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11: 14.24 Analytic Continuation

… ►For fixed $z$, other than $\pm 1$ or $\mathrm{\infty }$, each branch of $P_{\nu }^{-\mu }\left(z\right)$ and ${𝑸}_{\nu }^{\mu }\left(z\right)$ is an entire function of each parameter $\nu$ and $\mu$. …

12: 28.7 Analytic Continuation of Eigenvalues

… ►Therefore $w_{\text{I}}^{\prime }(\frac{1}{2}\pi ;a,q)$ is irreducible, in the sense that it cannot be decomposed into a product of entire functions that contain its zeros; see Meixner et al. (1980, p. 88). …

13: 8.2 Definitions and Basic Properties

… ►The function ${\gamma }^{\ast }(a,z)$ is entire in $z$ and $a$. When $z\ne 0$, $\mathrm{\Gamma }(a,z)$ is an entire function of $a$, and $\gamma (a,z)$ is meromorphic with simple poles at $a=-n$, $n=0,1,2,\mathrm{\dots }$, with residue ${(-1)}^n/n!$. …

14: 16.2 Definition and Analytic Properties

… ►When $p\le q$ the series (16.2.1) converges for all finite values of $z$ and defines an entire function. … ►When $p\le q+1$ and $z$ is fixed and not a branch point, any branch of ${}_p{}^{}𝐅_q^{}(𝐚;𝐛;z)$ is an entire function of each of the parameters $a_1,\mathrm{\dots },a_p,b_1,\mathrm{\dots },b_q$.

15: 28.29 Definitions and Basic Properties

… ►This is the characteristic equation of (28.29.1), and $\cos \left(\pi \nu \right)$ is an entire function of $\lambda$. … ►It is an entire function of $\lambda$. …

16: 10.25 Definitions

… ►For fixed $z$ $(\ne 0)$ each branch of $I_{\nu }\left(z\right)$ and $K_{\nu }\left(z\right)$ is entire in $\nu$. …

17: 13.2 Definitions and Basic Properties

… ► $M(a,b,z)$ is entire in $z$ and $a$, and is a meromorphic function of $b$. $𝐌(a,b,z)$ is entire in $z$, $a$, and $b$. … ►Except when $z=0$ each branch of $U(a,b,z)$ is entire in $a$ and $b$. …

18: 15.16 Products

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19: 25.15 Dirichlet $L$-functions

… ►If $\chi \ne {\chi }_1$, then $L(s,\chi )$ is an entire function of $s$. …

20: 12.2 Differential Equations

… ►All solutions are entire functions of $z$ and entire functions of $a$ or $\nu$. …