An elliptic function can be characterized by its real and imaginary half-periods and (Whittaker and Watson 1990, p. 428), sometimes
also denoted
(Abramowitz and Stegun 1972, p. 630). The Wolfram
Language command WeierstrassHalfPeriods[g2, g3] gives the half-periods and corresponding to the invariants and for a Weierstrass
elliptic function.
The notation
(1)
is sometimes also defined (Whittaker and Watson 1990, p. 443), although Abramowitz and Stegun (1972, p. 630) instead use the definition