Digital Library of Mathematical Functions
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23 Weierstrass Elliptic and Modular FunctionsWeierstrass Elliptic Functions

§23.4 Graphics

Contents

§23.4(i) Real Variables

Line graphs of the Weierstrass functions (x), ζ(x), and σ(x), illustrating the lemniscatic and equianharmonic cases. (The figures in this subsection may be compared with the figures in §22.3(i).)

See accompanying text
Figure 23.4.1: (x;g2,0) for 0x9, g2 = 0.1, 0.2, 0.5, 0.8. (Lemniscatic case.) Magnify
See accompanying text
Figure 23.4.2: (x;0,g3) for 0x9, g3 = 0.1, 0.2, 0.5, 0.8. (Equianharmonic case.) Magnify
See accompanying text
Figure 23.4.3: ζ(x;g2,0) for 0x8, g2 = 0.1, 0.2, 0.5, 0.8. (Lemniscatic case.) Magnify
See accompanying text
Figure 23.4.4: ζ(x;0,g3) for 0x8, g3 = 0.1, 0.2, 0.5, 0.8. (Equianharmonic case.) Magnify
See accompanying text
Figure 23.4.5: σ(x;g2,0) for -5x5, g2 = 0.1, 0.2, 0.5, 0.8. (Lemniscatic case.) Magnify
See accompanying text
Figure 23.4.6: σ(x;0,g3) for -5x5, g3 = 0.1, 0.2, 0.5, 0.8. (Equianharmonic case.) Magnify
See accompanying text
Figure 23.4.7: (x) with ω1=K(k), ω3=K(k) for 0x9, k2 = 0.2, 0.8, 0.95, 0.99. (Lemniscatic case.) Magnify

§23.4(ii) Complex Variables

Surfaces for the Weierstrass functions (z), ζ(z), and σ(z). Height corresponds to the absolute value of the function and color to the phase. See also About Color Map. (The figures in this subsection may be compared with the figures in §22.3(iii).)

Figure 23.4.8: (x+y) with ω1=K(k), ω3=K(k) for -2K(k)x2K(k), 0y6K(k), k2=0.9. (The scaling makes the lattice appear to be square.) Magnify
Figure 23.4.9: (x+y;1,4) for -3.8x3.8, -3.8y3.8. (The variables are unscaled and the lattice is skew.) Magnify
Figure 23.4.10: ζ(x+y;1,0) for -5x5, -5y5. Magnify
Figure 23.4.11: σ(x+y;1,) for -2.5x2.5, -2.5y2.5. Magnify
Figure 23.4.12: (3.7;a+b,0) for -5a3, -4b4. There is a double zero at a=b=0 and double poles on the real axis. Magnify