## Kelvin Functions

Kelvin defined the Kelvin functions Bei and Ber according to

 (1)

where is a Bessel Function of the First Kind, and the functions Kei and Ker by
 (2)

where is a Modified Bessel Function of the Second Kind. For the special case ,
 (3)

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.
Spanier, J. and Oldham, K. B. The Kelvin Functions.'' Ch. 55 in An Atlas of Functions. Washington, DC: Hemisphere, pp. 543-554, 1987.