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

Table of contents


NAME

eljzf, eljz, eljzl, eljzw, eljzq, eljzll, eljzdf, eljzd, eljzdl, eljzdll - Jacobian Zeta function

SYNOPSIS

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

#include <mathcw.h>

extern float eljzf (float u, float k);

extern double eljz (double u, double k);

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

extern __float80 eljzw (__float80 u, __float80 k);

extern __float128 eljzq (__float128 u, __float128 k);

extern long_long_double eljzll (long_long_double u, long_long_double k);

extern decimal_float eljzdf (decimal_float u, decimal_float k);

extern decimal_double eljzd (decimal_double u, decimal_double k);

extern decimal_long_double eljzdl (decimal_long_double u, decimal_long_double k);

extern decimal_long_long_double eljzdll (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 Zeta function defined by
Zeta(u,k) = eljz(u,k).

The argument u is unrestricted, but k is required to be in [-1,+1].

Equivalents in other systems are:

Maple: JacobiZeta(u, k) Mathematica: JacobiZeta[JacobiAmplitude[u, k^2], k^2]

See M. Abramowitz & I. A. Stegun, Handbook of Mathematical Functions, Chapter 16, for definitions of the Jacobian elliptic, Eta, theta, Theta, and Zeta functions, and section 16.34 for Zeta(u,k).


RETURN VALUES

Return the value of the Jacobian zeta function, Zeta(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), eljds(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), elk(3CW), elkm1(3CW), elq(3CW), elq1p(3CW), elqc(3CW), elqc1p(3CW).