public static MultiPrecision <N> BesselI(MultiPrecision <N> nu, MultiPrecision <N> x)
{
if (Abs(nu) > 64)
{
throw new ArgumentOutOfRangeException(
nameof(nu),
"In the calculation of the Bessel function, nu with an absolute value greater than 64 is not supported."
);
}
if (nu.IsNaN || x.IsNaN || x.Sign == Sign.Minus)
{
return(NaN);
}
if (nu.Sign == Sign.Minus && nu == Truncate(nu))
{
return(BesselI(Abs(nu), x));
}
if (nu - Point5 == Floor(nu))
{
long n = (long)Floor(nu);
if (n >= -2 && n < 2)
{
MultiPrecision <Plus1 <N> > x_ex = x.Convert <Plus1 <N> >();
MultiPrecision <Plus1 <N> > r = MultiPrecision <Plus1 <N> > .Sqrt2 / MultiPrecision <Plus1 <N> > .Sqrt(MultiPrecision <Plus1 <N> > .PI *x_ex);
if (n == -2)
{
return(-(r * (MultiPrecision <Plus1 <N> > .Cosh(x_ex) / x_ex - MultiPrecision <Plus1 <N> > .Sinh(x_ex))).Convert <N>());
}
if (n == -1)
{
return((r * MultiPrecision <Plus1 <N> > .Cosh(x_ex)).Convert <N>());
}
if (n == 0)
{
MultiPrecision <N> y = (r * MultiPrecision <Plus1 <N> > .Sinh(x_ex)).Convert <N>();
return(y.IsNormal ? y : 0);
}
if (n == 1)
{
MultiPrecision <N> y = -(r * (MultiPrecision <Plus1 <N> > .Sinh(x_ex) / x_ex - MultiPrecision <Plus1 <N> > .Cosh(x_ex))).Convert <N>();
return(y.IsNormal ? y : 0);
}
}
}
if (x.Exponent <= -0x1000000)
{
return(nu.IsZero ? 1 : ((nu.Sign == Sign.Plus || nu == Truncate(nu)) ? 0 : NaN));
}
if (x < Consts.BesselIK.ApproxThreshold)
{
return(BesselINearZero(nu, x));
}
else
{
return(BesselILimit(nu, x));
}
}
