/// <summary>
/// This function returns the complex arcsine of the real number a,
/// arcsin(a).
/// </summary>
/// <param name="a">The function argument.</param>
/// <returns>The complex arcsine of the real number a.</returns>
/// <remarks>
/// For a between -1 and 1, the
/// function returns a real value in the range -(pi,pi]. For
/// a less than -1 the result has a real part of -pi/2
/// and a positive imaginary part. For a greater than 1 the
/// result has a real part of pi/2 and a negative imaginary part.
/// </remarks>
public static Complex Asin(double a)
{
Complex z;
if (Math.Abs(a) <= 1.0)
{
z = new Complex(Math.Asin(a), 0.0);
}
else
{
if (a < 0.0)
{
z = new Complex(-M_PI_2, RMath.Acosh(-a));
}
else
{
z = new Complex(M_PI_2, -RMath.Acosh(a));
}
}
return(z);
}
/// <summary>
/// This function returns the complex hyperbolic arccosine of
/// the real number a, arccosh(a).
/// </summary>
/// <param name="a">Function argument.</param>
/// <returns>The complex hyperbolic arccosine of
/// the real number a.</returns>
public static Complex Acosh(double a)
{
Complex z;
if (a >= 1)
{
z = new Complex(RMath.Acosh(a), 0);
}
else
{
if (a >= -1.0)
{
z = new Complex(0, Math.Acos(a));
}
else
{
z = new Complex(RMath.Acosh(-a), M_PI);
}
}
return(z);
}
/// <summary>
/// This function returns the complex arcsecant of the real number a,
/// arcsec(a) = arccos(1/a).
/// </summary>
/// <param name="a">Function argument.</param>
/// <returns>The complex arcsecant of the real number a.</returns>
public static Complex Asec(double a)
{
Complex z;
if (a <= -1.0 || a >= 1.0)
{
z = new Complex(Math.Acos(1 / a), 0.0);
}
else
{
if (a >= 0.0)
{
z = new Complex(0, RMath.Acosh(1 / a));
}
else
{
z = new Complex(M_PI, -RMath.Acosh(-1 / a));
}
}
return(z);
}
/// <summary>
/// This function returns the complex arccosine of the real number a, arccos(a).
/// </summary>
/// <param name="a">The function argument.</param>
/// <returns>The complex arccosine of the real number a.</returns>
/// <remarks>
/// For a between -1 and 1, the
/// function returns a real value in the range [0,pi]. For a
/// less than -1 the result has a real part of pi/2 and a
/// negative imaginary part. For a greater than 1 the result
/// is purely imaginary and positive.
/// </remarks>
public static Complex Acos(double a)
{
Complex z;
if (Math.Abs(a) <= 1.0)
{
z = new Complex(Math.Acos(a), 0);
}
else
{
if (a < 0.0)
{
z = new Complex(Math.PI, -RMath.Acosh(-a));
}
else
{
z = new Complex(0, RMath.Acosh(a));
}
}
return(z);
}
