Kelvin-function Definition

(mathematics) A class of special functions usually denoted as two pairs of functions ber_n(x), bei_n(x), ker_n(x) and kei_n(x) with variable x and given order number n. The former two functions ber_n(x) and bei_n(x) respectively correspond to the real part and the imaginary part of the Kelvin differential equation's solution that can be expressed with the Bessel function of the first kind J_n(x), and the latter ker_n(x) and kei_n(x) correspond to those that can be expressed with the modified Bessel function of the second kind K_n(x).