/// <summary>
/// Incomplete elliptic integral of the second kind E(φ | m).
/// </summary>
/// <param name="φ">Argument.</param>
/// <param name="m">Parameter, equal to k², the square of the modulus.</param>
public static Double E(Double φ, double m)
{
if (φ == 0)
{
return(0);
}
Double
sinφ = Math.Sin(φ),
c = 1 / (sinφ * sinφ);
return(CarlsonSymmetric.RF(c - 1, c - m, c) - (m / 3) * CarlsonSymmetric.RD(c - 1, c - m, c));
}
/// <summary>
/// Incomplete elliptic integral of the second kind E(φ | m).
/// </summary>
/// <param name="φ">Argument.</param>
/// <param name="m">Parameter, equal to k², the square of the modulus.</param>
public static Complex E(Complex φ, double m)
{
if (φ == 0)
{
return(0);
}
Complex
sinφ = Complex.Sin(φ),
c = 1 / (sinφ * sinφ);
return(CarlsonSymmetric.RF(c - 1, c - m, c) - (m / 3) * CarlsonSymmetric.RD(c - 1, c - m, c));
}
