ELK 3CW "07 February 2010" "mathcw-1.00"

Table of contents


NAME

elkf, elk, elkl, elkw, elkq, elkll, elkdf, elkd, elkdl, elkdll - elliptic function modulus from nome

SYNOPSIS

cc [ flags ] -I/usr/local/include file(s) -L/usr/local/lib -lmcw [ ... ]

#include <mathcw.h>

extern float elkf (float q);

extern double elk (double q);

extern long double elkl (long double q);

extern __float80 elkw (__float80 q);

extern __float128 elkq (__float128 q);

extern long_long_double elkll (long_long_double q);

extern decimal_float elkdf (decimal_float q);

extern decimal_double elkd (decimal_double q);

extern decimal_long_double elkdl (decimal_long_double q);

extern decimal_long_long_double elkdll (decimal_long_long_double q);

NB: Functions with prototypes containing underscores in type names may be available only with certain extended compilers.


DESCRIPTION

Compute the elliptic function modulus k, a real value in [-1,+1], from the nome q, a real value in [0,1).

The companion function elq(k) provides the inverse operation, such that

q = elq(k), k = elk(q).

For q > 1/2, we have k > 0.999995, so expressions requiring elk(q) can be replaced by 1 + elkm1(q) for higher effective precision.

See M. Abramowitz & I. A. Stegun, Handbook of Mathematical Functions, Chapter 16, for definitions of the Jacobian elliptic, theta, and zeta functions.


RETURN VALUES

Return the Jacobian elliptic function modulus k.

ERRORS

If the argument is a NaN, return that argument. If the argument is out of range, set errno to EDOM and return a quiet NaN.

SEE ALSO

elkm1(3CW), elq(3CW), elq1p(3CW), elqc(3CW), elqc1p(3CW).