
Definition of Kelvin function
1. Noun. (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). ¹
¹ Source: wiktionary.com