Function bessel_k1_impl 

pub fn bessel_k1_impl<P, E, V, const NS: usize, const DS: usize, const NL: usize, const DL: usize, const IS: usize, const IL: usize, const IF: usize, const SCALED: bool>(
    x: V,
    t: &BesselK<E, NS, DS, NL, DL>,
    ti: &BesselI<E, IS, IL, IF>,
) -> V
where
    E: FloatElement,
    V: FloatVector<Element = E> + TranscendentalMathWithPolicy,
    P: Policy,

$K_1(x)$, or $e^{x} K_1(x)$ when SCALED.

K_1(x) = R(x^2)\,x + \frac{1}{x} + \ln(x)\,I_1(x), \qquad
K_1(x) = \frac{e^{-x}}{\sqrt{x}}\left(Y + \frac{P(1/x)}{Q(1/x)}\right)

The $1/x$ is the singularity and is left as a bare reciprocal rather than folded into the rational, because it is the entire value as $x \to 0$ and any rearrangement that mixes it with the $O(x)$ terms cancels it away.