Ker

The Real Part of

$$e^{-\nu\pi i/2}K_\nu(xe^{\pi i/4})=\mathop{\rm ker}\nolimits _\nu(x)+i\mathop{\rm kei}\nolimits _\nu(x),$$

where $K_\nu(x)$ is a Modified Bessel Function of the Second Kind.

See also Bei, Ber, Kei, Kelvin Functions

References

Abramowitz, M. and Stegun, C. A. (Eds.). ``Kelvin Functions.'' §9.9 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 379-381, 1972.