Computation of Interval Bounds for Weierstrass’ Elliptic Function ℘(z)

Computation of Interval Bounds for Weierstrass’ Elliptic Function ℘(z. A method to enclose the values of Weierstrass’ elliptic function ℘(z) = ℘(z|g₂,g₃) for arbitrary complex invariants g₂,g₃ or arbitrary given zeros of the characteristic polynomial (arbitrary period lattices) is presented. The function is approximated by its truncated Laurent series at zero. An error bound is derived for the remainder term. If necessary, the periodicity of ℘, the homogeneity relations and the addition formulas are used to perform the reduction of the argument and the corresponding adaptation of the result.