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

Table of contents


NAME

eljkf, eljk, eljkl, eljkw, eljkq, eljkll, eljkdf, eljkd, eljkdl, eljkdll - Jacobian elliptic function modulus from nome

SYNOPSIS

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

#include <mathcw.h>

extern float eljkf (float u, float k);

extern double eljk (double u, double k);

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

extern __float80 eljkw (__float80 u, __float80 k);

extern __float128 eljkq (__float128 u, __float128 k);

extern long_long_double eljkll (long_long_double u, long_long_double k);

extern decimal_float eljkdf (decimal_float u, decimal_float k);

extern decimal_double eljkd (decimal_double u, decimal_double k);

extern decimal_long_double eljkdl (decimal_long_double u, decimal_long_double k);

extern decimal_long_long_double eljkdll (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, a real value in [-1,+1], 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 = eljk(q).

For q > 1/2, we have k > 0.999995, so expressions requiring eljk(q) can be replaced by 1 + eljkm1(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

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), eljkm1(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).