Published online by Cambridge University Press: 24 October 2008
Let ℘ be a Weierstrass elliptic function satisfying the differential equation
and let ζ(z) be the associated Weierstrass ζ-function satisfying (z) = −℘(z). Corresponding to a pair of fundamental periods ω1, ω2 of ℘(z), there is a pair of quasi-periods η1, η2 of ζ(z) defined by
and we have ηi = 2ζ(ωi/2) for i = 1, 2.