/// Carlson elliptic integrals R_J.
double
ellint_rj(double x, double y, double z, double p)
{
if (x == 0.0 && y == 0.0 && z == 0.0)
return 0.0;
const gsl_mode_t mode = GSL_PREC_DOUBLE;
gsl_sf_result result;
int stat = gsl_sf_ellint_RJ_e(x, y, z, p, mode, &result);
if (stat != GSL_SUCCESS)
{
std::ostringstream msg("Error in ellint_rj:");
msg << " x=" << x << " y=" << y << " z=" << z << " p=" << p;
throw std::runtime_error(msg.str());
}
else
return result.val;
}
/* [Carlson, Numer. Math. 33 (1979) 1, (4.3)] */
int
gsl_sf_ellint_P_e(double phi, double k, double n, gsl_mode_t mode, gsl_sf_result * result)
{
const double sin_phi = sin(phi);
const double sin2_phi = sin_phi * sin_phi;
const double sin3_phi = sin2_phi * sin_phi;
const double x = 1.0 - sin2_phi;
const double y = 1.0 - k*k*sin2_phi;
gsl_sf_result rf;
gsl_sf_result rj;
const int rfstatus = gsl_sf_ellint_RF_e(x, y, 1.0, mode, &rf);
const int rjstatus = gsl_sf_ellint_RJ_e(x, y, 1.0, 1.0 + n*sin2_phi, mode, &rj);
result->val = sin_phi * rf.val - n/3.0*sin3_phi * rj.val;
result->err = GSL_DBL_EPSILON * fabs(sin_phi * rf.val);
result->err += n/3.0 * fabs(sin3_phi*rj.err);
return GSL_ERROR_SELECT_2(rfstatus, rjstatus);
}
double gsl_sf_ellint_RJ(double x, double y, double z, double p, gsl_mode_t mode)
{
EVAL_RESULT(gsl_sf_ellint_RJ_e(x, y, z, p, mode, &result));
}
/**
* C++ version of gsl_sf_ellint_RJ_e().
* Carlson's symmetric basis of functions
*
* RJ(x,y,z,p) = 3/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2) (t+p)^(-1), {t,0,Inf}]
* @param x A real number
* @param y A real number
* @param z A real number
* @param p A real number
* @param mode The mode
* @param result The result as a @c gsl::sf::result object
* @return GSL_SUCCESS or GSL_EDOM
*/
inline int RJ_e( double x, double y, double z, double p, mode_t mode, result& result ){
return gsl_sf_ellint_RJ_e( x, y, z, p, mode, &result ); }