/// <summary> /// Incomplete elliptic integral of the third kind Π(φ | m, n). /// </summary> /// <param name="φ">Argument.</param> /// <param name="m">Parameter, equal to k², the square of the modulus.</param> /// <param name="n" /> public static Double Π(Double φ, double m, Double n) { Double sinφ = Math.Sin(φ), c = 1 / (sinφ * sinφ); return(CarlsonSymmetric.RF(c - 1, c - m, c) - (n / 3) * CarlsonSymmetric.RJ(c - 1, c - m, c, c + n)); }
/// <summary> /// Incomplete elliptic integral of the third kind Π(φ | m, n). /// </summary> /// <param name="φ">Argument.</param> /// <param name="m">Parameter, equal to k², the square of the modulus.</param> /// <param name="n" /> public static Complex Π(Complex φ, double m, Complex n) { Complex sinφ = Complex.Sin(φ), c = 1 / (sinφ * sinφ); return(CarlsonSymmetric.RF(c - 1, c - m, c) - (n / 3) * CarlsonSymmetric.RJ(c - 1, c - m, c, c + n)); }