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23 Weierstrass Elliptic and Modular FunctionsComputation

§23.23 Tables

Table 18.2 in Abramowitz and Stegun (1964) gives values of (z), (z), and ζ(z) to 7 or 8D in the rectangular and rhombic cases, normalized so that ω1=1 and ω3=ia (rectangular case), or ω1=1 and ω3=12+ia (rhombic case), for a = 1.00, 1.05, 1.1, 1.2, 1.4, 2, 4. The values are tabulated on the real and imaginary z-axes, mostly ranging from 0 to 1 or i in steps of length 0.05, and in the case of (z) the user may deduce values for complex z by application of the addition theorem (23.10.1).

Abramowitz and Stegun (1964) also includes other tables to assist the computation of the Weierstrass functions, for example, the generators as functions of the lattice invariants g2 and g3.

For earlier tables related to Weierstrass functions see Fletcher et al. (1962, pp. 503–505) and Lebedev and Fedorova (1960, pp. 223–226).