu}\left(z\right)$ is entire in $\nu$. … For fixed $z$ $(\neq 0)$ each branch of ${H^{(1)}_{\nu}}\left(z\right)$ and ${H^{(2)}_{\nu}}\left(z\right)$ is entire in $\nu$. …
##### 4: 19.32 Conformal Map onto a Rectangle
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. …
##### 5: 7.2 Definitions
$\operatorname{erf}z$, $\operatorname{erfc}z$, and $w\left(z\right)$ are entire functions of $z$, as is $F\left(z\right)$ in the next subsection. … $\mathcal{F}\left(z\right)$, $C\left(z\right)$, 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. …
##### 6: 18.24 Hahn Class: Asymptotic Approximations
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 $n\to\infty$ ) 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. …
##### 7: 6.2 Definitions and Interrelations
It is entire. … $\operatorname{Si}\left(z\right)$ is an odd entire function. …$\operatorname{Cin}\left(z\right)$ is an even entire function. …
##### 8: 1.9 Calculus of a Complex Variable
###### Analyticity
A function analytic at every point of $\mathbb{C}$ is said to be entire. …
###### Liouville’s Theorem
Any bounded entire function is a constant. …
##### 9: 2.10 Sums and Sequences
###### §2.10(iii) Asymptotic Expansions of Entire Functions
The asymptotic behavior of entire functions defined by Maclaurin series can be approached by converting the sum into a contour integral by use of the residue theorem and applying the methods of §§2.4 and 2.5. …
##### 10: 5.2 Definitions
$1/\Gamma\left(z\right)$ is entire, with simple zeros at $z=-n$. …