DLMF:

23 Weierstrass Elliptic and Modular Functions Weierstrass Elliptic Functions 23.4 Graphics 23.4 Graphics 23.5 Special Lattices

Figure 23.4.8 (See in context.)

Figure 23.4.8: $\mathop{\wp\/}\nolimits\!\left(x+iy\right)$ with $\omega_{{1}}=\mathop{K\/}\nolimits\!\left(k\right)$ , $\omega_{{3}}=i\!\mathop{{K^{{\prime}}}\/}\nolimits\!\left(k\right)$ for $-2\!\mathop{K\/}\nolimits\!\left(k\right)\leq x\leq 2\!\mathop{K\/}\nolimits\!% \left(k\right)$ , $0\leq y\leq 6\!\mathop{{K^{{\prime}}}\/}\nolimits\!\left(k\right)$ , $k^{2}=0.9$ . (The scaling makes the lattice appear to be square.)

Annotations:

Symbols:: $\mathop{\wp\/}\nolimits\!\left(z\right)$ (= $\mathop{\wp\/}\nolimits\!\left(z|\mathbb{L}\right)$ = $\mathop{\wp\/}\nolimits\!\left(z;g_{2},g_{3}\right)$ ): Weierstrass $\mathop{\wp\/}\nolimits$ -function, $\mathop{{K^{{\prime}}}\/}\nolimits\!\left(k\right)$ : Legendre’s complementary complete elliptic integral of the first kind, $\mathop{K\/}\nolimits\!\left(k\right)$ : Legendre’s complete elliptic integral of the first kind, $\mathbb{L}$ : lattice, : real part of , : imaginary part of , $\omega_{1}$ , $\omega_{3}$ , $\omega_{2}=-\omega_{1}-\omega_{3}$ : lattice generators and : modulus
Permalink:: http://dlmf.nist.gov/23.4.F8.mag
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