public static MultiPrecision <N> BesselJ(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)
{
return(NaN);
}
if (x.Sign == Sign.Minus)
{
if (nu != Truncate(nu))
{
return(NaN);
}
long n = (long)nu;
return(((n & 1L) == 0) ? BesselJ(nu, Abs(x)) : -BesselJ(nu, Abs(x)));
}
if (!x.IsFinite)
{
return(0);
}
if (x.Exponent >= Bits)
{
return(NaN);
}
if (nu.Sign == Sign.Minus && nu == Truncate(nu))
{
long n = (long)nu;
return(((n & 1L) == 0) ? BesselJ(Abs(nu), x) : -BesselJ(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> > envelope = MultiPrecision <Plus1 <N> > .Sqrt(2 / (MultiPrecision <Plus1 <N> > .PI * x_ex));
if (n == -2)
{
return(-(envelope * (MultiPrecision <Plus1 <N> > .Cos(x_ex) / x_ex + MultiPrecision <Plus1 <N> > .Sin(x_ex))).Convert <N>());
}
if (n == -1)
{
return((envelope * MultiPrecision <Plus1 <N> > .Cos(x_ex)).Convert <N>());
}
if (n == 0)
{
MultiPrecision <N> y = (envelope * MultiPrecision <Plus1 <N> > .Sin(x_ex)).Convert <N>();
return(y.IsNaN ? 0 : y);
}
if (n == 1)
{
MultiPrecision <N> y = (envelope * (MultiPrecision <Plus1 <N> > .Sin(x_ex) / x_ex - MultiPrecision <Plus1 <N> > .Cos(x_ex))).Convert <N>();
return(y.IsNaN ? 0 : y);
}
}
}
if (x.Exponent <= -0x1000000)
{
return(nu.IsZero ? 1 : ((nu.Sign == Sign.Plus || nu == Truncate(nu)) ? 0 : NaN));
}
if (x < Consts.BesselJY.ApproxThreshold)
{
return(MultiPrecision <Plus2 <N> > .BesselJNearZero(nu.Convert <Plus2 <N> >(), x.Convert <Plus2 <N> >()).Convert <N>());
}
else
{
return(BesselJLimit(nu, x));
}
}
