Some series formulas for mutual inductance of solenoids

ABSOLUTE formulas for the mutual inductance of coaxial solenoids have been derived by Nagaoka, Terezawa, and Olshausen. These all give the mutual inductance as a combination of 4 integrals — 2 positive and 2 negative — each of which is a function of one of the 4 distances measured between an end of one solenoid and an end of the other. The expressions for these terms involve elliptic integrals of all 3 kinds, and numerical computations of their values are exacting.