The complementary parameter associated with an elliptic
parameter
is
If , where
is the elliptic modulus,
then
, where
is the complementary
modulus. Thus the complementary parameter is the square of the complementary
modulus, rather than the complementary modulus
itself (Abramowitz and Stegun 1972, p. 590). The prime denotes complementation,
not a derivative. Abramowitz and Stegun use
for the complementary parameter.