/// <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));
}
