/// Elliptic integrals of the first kind. double ellint_1(double k, double phi) { const gsl_mode_t mode = GSL_PREC_DOUBLE; gsl_sf_result result; int stat = gsl_sf_ellint_F_e(phi, k, mode, &result); if (stat != GSL_SUCCESS) { std::ostringstream msg("Error in ellint_1:"); msg << " k=" << k << " phi=" << phi; throw std::runtime_error(msg.str()); } else return result.val; }
double gsl_sf_ellint_F(double phi, double k, gsl_mode_t mode) { EVAL_RESULT(gsl_sf_ellint_F_e(phi, k, mode, &result)); }
/** * C++ version of gsl_sf_ellint_F_e(). * F(phi,k) = Integral[1/Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}] * @param phi A real number * @param k A real number * @param mode The mode * @param result The result as a @c gsl::sf::result object * @return Error code on failure */ inline int F_e( double phi, double k, mode_t mode, result& result ){ return gsl_sf_ellint_F_e( phi, k, mode, &result ); }