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)
Famous quotes containing the word functions:
“The English masses are lovable: they are kind, decent, tolerant, practical and not stupid. The tragedy is that there are too many of them, and that they are aimless, having outgrown the servile functions for which they were encouraged to multiply. One day these huge crowds will have to seize power because there will be nothing else for them to do, and yet they neither demand power nor are ready to make use of it; they will learn only to be bored in a new way.”
—Cyril Connolly (1903–1974)