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1: 21.10 Methods of Computation

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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 $z$ $(\ne 0)$ each branch of $J_{\nu }\left(z\right)$ is entire in $\nu$. … ►For fixed $z$ $(\ne 0)$ each branch of $Y_{\nu }\left(z\right)$ is entire in $\nu$. … ►For fixed $z$ $(\ne 0)$ each branch of $H_{\nu }^{(1)}\left(z\right)$ and $H_{\nu }^{(2)}\left(z\right)$ is entire in $\nu$. …

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

… ► $\mathrm{erf}z$, $\mathrm{erfc}z$, and $w\left(z\right)$ are entire functions of $z$, as is $F\left(z\right)$ in the next subsection. … ► $ℱ\left(z\right)$, $C\left(z\right)$, 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 $n\to \mathrm{\infty }$ ) 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. …

7: 6.2 Definitions and Interrelations

… ►It is entire. … ► $\mathrm{Si}\left(z\right)$ is an odd entire function. …$\mathrm{Cin}\left(z\right)$ is an even entire function. …

8: 1.9 Calculus of a Complex Variable

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Analyticity

… ►A function analytic at every point of $ℂ$ 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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§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

… ► $1/\mathrm{\Gamma }\left(z\right)$ is entire, with simple zeros at $z=-n$. …