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21: 4.2 Definitions

… ►The function $\exp$ is an entire function of $z$, with no real or complex zeros. …

22: 11.2 Definitions

… ►The functions $z^{-\nu -1}{𝐇}_{\nu }\left(z\right)$ and $z^{-\nu -1}{𝐋}_{\nu }\left(z\right)$ are entire functions of $z$ and $\nu$. …

23: 2.5 Mellin Transform Methods

… ►Furthermore, $ℳf_1\left(z\right)$ can be continued analytically to a meromorphic function on the entire $z$-plane, whose singularities are simple poles at $-{\alpha }_s$, $s=0,1,2,\mathrm{\dots }$, with principal part … ►Similarly, if $\kappa =0$ in (2.5.18), then $ℳh_2\left(z\right)$ can be continued analytically to a meromorphic function on the entire $z$-plane with simple poles at ${\beta }_s$, $s=0,1,2,\mathrm{\dots }$, with principal part …Alternatively, if $\kappa \ne 0$ in (2.5.18), then $ℳh_2\left(z\right)$ can be continued analytically to an entire function. … ►Similarly, since $ℳh_2\left(z\right)$ can be continued analytically to a meromorphic function (when $\kappa =0$) or to an entire function (when $\kappa \ne 0$), we can choose $\rho$ so that $ℳh_2\left(z\right)$ has no poles in . …

24: 8.21 Generalized Sine and Cosine Integrals

… ►Furthermore, $\mathrm{si}(a,z)$ and $\mathrm{ci}(a,z)$ are entire functions of $a$, and $\mathrm{Si}(a,z)$ and $\mathrm{Ci}(a,z)$ are meromorphic functions of $a$ with simple poles at $a=-1,-3,-5,\mathrm{\dots }$ and $a=0,-2,-4,\mathrm{\dots }$, respectively. …

25: 8.19 Generalized Exponential Integral

… ►For $z\ne 0$ each branch of $E_p\left(z\right)$ is an entire function of $p$. …

26: 10.47 Definitions and Basic Properties

… ►For example, $z^{-n}{𝗃}_n\left(z\right)$, $z^{n+1}{𝗒}_n\left(z\right)$, $z^{n+1}{𝗁}_n^{(1)}\left(z\right)$, $z^{n+1}{𝗁}_n^{(2)}\left(z\right)$, $z^{-n}{𝗂}_n^{(1)}\left(z\right)$, $z^{n+1}{𝗂}_n^{(2)}\left(z\right)$, and $z^{n+1}{𝗄}_n\left(z\right)$ are all entire functions of $z$. …

27: 13.2 Definitions and Basic Properties

… ► $M(a,b,z)$ is entire in $z$ and $a$, and is a meromorphic function of $b$. …

28: 11.10 Anger–Weber Functions

… ►Each is an entire function of $z$ and $\nu$. …

29: 9.12 Scorer Functions

… ► $\mathrm{Gi}\left(z\right)$ and $\mathrm{Hi}\left(z\right)$ are entire functions of $z$. …

30: 9.13 Generalized Airy Functions

… ►(All solutions of (9.13.1) are entire functions of $z$.) …