k0_over_k1

pmrf.math.k0_over_k1(x: Array) → Array

Ratio \(K_0(x)/K_1(x)\) of modified Bessel functions for complex \(x\).

Mathematical Formulation

Below \(|x|=8\), \(K_0\) is evaluated from its logarithmic series and \(K_1\) from \(K_1=-K_0'\). Above the switch, the ratio is evaluated directly from its ten-term large-argument expansion. This covers the \(45^\circ\) ray of a good conductor from the weak-skin regime through the half-space limit without evaluating exponentially small Bessel functions separately.

Parameters:

x (jnp.ndarray) – Argument, real or complex.

Returns:

\(K_0(x)/K_1(x)\).

Return type:

jnp.ndarray