The quasiperiodic function defined by d/(d z) ln σ(z;g_2, g_3) = ζ(z;g_2, g_3), where ζ(z;g_2, g_3) is the Weierstrass zeta function and lim_(z->0) (σ(z))/z = 1. (As in the case of other Weierstrass elliptic functions, the invariants g_2 and g_3 are frequently suppressed for compactness.) Then σ(z) = z product_(m, n = - ∞)^∞'[(1 - z/Ω_(m n)) exp(z/Ω_(m n) + z^2/(2Ω_(m n)^2))], where the term with m = n = 0 is omitted from the product and Ω_(m n) = 2m ω_1 + 2n ω_2.

Weierstrass constant | Weierstrass elliptic function | Weierstrass zeta function