private static MultiPrecision <N> BesselKLimit(MultiPrecision <N> nu, MultiPrecision <N> z)
{
Consts.BesselLimitCoef table = Consts.Bessel.LimitCoef(nu);
MultiPrecision <Plus4 <N> > z_ex = z.Convert <Plus4 <N> >();
MultiPrecision <Plus4 <N> > v = 1 / z_ex;
MultiPrecision <Plus4 <N> > x = 0, p = 1;
for (int k = 0; k <= Consts.BesselIK.LimitApproxTerms; k++, p *= v)
{
MultiPrecision <Plus4 <N> > c = p * table.Value(k);
x += c;
if (c.IsZero || x.Exponent - c.Exponent > MultiPrecision <Plus1 <N> > .Bits)
{
break;
}
}
MultiPrecision <Plus1 <N> > z_ex1 = z.Convert <Plus1 <N> >();
MultiPrecision <Plus1 <N> > r =
MultiPrecision <Plus1 <N> > .Exp(-z_ex1) * MultiPrecision <Plus1 <N> > .Sqrt(MultiPrecision <Plus1 <N> > .PI / (2 * z_ex1));
MultiPrecision <Plus1 <N> > y = r * x.Convert <Plus1 <N> >();
return(y.Convert <N>());
}
private static MultiPrecision <N> BesselYLimit(MultiPrecision <N> nu, MultiPrecision <N> z)
{
Consts.BesselLimitCoef table = Consts.Bessel.LimitCoef(nu);
MultiPrecision <Plus4 <N> > z_ex = z.Convert <Plus4 <N> >();
MultiPrecision <Plus4 <N> > v = 1 / z_ex;
MultiPrecision <Plus4 <N> > w = v * v;
MultiPrecision <Plus4 <N> > x = 0, y = 0, p = 1, q = v;
Sign sign = Sign.Plus;
for (int k = 0; k <= Consts.BesselJY.LimitApproxTerms; k++, p *= w, q *= w)
{
MultiPrecision <Plus4 <N> > c = p * table.Value(k * 2);
MultiPrecision <Plus4 <N> > s = q * table.Value(k * 2 + 1);
if (sign == Sign.Plus)
{
x += c;
y += s;
sign = Sign.Minus;
}
else
{
x -= c;
y -= s;
sign = Sign.Plus;
}
if (!c.IsZero && x.Exponent - c.Exponent <= MultiPrecision <Plus2 <N> > .Bits)
{
continue;
}
if (!s.IsZero && y.Exponent - s.Exponent <= MultiPrecision <Plus2 <N> > .Bits)
{
continue;
}
break;
}
MultiPrecision <Plus4 <N> > omega = z_ex - (2 * nu.Convert <Plus4 <N> >() + 1) * MultiPrecision <Plus4 <N> > .PI / 4;
MultiPrecision <Plus4 <N> > m = x * MultiPrecision <Plus4 <N> > .Sin(omega) + y * MultiPrecision <Plus4 <N> > .Cos(omega);
MultiPrecision <Plus4 <N> > t = m * MultiPrecision <Plus4 <N> > .Sqrt(2 / (MultiPrecision <Plus4 <N> > .PI *z_ex));
return(t.Convert <N>());
}
private static MultiPrecision <N> BesselILimit(MultiPrecision <N> nu, MultiPrecision <N> z)
{
Consts.BesselLimitCoef table = Consts.Bessel.LimitCoef(nu);
MultiPrecision <Plus4 <N> > z_ex = z.Convert <Plus4 <N> >();
MultiPrecision <Plus4 <N> > v = 1 / z_ex;
MultiPrecision <Plus4 <N> > x = 0, p = 1;
Sign sign = Sign.Plus;
for (int k = 0; k <= Consts.BesselIK.LimitApproxTerms; k++, p *= v)
{
MultiPrecision <Plus4 <N> > c = p * table.Value(k);
if (sign == Sign.Plus)
{
x += c;
sign = Sign.Minus;
}
else
{
x -= c;
sign = Sign.Plus;
}
if (c.IsZero || x.Exponent - c.Exponent > MultiPrecision <Plus1 <N> > .Bits)
{
break;
}
}
MultiPrecision <Plus1 <N> > z_ex1 = z.Convert <Plus1 <N> >();
MultiPrecision <Plus1 <N> > r =
MultiPrecision <Plus1 <N> > .Exp(z_ex1) / MultiPrecision <Plus1 <N> > .Sqrt(2 *MultiPrecision <Plus1 <N> > .PI *z_ex1);
MultiPrecision <Plus1 <N> > y = r * x.Convert <Plus1 <N> >();
return(y.Convert <N>());
}