41 T ellint_pi_imp(T v, T k, T vc, const Policy& pol);
45 T ellint_pi_imp(T v, T phi, T k, T vc, const Policy& pol)
55          "Got k = %1%, function requires |k| <= 1", k, pol);
65       return (k == 0) ? phi : ellint_f_imp(phi, k, pol);
71          "Got v = %1%, but result is complex for v > 1 / sin^2(phi)", v, pol);
78       result = sqrt(1 - m * sphi * sphi) * tan(phi) - ellint_e_imp(phi, k, pol);
80       result += ellint_f_imp(phi, k, pol);
92       return ellint_pi_imp(v, k, vc, pol);
110             "Got v = %1%, but this is only supported for 0 <= phi <= pi/2", v, pol);
115          result = 2 * fabs(phi) * ellint_pi_imp(v, k, vc, pol) / constants::pi<T>();
124 …omain_error<T>(function, "Got k=1 and phi=%1% but the result is complex in that domain", phi, pol);
132          result = sign * ellint_pi_imp(v, rphi, k, vc, pol);
134             result += m * ellint_pi_imp(v, k, vc, pol);
155          return (boost::math::log1p(arg, pol) - boost::math::log1p(-arg, pol)) / (2 * vcr);
191          result = ellint_pi_imp(N, phi, k, Nm1, pol);
198          t = ellint_f_imp(phi, k, pol);
240       result = -ellint_pi_imp(N, phi, k, Nm1, pol);
241       result += ellint_f_imp(phi, k, pol);
269    result = sphi * (ellint_rf_imp(x, y, z, pol) + v * t * ellint_rj_imp(x, y, z, p, pol) / 3);
276 T ellint_pi_imp(T v, T k, T vc, const Policy& pol)
287             "Got k = %1%, function requires |k| <= 1", k, pol);
293             "Got v = %1%, function requires v < 1", v, pol);
298        return (k == 0) ? boost::math::constants::pi<T>() / 2 : ellint_k_imp(k, pol);
308        result = boost::math::detail::ellint_pi_imp(N, k, Nm1, pol);
312        result += ellint_k_imp(k, pol) * k2 / (k2 - v);
320     T value = ellint_rf_imp(x, y, z, pol) + v * ellint_rj_imp(x, y, z, p, pol) / 3;
332 inline typename tools::promote_args<T1, T2>::type ellint_3(T1 k, T2 v, const Policy& pol, const mpl…  in ellint_3()  argument
341          pol), "boost::math::ellint_3<%1%>(%1%,%1%)");  in ellint_3()
347 …line typename tools::promote_args<T1, T2, T3>::type ellint_3(T1 k, T2 v, T3 phi, const Policy& pol)  in ellint_3()  argument
357          pol), "boost::math::ellint_3<%1%>(%1%,%1%,%1%)");  in ellint_3()