ELKM1 3CW "12 February 2010" "mathcw-1.00"

Table of contents


NAME

elkm1f, elkm1, elkm1l, elkm1w, elkm1q, elkm1ll, elkm1df, elkm1d, elkm1dl, elkm1dll - elliptic function modulus, less one, from nome

SYNOPSIS

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

#include <mathcw.h>

extern float elkm1f (float q);

extern double elkm1 (double q);

extern long double elkm1l (long double q);

extern __float80 elkm1w (__float80 q);

extern __float128 elkm1q (__float128 q);

extern long_long_double elkm1ll (long_long_double q);

extern decimal_float elkm1df (decimal_float q);

extern decimal_double elkm1d (decimal_double q);

extern decimal_long_double elkm1dl (decimal_long_double q);

extern decimal_long_long_double elkm1dll (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, less one, a real value in [-1,0], 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 = 1 + elkm1(q), = elk(q).

For q > 1/2, we have k > 0.999995, so this function computes an accurate difference of that value from one.

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 elliptic function modulus k, less one.

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

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