public static Complex modifiedBesselFunction_i_impl <T, I>(double nu, Complex x)
where T : Weight <Complex>, new()
where I : baseValue <Complex>, new()
{
if (Complex.Abs(x) < 13.0)
{
Complex alpha = Complex.Pow(0.5 * x, nu) / GammaFunction.value(1.0 + nu);
Complex Y = 0.25 * x * x;
int k = 1;
Complex sum = alpha, B_k = alpha;
while (Complex.Abs(B_k *= Y / (k * (k + nu))) > Complex.Abs(sum) * Const.QL_EPSILON)
{
sum += B_k;
Utils.QL_REQUIRE(++k < 1000, () => "max iterations exceeded");
}
return(sum * FastActivator <T> .Create().weightSmallX(x));
}
else
{
double na_k = 1.0, sign = 1.0;
Complex da_k = new Complex(1.0, 0.0);
Complex s1 = new Complex(1.0, 0.0), s2 = new Complex(1.0, 0.0);
for (int k = 1; k < 30; ++k)
{
sign *= -1;
na_k *= (4.0 * nu * nu -
(2.0 * (double)k - 1.0) *
(2.0 * (double)k - 1.0));
da_k *= (8.0 * k) * x;
Complex a_k = na_k / da_k;
s2 += a_k;
s1 += sign * a_k;
}
Complex i = FastActivator <I> .Create().value();
return(1.0 / Complex.Sqrt(2 * Const.M_PI * x) *
(FastActivator <T> .Create().weight1LargeX(x) * s1 +
i * Complex.Exp(i * nu * Const.M_PI) * FastActivator <T> .Create().weight2LargeX(x) * s2));
}
}
public static double modifiedBesselFunction_i_impl <T, I>(double nu, double x)
where T : Weight <double>, new()
where I : baseValue <double>, new()
{
if (Math.Abs(x) < 13.0)
{
double alpha = Math.Pow(0.5 * x, nu) / GammaFunction.value(1.0 + nu);
double Y = 0.25 * x * x;
int k = 1;
double sum = alpha, B_k = alpha;
while (Math.Abs(B_k *= Y / (k * (k + nu))) > Math.Abs(sum) * Const.QL_EPSILON)
{
sum += B_k;
Utils.QL_REQUIRE(++k < 1000, () => "max iterations exceeded");
}
return(sum * FastActivator <T> .Create().weightSmallX(x));
}
else
{
double na_k = 1.0, sign = 1.0;
double da_k = 1.0;
double s1 = 1.0, s2 = 1.0;
for (int k = 1; k < 30; ++k)
{
sign *= -1;
na_k *= (4.0 * nu * nu -
(2.0 * k - 1.0) *
(2.0 * k - 1.0));
da_k *= (8.0 * k) * x;
double a_k = na_k / da_k;
s2 += a_k;
s1 += sign * a_k;
}
double i = FastActivator <I> .Create().value();
return(1.0 / Math.Sqrt(2 * Const.M_PI * x) *
(FastActivator <T> .Create().weight1LargeX(x) * s1 +
i * Math.Exp(i * nu * Const.M_PI) * FastActivator <T> .Create().weight2LargeX(x) * s2));
}
}
