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23 Weierstrass Elliptic and Modular FunctionsWeierstrass Elliptic Functions

§23.4 Graphics

Contents
  1. §23.4(i) Real Variables
  2. §23.4(ii) Complex Variables

§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).)

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Figure 23.4.1: (x;g2,0) for 0x9, g2 = 0.1, 0.2, 0.5, 0.8. (Lemniscatic case.) Magnify
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Figure 23.4.2: (x;0,g3) for 0x9, g3 = 0.1, 0.2, 0.5, 0.8. (Equianharmonic case.) Magnify
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Figure 23.4.3: ζ(x;g2,0) for 0x8, g2 = 0.1, 0.2, 0.5, 0.8. (Lemniscatic case.) Magnify
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Figure 23.4.4: ζ(x;0,g3) for 0x8, g3 = 0.1, 0.2, 0.5, 0.8. (Equianharmonic case.) Magnify
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Figure 23.4.5: σ(x;g2,0) for 5x5, g2 = 0.1, 0.2, 0.5, 0.8. (Lemniscatic case.) Magnify
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Figure 23.4.6: σ(x;0,g3) for 5x5, g3 = 0.1, 0.2, 0.5, 0.8. (Equianharmonic 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).)

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Figure 23.4.8: (x+iy) with ω1=K(k), ω3=iK(k) for 2K(k)x2K(k), 0y6K(k), k2=0.9. (The scaling makes the lattice appear to be square.) Magnify 3D Help
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Figure 23.4.9: (x+iy;1,4i) for 3.8x3.8, 3.8y3.8. (The variables are unscaled and the lattice is skew.) Magnify 3D Help
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Figure 23.4.10: ζ(x+iy;1,0) for 5x5, 5y5. Magnify 3D Help
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Figure 23.4.11: σ(x+iy;1,i) for 2.5x2.5, 2.5y2.5. Magnify 3D Help
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Figure 23.4.12: (3.7;a+ib,0) for 5a3, 4b4. There is a double zero at a=b=0 and double poles on the real axis. Magnify 3D Help