cc [ flags ] -I/usr/local/include file(s) -L/usr/local/lib -lmcw [ ... ] #include <mathcw.h> extern float ellrhf (float x, float y, float z, float rho); extern double ellrh (double x, double y, double z, double rho); extern long double ellrhl (long double x, long double y, long double z, long double rho); extern __float80 ellrhw (__float80 x, __float80 y, __float80 z, __float80 rho); extern __float128 ellrhq (__float128 x, __float128 y, __float128 z, __float128 rho); extern long_long_double ellrhll (long_long_double x, long_long_double y, long_long_double z, long_long_double rho); extern decimal_float ellrhdf (decimal_float x, decimal_float y, decimal_float z, decimal_float rho); extern decimal_double ellrhd (decimal_double x, decimal_double y, decimal_double z, decimal_double rho); extern decimal_long_double ellrhdl (decimal_long_double x, decimal_long_double y, decimal_long_double z, decimal_long_double rho); extern decimal_long_long_double ellrhdll (decimal_long_long_double x, decimal_long_long_double y, decimal_long_long_double z, decimal_long_long_double rho);
NB: Functions with prototypes containing underscores in type names may be available only with certain extended compilers.
where x >= 0, y > 0, z > 0, and rho > 0.ellrh(x, y, z, rho) = R(1/2; 1/2, 1/2, 1/2, 1; x, y, z, rho) = (3/2) * integral(t=0:Infinity) (t + x)**(-1/2) * (t + y)**(-1/2) * (t + z)**(-1/2) * (t + rho)**(-1) * t * dt = (3/2) * ellrf(x, y, z) - (1/2) * rho * ellrj(x, y, z, rho)
The function is symmetric in x, y, and z.
The normalization condition satisfied is
ellrh(x, x, x, x) = x**(-1/2).