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1: 23.23 Tables

… ►2 in Abramowitz and Stegun (1964) gives values of $\mathrm{\wp }\left(z\right)$, ${\mathrm{\wp }}^{\prime }\left(z\right)$, and $\zeta \left(z\right)$ to 7 or 8D in the rectangular and rhombic cases, normalized so that ${\omega }_1=1$ and ${\omega }_3=\mathrm{i}a$ (rectangular case), or ${\omega }_1=1$ and ${\omega }_3=\frac{1}{2}+\mathrm{i}a$ (rhombic case), for $a$ = 1. …

2: 23.7 Quarter Periods

… ►where $k,k^{\prime }$ and the square roots are real and positive when the lattice is rectangular; otherwise they are determined by continuity from the rectangular case.

3: 20.1 Special Notation

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$m$, $n$	integers.
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$q$ $(\in ℂ)$	the nome, $q={\mathrm{e}}^{\mathrm{i}\pi \tau }$, . Since $\tau$ is not a single-valued function of $q$, it is assumed that $\tau$ is known, even when $q$ is specified. Most applications concern the rectangular case $\mathrm{\Re }\tau =0$, $\mathrm{\Im }\tau >0$, so that and $\tau$ and $q$ are uniquely related.
$q^{\alpha }$	${\mathrm{e}}^{\mathrm{i}\alpha \pi \tau }$ for $\alpha \in ℝ$ (resolving issues of choice of branch).
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4: 23.5 Special Lattices

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§23.5(ii) Rectangular Lattice

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5: 23.1 Special Notation

… ►Abramowitz and Stegun (1964, Chapter 18) considers only rectangular and rhombic lattices (§23.5); ${\omega }_1$, ${\omega }_3$ are replaced by $\omega$, ${\omega }^{\prime }$ for the former and by ${\omega }_2$, ${\omega }^{\prime }$ for the latter. …

6: 23.20 Mathematical Applications

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Rectangular Lattice

… ►These cases correspond to rhombic and rectangular lattices, respectively. …

7: 4.15 Graphics

… ►Lines parallel to the real axis in the $z$-plane map onto ellipses in the $w$-plane with foci at $w=\pm 1$, and lines parallel to the imaginary axis in the $z$-plane map onto rectangular hyperbolas confocal with the ellipses. …

8: 4.24 Inverse Trigonometric Functions: Further Properties

… ►which requires $z$ $(=x+\mathrm{i}y)$ to lie between the two rectangular hyperbolas given by …

9: 4.38 Inverse Hyperbolic Functions: Further Properties

… ►which requires $z$ $(=x+\mathrm{i}y)$ to lie between the two rectangular hyperbolas given by …

10: 20.2 Definitions and Periodic Properties

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Figure 20.2.1: $z$-plane. …Left-hand diagram is the rectangular case ($\tau$ purely imaginary); right-hand diagram is the general case. …

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