/// Elliptic integrals of the third kind. double ellint_3(double k, double nu, double phi) { const gsl_mode_t mode = GSL_PREC_DOUBLE; gsl_sf_result result; int stat = gsl_sf_ellint_P_e(phi, k, nu, mode, &result); if (stat != GSL_SUCCESS) { std::ostringstream msg("Error in ellint_3:"); msg << " k=" << k << " nu=" << nu << " phi=" << phi; throw std::runtime_error(msg.str()); } else return result.val; }
double gsl_sf_ellint_P(double phi, double k, double n, gsl_mode_t mode) { EVAL_RESULT(gsl_sf_ellint_P_e(phi, k, n, mode, &result)); }
/** * C++ version of gsl_sf_ellint_P_e(). * P(phi,k,n) = Integral[(1 + n Sin[t]^2)^(-1)/Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}] * @param phi A real number * @param k A real number * @param n 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 P_e( double phi, double k, double n, mode_t mode, result& result ){ return gsl_sf_ellint_P_e( phi, k, n, mode, &result ); }