ELJT1 3CW "07 February 2010" "mathcw-1.00"

Table of contents


NAME

eljt1f, eljt1, eljt1l, eljt1w, eljt1q, eljt1ll, eljt1df, eljt1d, eljt1dl, eljt1dll - Jacobian elliptic theta function

SYNOPSIS

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

#include <mathcw.h>

extern float eljt1f (float u, float q);

extern double eljt1 (double u, double q);

extern long double eljt1l (long double u, long double q);

extern __float80 eljt1w (__float80 u, __float80 q);

extern __float128 eljt1q (__float128 u, __float128 q);

extern long_long_double eljt1ll (long_long_double u, long_long_double q);

extern decimal_float eljt1df (decimal_float u, decimal_float q);

extern decimal_double eljt1d (decimal_double u, decimal_double q);

extern decimal_long_double eljt1dl (decimal_long_double u, decimal_long_double q);

extern decimal_long_long_double eljt1dll (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
theta1(u,q) = 2 * q**(-1/4) * sum(n = 0:Infinity) (-1)**n * q**(n*(n + 1)) * sin((2*n + 1)*u) = eljt1(u,q).

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

Equivalents in other systems are:

Maple: JacobiTheta1(u, q) Mathematica: EllipticTheta[1, 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, theta1(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), 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).