/// <summary>
/// Returns the Cylindrical Bessel I function: I<sub>v</sub>(x)
/// </summary>
/// <param name="v">Order</param>
/// <param name="x">Argument</param>
/// <returns></returns>
public static double BesselI(double v, double x)
{
//
// This handles all the bessel I functions, note that we don't optimise
// for integer v, other than the v = 0 or 1 special cases, as Millers
// algorithm is at least as inefficient as the general case (the general
// case has better error handling too).
//
if (double.IsNaN(v) || double.IsInfinity(v) || double.IsNaN(x)) {
Policies.ReportDomainError("BesselI(v: {0}, x: {1}): NaNs not allowed; Requres v != Infinity", v, x);
return double.NaN;
}
if (x < 0) {
// better have integer v:
if (!IsInteger(v)) {
Policies.ReportDomainError("BesselI(v: {0}, x: {1}): Requires integer v when x < 0", v, x);
return double.NaN;
}
double r = Math2.BesselI(v, -x);
if (IsOdd(v))
r = -r;
return r;
}
if (x == 0)
return (v == 0) ? 1 : 0;
// at this point x > 0
if (double.IsInfinity(x))
return double.PositiveInfinity;
if (v == 0)
return _Bessel.I0(x);
if (v == 1)
return _Bessel.I1(x);
if (v == 0.5)
return _Bessel.I0_5(x);
if (v > 0 && (x < 2 || 3*(v + 1) > x * x))
return _Bessel.I_SmallArg(v, x);
double Iv = _Bessel.IK(v, x, true, false).I;
return Iv;
}