/// <summary> Returns the exponentially scaled modified Bessel function
/// of the second 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>
public static double BesselK1e(double x)
{
if (x <= 0.0)
{
throw new ArithmeticException();
}
if (x <= 2.0)
{
double y = x * x - 2.0;
return(Math.Log(0.5 * x) * BesselI1(x) + Evaluate.ChebyshevA(BesselK1A, y) / x * Math.Exp(x));
}
double x1 = 8.0 / x - 2.0;
return(Evaluate.ChebyshevA(BesselK1B, x1) / Math.Sqrt(x));
}
/// <summary> Returns the modified Bessel function of the second kind
/// of order 0 of the argument.
/// <p/>
/// The range is partitioned into the two intervals [0, 8] and
/// (8, infinity). Chebyshev polynomial expansions are employed
/// in each interval.
/// </summary>
/// <param name="x">The value to compute the Bessel function of.
/// </param>
public static double BesselK0(double x)
{
if (x <= 0.0)
{
throw new ArithmeticException();
}
if (x <= 2.0)
{
double y = x * x - 2.0;
return(Evaluate.ChebyshevA(BesselK0A, y) - Math.Log(0.5 * x) * BesselI0(x));
}
double z = 8.0 / x - 2.0;
return(Math.Exp(-x) * Evaluate.ChebyshevA(BesselK0B, z) / Math.Sqrt(x));
}
/// <summary>Returns the modified Bessel function of first kind, order 0 of the argument.
/// <p/>
/// The function is defined as <tt>i0(x) = j0( ix )</tt>.
/// <p/>
/// The range is partitioned into the two intervals [0, 8] and
/// (8, infinity). Chebyshev polynomial expansions are employed
/// in each interval.
/// </summary>
/// <param name="x">The value to compute the Bessel function of.
/// </param>
public static double BesselI0(double x)
{
if (x < 0)
{
x = -x;
}
if (x <= 8.0)
{
double y = (x / 2.0) - 2.0;
return(Math.Exp(x) * Evaluate.ChebyshevA(BesselI0A, y));
}
double x1 = 32.0 / x - 2.0;
return(Math.Exp(x) * Evaluate.ChebyshevA(BesselI0B, x1) / Math.Sqrt(x));
}
/// <summary>Returns the modified Bessel function of first kind,
/// order 1 of the argument.
/// <p/>
/// The function is defined as <tt>i1(x) = -i j1( ix )</tt>.
/// <p/>
/// The range is partitioned into the two intervals [0, 8] and
/// (8, infinity). Chebyshev polynomial expansions are employed
/// in each interval.
/// </summary>
/// <param name="x">The value to compute the Bessel function of.
/// </param>
public static double BesselI1(double x)
{
double z = Math.Abs(x);
if (z <= 8.0)
{
double y = (z / 2.0) - 2.0;
z = Evaluate.ChebyshevA(BesselI1A, y) * z * Math.Exp(z);
}
else
{
double x1 = 32.0 / z - 2.0;
z = Math.Exp(z) * Evaluate.ChebyshevA(BesselI1B, x1) / Math.Sqrt(z);
}
if (x < 0.0)
{
z = -z;
}
return(z);
}
