ELJKM1 3CW "12 February 2010" "mathcw-1.00"

Table of contents


NAME

eljkm1f, eljkm1, eljkm1l, eljkm1w, eljkm1q, eljkm1ll, eljkm1df, eljkm1d, eljkm1dl, eljkm1dll - Jacobian 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 eljkm1f (float u, float k);

extern double eljkm1 (double u, double k);

extern long double eljkm1l (long double u, long double k);

extern __float80 eljkm1w (__float80 u, __float80 k);

extern __float128 eljkm1q (__float128 u, __float128 k);

extern long_long_double eljkm1ll (long_long_double u, long_long_double k);

extern decimal_float eljkm1df (decimal_float u, decimal_float k);

extern decimal_double eljkm1d (decimal_double u, decimal_double k);

extern decimal_long_double eljkm1dl (decimal_long_double u, decimal_long_double k);

extern decimal_long_long_double eljkm1dll (decimal_long_long_double u, decimal_long_long_double k);

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


DESCRIPTION

Compute the Jacobian 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 eljq(k) provides the inverse operation, such that

q = eljq(k), k = 1 + eljkm1(q), = eljk(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 Jacobian 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

agm(3CW), eljacd(3CW), eljacn(3CW), eljacs(3CW), eljadc(3CW), eljadn(3CW), eljads(3CW), eljag(3CW), eljam(3CW), eljanc(3CW), eljand(3CW), eljans(3CW), eljasc(3CW), eljasd(3CW), eljasn(3CW), eljcd(3CW), eljcn(3CW), eljcs(3CW), eljdc(3CW), eljdn(3CW), eljds(3CW), eljh(3CW), eljh4(3CW), eljk(3CW), eljnc(3CW), eljnd(3CW), eljns(3CW), eljq(3CW), eljsc(3CW), eljsd(3CW), eljsn(3CW), eljt(3CW), eljt1(3CW), eljt2(3CW), eljt3(3CW), eljt4(3CW), eljta(3CW), eljtd1(3CW), eljtd2(3CW), eljtd3(3CW), eljtd4(3CW), eljtda(3CW), eljz(3CW).