A Landen-type method for computation of Weierstrass functions
Complex Variables
2024-08-13 v1
Abstract
We establish a version of the Landen's transformation for Weierstrass functions and invariants that is applicable to general lattices in complex plane. Using it we present an effective method for computing Weierstrass functions, their periods, and elliptic integral in Weierstrass form given Weierstrass invariants and of an elliptic curve. Similarly to the classical Landen's method our algorithm has quadratic rate of convergence.
Cite
@article{arxiv.2408.05252,
title = {A Landen-type method for computation of Weierstrass functions},
author = {Matvey Smirnov and Kirill Malkov and Sergey Rogovoy},
journal= {arXiv preprint arXiv:2408.05252},
year = {2024}
}