Calculation of Fuchs networks
The Austrian radio amateur named Josef Fuchs, OE1JF, used for matching of a ½ λ dipole at its feedpoint a resonant circuit, which would named later as Fuchs network. The calculation of Fuchs networks is possible, based an the finite impedance at the antenna ends an the used frequency. Such networks with coils and capacitors are usable only for one frequency.
The permeability for example from Amidon cores you can learn from the Mini Ring Core Calculator by Wilfried Burmeister, DL5SWB. If you want to know, how looks the equations used into the script, then see at the mathematical background: Fuchs network.