nag_real_jacobian_elliptic (s21cac) evaluates the Jacobian elliptic functions sn, cn and dn.
nag_real_jacobian_elliptic (s21cac) evaluates the Jacobian elliptic functions of argument
and argument
,
where
, called the
amplitude of
, is defined by the integral
The elliptic functions are sometimes written simply as
,
and
, avoiding explicit reference to the argument
.
Another nine elliptic functions may be computed via the formulae
(see
Abramowitz and Stegun (1972)).
nag_real_jacobian_elliptic (s21cac) is based on a procedure given by
Bulirsch (1960), and uses the process of the arithmetic-geometric mean (16.9 in
Abramowitz and Stegun (1972)). Constraints are placed on the values of
and
in order to avoid the possibility of machine overflow.
Bulirsch R (1960) Numerical calculation of elliptic integrals and elliptic functions Numer. Math. 7 76–90
In principle the function is capable of achieving full relative precision in the computed values. However, the accuracy obtainable in practice depends on the accuracy of the standard elementary functions such as SIN and COS.
Not applicable.
None.