cc [ flags ] -I/usr/local/include file(s) -L/usr/local/lib -lmcw [ ... ] #include <mathcw.h> extern float ellrmf (float x, float y, float rho); extern double ellrm (double x, double y, double rho); extern long double ellrml (long double x, long double y, long double rho); extern __float80 ellrmw (__float80 x, __float80 y, __float80 rho); extern __float128 ellrmq (__float128 x, __float128 y, __float128 rho); extern long_long_double ellrmll (long_long_double x, long_long_double y, long_long_double rho); extern decimal_float ellrmdf (decimal_float x, decimal_float y, decimal_float rho); extern decimal_double ellrmd (decimal_double x, decimal_double y, decimal_double rho); extern decimal_long_double ellrmdl (decimal_long_double x, decimal_long_double y, decimal_long_double rho); extern decimal_long_long_double ellrmdll (decimal_long_long_double x, decimal_long_long_double y, 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, and rho > 0.ellrm(x, y, rho) = R(3/2; 1/2, 1/2, 1; x, y, rho) = (2 / pi) * integral(t=0:Infinity) t**(-1/2) * (t + x)**(-1/2) * (t + y)**(-1/2) * (t + rho)**(-1) dt = ellrl(x, y, x * y / rho) / rho
The function is symmetric in x and y.
The normalization condition satisfied is
ellrm(x, x, x) = x**(-3/2).