The treatment of hyperelliptic transformations for inductance calculations in magnetostatic circuits

A method is derived to reduce hyperelliptic integrals that arise in inductance calculations of cores with flanged gaps. Hyperelliptic integrals arise in higher order conformal transformations of polygons with more than 4 vertices. The solution is based on the principle of separation of moduli. The method provides accurate, closed-form, analytic solutions. It is used in the optimization of the design of inductors with protruding flanges at the gap region.