/// Complete elliptic integrals of the first kind.
double
comp_ellint_1(double k)
{
const gsl_mode_t mode = GSL_PREC_DOUBLE;
gsl_sf_result result;
int stat = gsl_sf_ellint_Kcomp_e(k, mode, &result);
if (stat != GSL_SUCCESS)
{
std::ostringstream msg("Error in ellint_1:");
msg << " k=" << k;
throw std::runtime_error(msg.str());
}
else
return result.val;
}
double gsl_sf_ellint_Kcomp(double k, gsl_mode_t mode)
{
EVAL_RESULT(gsl_sf_ellint_Kcomp_e(k, mode, &result));
}
/**
* C++ version of gsl_sf_ellint_Kcomp_e().
* Legendre form of complete elliptic integrals
*
* K(k) = Integral[1/Sqrt[1 - k^2 Sin[t]^2], {t, 0, Pi/2}]
*
* @param k 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 Kcomp_e( double k, mode_t mode, result& result ){
return gsl_sf_ellint_Kcomp_e( k, mode, &result ); }
