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

Table of contents


NAME

eljdsf, eljds, eljdsl, eljdsw, eljdsq, eljdsll, eljdsdf, eljdsd, eljdsdl, eljdsdll - Jacobian elliptic function

SYNOPSIS

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

#include <mathcw.h>

extern float eljdsf (float u, float k);

extern double eljds (double u, double k);

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

extern __float80 eljdsw (__float80 u, __float80 k);

extern __float128 eljdsq (__float128 u, __float128 k);

extern long_long_double eljdsll (long_long_double u, long_long_double k);

extern decimal_float eljdsdf (decimal_float u, decimal_float k);

extern decimal_double eljdsd (decimal_double u, decimal_double k);

extern decimal_long_double eljdsdl (decimal_long_double u, decimal_long_double k);

extern decimal_long_long_double eljdsdll (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 defined by
eljds(u, k) = ds(u, k) = dn(u, k) / sn(u, k) = eljdn(u, k) / eljsn(u, k).

The argument u is unrestricted.The argument k (the modulus) is normally in [-1,+1]. If it is not, then a standard reciprocal modulus transformation is used to convert the function to another with second argument 1/k.

Using this function is almost always more efficient than making separate calls to the two Jacobian elliptic functions in its definition.

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 ds(u,k).

ERRORS

If either argument is a NaN, return that argument. If k 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), eljh(3CW), eljh4(3CW), eljnc(3CW), eljnd(3CW), eljns(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), elk(3CW), elkm1(3CW), elq(3CW), elq1p(3CW), elqc(3CW), elqc1p(3CW).