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
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 xeiφ, 0 ≤ φ < 2π. With the exception of bern(x) and bein(x) for integral n, the Kelvin functions have a branch point at x = 0.
Olver, F. W. J.; Maximon, L. C. (2010), "Bessel functions", in Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (eds.), NIST Handbook of Mathematical Functions, Cambridge University Press, ISBN 978-0-521-19225-5, MR 2723248.
External linksedit
Weisstein, Eric W. "Kelvin Functions." From MathWorld—A Wolfram Web Resource. [1]
GPL-licensed C/C++ source code for calculating Kelvin functions at codecogs.com: [2]