/// <summary>
/// Returns the exponentially scaled modified Bessel function
/// of order 0 of the argument.
/// <p>
/// The function is defined as <tt>i0e(x) = exp(-|x|) j0( ix )</tt>.
/// </summary>
/// <param name="x">the value to compute the bessel function of.</param>
/// <returns></returns>
static public double i0e(double x)
{
double y;
if (x < 0)
{
x = -x;
}
if (x <= 8.0)
{
y = (x / 2.0) - 2.0;
return(Arithmetic.Chbevl(y, A_i0, 30));
}
return(Arithmetic.Chbevl(32.0 / x - 2.0, B_i0, 25) / System.Math.Sqrt(x));
}
/// <summary>
/// Returns the exponentially scaled modified Bessel function
/// of the third kind of order 1 of the argument.
/// <p>
/// <tt>k1e(x) = exp(x) * k1(x)</tt>.
/// </summary>
/// <param name="x">the value to compute the bessel function of.</param>
/// <returns></returns>
static public double k1e(double x)
{
double y;
if (x <= 0.0)
{
throw new ArithmeticException();
}
if (x <= 2.0)
{
y = x * x - 2.0;
y = System.Math.Log(0.5 * x) * i1(x) + Arithmetic.Chbevl(y, A_k1, 11) / x;
return(y * System.Math.Exp(x));
}
return(Arithmetic.Chbevl(8.0 / x - 2.0, B_k1, 25) / System.Math.Sqrt(x));
}
/// <summary>
/// Returns the exponentially scaled modified Bessel function of the third kind of order 0 of the argument.
/// </summary>
/// <param name="x"></param>
/// <returns></returns>
static public double k0e(double x)
{
double y;
if (x <= 0.0)
{
throw new ArithmeticException();
}
if (x <= 2.0)
{
y = x * x - 2.0;
y = Arithmetic.Chbevl(y, A_k0, 10) - System.Math.Log(0.5 * x) * i0(x);
return(y * System.Math.Exp(x));
}
y = Arithmetic.Chbevl(8.0 / x - 2.0, B_k0, 25) / System.Math.Sqrt(x);
return(y);
}
/// <summary>
/// Returns the exponentially scaled modified Bessel function
/// of order 1 of the argument.
/// <p>
/// The function is defined as <tt>i1(x) = -i exp(-|x|) j1( ix )</tt>.
/// </summary>
/// <param name="x">the value to compute the bessel function of.</param>
/// <returns></returns>
static public double i1e(double x)
{
double y, z;
z = System.Math.Abs(x);
if (z <= 8.0)
{
y = (z / 2.0) - 2.0;
z = Arithmetic.Chbevl(y, A_i1, 29) * z;
}
else
{
z = Arithmetic.Chbevl(32.0 / z - 2.0, B_i1, 25) / System.Math.Sqrt(z);
}
if (x < 0.0)
{
z = -z;
}
return(z);
}