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##### 1: 25.1 Special Notation
 $k,m,n$ nonnegative integers. … complex variable. …
The main function treated in this chapter is the Riemann zeta function $\zeta\left(s\right)$. … The main related functions are the Hurwitz zeta function $\zeta\left(s,a\right)$, the dilogarithm $\operatorname{Li}_{2}\left(z\right)$, the polylogarithm $\operatorname{Li}_{s}\left(z\right)$ (also known as Jonquière’s function $\phi\left(z,s\right)$), Lerch’s transcendent $\Phi\left(z,s,a\right)$, and the Dirichlet $L$-functions $L\left(s,\chi\right)$.
##### 2: 35.4 Partitions and Zonal Polynomials
###### §35.4 Partitions and Zonal Polynomials
For any partition $\kappa$, the zonal polynomial $Z_{\kappa}:\boldsymbol{\mathcal{S}}\to\mathbb{R}$ is defined by the properties …
##### 3: 23.13 Zeros
###### §23.13 Zeros
For information on the zeros of $\wp\left(z\right)$ see Eichler and Zagier (1982).
##### 4: 25.11 Hurwitz Zeta Function
###### §25.11(i) Definition
The Riemann zeta function is a special case: …
##### 5: 10.58 Zeros
###### §10.58 Zeros
$a_{n,m}=j_{n+\frac{1}{2},m},$
$b_{n,m}=y_{n+\frac{1}{2},m},$
$\mathsf{j}_{n}'\left(a_{n,m}\right)=\sqrt{\frac{\pi}{2j_{n+\frac{1}{2},m}}}J_{% n+\frac{1}{2}}'\left(j_{n+\frac{1}{2},m}\right),$
$\mathsf{y}_{n}'\left(b_{n,m}\right)=\sqrt{\frac{\pi}{2y_{n+\frac{1}{2},m}}}Y_{% n+\frac{1}{2}}'\left(y_{n+\frac{1}{2},m}\right).$
##### 6: 9.9 Zeros
###### §9.9 Zeros
They are denoted by $a_{k}$, $a^{\prime}_{k}$, $b_{k}$, $b^{\prime}_{k}$, respectively, arranged in ascending order of absolute value for $k=1,2,\ldots.$For error bounds for the asymptotic expansions of $a_{k}$, $b_{k}$, $a^{\prime}_{k}$, and $b^{\prime}_{k}$ see Pittaluga and Sacripante (1991), and a conjecture given in Fabijonas and Olver (1999). …
##### 7: 32.5 Integral Equations
Let $K(z,\zeta)$ be the solution of
32.5.1 $K(z,\zeta)=k\operatorname{Ai}\left(\frac{z+\zeta}{2}\right)+\frac{k^{2}}{4}\*% \int_{z}^{\infty}\!\!\!\int_{z}^{\infty}K(z,s)\operatorname{Ai}\left(\frac{s+t% }{2}\right)\operatorname{Ai}\left(\frac{t+\zeta}{2}\right)\,\mathrm{d}s\,% \mathrm{d}t,$
where $k$ is a real constant, and $\operatorname{Ai}\left(z\right)$ is defined in §9.2. …
32.5.2 $w(z)=K(z,z),$
32.5.3 $w(z)\sim k\operatorname{Ai}\left(z\right),$ $z\to+\infty$.
##### 8: 4.14 Definitions and Periodicity
4.14.7 $\cot z=\frac{\cos z}{\sin z}=\frac{1}{\tan z}.$
The functions $\sin z$ and $\cos z$ are entire. In $\mathbb{C}$ the zeros of $\sin z$ are $z=k\pi$, $k\in\mathbb{Z}$; the zeros of $\cos z$ are $z=\left(k+\tfrac{1}{2}\right)\pi$, $k\in\mathbb{Z}$. The functions $\tan z$, $\csc z$, $\sec z$, and $\cot z$ are meromorphic, and the locations of their zeros and poles follow from (4.14.4) to (4.14.7). For $k\in\mathbb{Z}$
##### 9: 4.28 Definitions and Periodicity
4.28.2 $\cosh z=\frac{e^{z}+e^{-z}}{2},$
###### Periodicity and Zeros
The zeros of $\sinh z$ and $\cosh z$ are $z=ik\pi$ and $z=i\left(k+\frac{1}{2}\right)\pi$, respectively, $k\in\mathbb{Z}$.
##### 10: 10.21 Zeros
###### §10.21 Zeros
${j^{\prime}_{0,1}}=0,$
${j^{\prime}_{0,m}}=j_{1,m-1},$ $m=2,3,\dotsc$.
$j_{\nu,1}
Next, $z(\zeta)$ is the inverse of the function $\zeta=\zeta(z)$ defined by (10.20.3). …