The Weierstrass zeta function ζ(z;g_2, g_3) is the quasiperiodic function defined by (d ζ(z;g_2, g_3))/(d z) congruent - ℘(z;g_2, g_3), where ℘(z;g_2, g_3) is the Weierstrass elliptic function with invariants g_2 and g_3, with lim_(z->0)[ζ(z;g_2, g_3) - z^(-1)] = 0. As in the case of other Weierstrass elliptic functions, the elliptic invariants g_2 and g_3 are frequently suppressed for compactness. The function is implemented in the Wolfram Language as WeierstrassZeta[u, {g2, g3}].

Weierstrass elliptic function | Weierstrass sigma function