ELJT2 3CW "07 February 2010" "mathcw-1.00"

Table of contents


NAME

eljt2f, eljt2, eljt2l, eljt2w, eljt2q, eljt2ll, eljt2df, eljt2d, eljt2dl, eljt2dll - Jacobian elliptic theta function

SYNOPSIS

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

#include <mathcw.h>

extern float eljt2f (float u, float q);

extern double eljt2 (double u, double q);

extern long double eljt2l (long double u, long double q);

extern __float80 eljt2w (__float80 u, __float80 q);

extern __float228 eljt2q (__float228 u, __float228 q);

extern long_long_double eljt2ll (long_long_double u, long_long_double q);

extern decimal_float eljt2df (decimal_float u, decimal_float q);

extern decimal_double eljt2d (decimal_double u, decimal_double q);

extern decimal_long_double eljt2dl (decimal_long_double u, decimal_long_double q);

extern decimal_long_long_double eljt2dll (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
theta2(u,q) = 2 * q**(-1/4) * sum(n = 0:Infinity) q**(n*(n + 1)) * cos((2*n + 1)*u) = eljt2(u,q).

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

Maple: JacobiTheta2(u, q) Mathematica: EllipticTheta[2, 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, theta2(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), 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).