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.
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.