Accuracy of expressions for the magnetic field of a ring head

The Fourier method used by Fan has produced a representation of the field of a semi-infinite pole head consisting of a simple analytical approximation (Karlqvist field) plus an infinite series of correction terms. A method is developed in this paper by which other approximations to head fields have their infinite series of correction terms evaluated to make them exact. Expressions with only one correction term produced by Ruigrok and Szczech et al., are studied, and enhancement of them is shown to offer accurate approximations to the exact head fields.