Kelvin functions

Summary

The Kelvin functions $\operatorname{ber}_\nu$, $\operatorname{bei}_\nu$, $\operatorname{ker}_\nu$ and $\operatorname{kei}_\nu$ are the real and imaginary parts of Bessel functions evaluated along the ray $\arg z = \frac{3\pi}{4}$ or $\frac{\pi}{4}$. They are real functions of a positive real variable. They describe alternating current in a round wire, where the current crowds toward the surface (the skin effect).