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R. COQUEREAUX, A. GROSSMANN, B. E. LAUTRUP, Iterative Method for Calculation of the Weierstrass Elliptic Function, IMA Journal of Numerical Analysis, Volume 10, Issue 1, January 1990, Pages 119–128, https://doi.org/10.1093/imanum/10.1.119
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Abstract
Let ℘ be the Weierstrass function associated with an arbitrary lattice in the complex plane. We describe a fast iterative method (based on the duplication property of ℘) which allows us to compute ℘(z) for an arbitrary complex number z. We also describe an iterative method for computing the values of periods associated with any pair of complex Weierstrass invariants g2 and g3: the last method relies upon the arithmetic-geometric mean property of elliptic integrals.
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© 1989 Oxford University Press
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