Analytic approximations to Kelvin functions with applications to electromagnetics

We present analytical approximations for the real Kelvin function ber x and the imaginary Kelvin function bei x, using the two-point quasi-fractional approximation procedure. We have applied these approximations to the calculation of the current distribution within a cylindrical conductor. Our approximations are simple and accurate. An infinite number of roots is also obtained with the approximation and precision increases with the value of the root. Our results could find useful applications in problems where analytical approximations of the Kelvin functions are needed.