In applied mathematics, the Kelvin functions Berν(x) and Beiν(x) are the real and imaginary parts, respectively, of
where x is real, and Jν(z), is the νth order Bessel function of the first kind. Similarly, the functions Kerν(x) and Keiν(x) are the real and imaginary parts, respectively, of, where is the νth order modified Bessel function of the second kind.
These functions are named after William Thomson, 1st Baron Kelvin.
While the Kelvin functions are defined as the real and imaginary parts of Bessel functions with x taken to be real, the functions can be analytically continued for complex arguments x ei φ, φ ∈ [0, 2π). With the exception of Bern(x) and Bein(x) for integral n, the Kelvin functions have a branch point at x = 0.
Read more about Kelvin Functions: Ber(x), Bei(x), Ker(x), Kei(x)
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—Edward T. Hall (b. 1914)