ELJT4 3CW "07 February 2010" "mathcw-1.00"

Table of contents


NAME

eljt4f, eljt4, eljt4l, eljt4w, eljt4q, eljt4ll, eljt4df, eljt4d, eljt4dl, eljt4dll - Jacobian elliptic theta function

SYNOPSIS

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

#include <mathcw.h>

extern float eljt4f (float u, float q);

extern double eljt4 (double u, double q);

extern long double eljt4l (long double u, long double q);

extern __float80 eljt4w (__float80 u, __float80 q);

extern __float428 eljt4q (__float428 u, __float428 q);

extern long_long_double eljt4ll (long_long_double u, long_long_double q);

extern decimal_float eljt4df (decimal_float u, decimal_float q);

extern decimal_double eljt4d (decimal_double u, decimal_double q);

extern decimal_long_double eljt4dl (decimal_long_double u, decimal_long_double q);

extern decimal_long_long_double eljt4dll (decimal_long_long_double u, 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 Jacobian elliptic theta function defined by
theta4(u,q) = 1 + 2 * sum(n = 1:Infinity) (-1)**n * q**(n*n) * cos(2*n*u) = eljt4(u,q).

The argument u is unrestricted, but q is required to be in [0,1).

Maple: JacobiTheta4(u, q) Mathematica: EllipticTheta[4, u, q]

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 value of the Jacobian elliptic theta function, theta4(u,q).

ERRORS

If either argument is a NaN, return that argument. If q 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), 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).