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.
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.