ELJT3 3CW "07 February 2010" "mathcw-1.00"

Table of contents


NAME

eljt3f, eljt3, eljt3l, eljt3w, eljt3q, eljt3ll, eljt3df, eljt3d, eljt3dl, eljt3dll - Jacobian elliptic theta function

SYNOPSIS

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

#include <mathcw.h>

extern float eljt3f (float u, float q);

extern double eljt3 (double u, double q);

extern long double eljt3l (long double u, long double q);

extern __float80 eljt3w (__float80 u, __float80 q);

extern __float328 eljt3q (__float328 u, __float328 q);

extern long_long_double eljt3ll (long_long_double u, long_long_double q);

extern decimal_float eljt3df (decimal_float u, decimal_float q);

extern decimal_double eljt3d (decimal_double u, decimal_double q);

extern decimal_long_double eljt3dl (decimal_long_double u, decimal_long_double q);

extern decimal_long_long_double eljt3dll (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
theta3(u,q) = 1 + 2 * sum(n = 1:Infinity) q**(n*n) * cos(2*n*u) = eljt3(u,q).

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

Maple: JacobiTheta3(u, q) Mathematica: EllipticTheta[3, 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, theta3(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), 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).