DLMF:

Figure 23.4.7 (See in context.)

Figure 23.4.7: $\mathop{\wp\/}\nolimits\!\left(x\right)$ with $\omega _{{1}}=\mathop{K\/}\nolimits\!\left(k\right)$ , $\omega _{{3}}=i\!\mathop{{K^{{\prime}}}\/}\nolimits\!\left(k\right)$ for $0\leq x\leq 9$ , $k^{2}$ = 0.2, 0.8, 0.95, 0.99. (Lemniscatic case.)

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, $x$ : real part of $z$ , $\omega _{1}$ , $\omega _{3}$ , $\omega _{2}=-\omega _{1}-\omega _{3}$ : lattice generators and $k$ : modulus
Keywords:: Weierstrass elliptic functions, lattice
Permalink:: http://dlmf.nist.gov/23.4.F7.mag
Encodings:: Magnified png, pdf