Recursive generation of higher-order terms in the Magnus expansion

Several methods for systematically calculating higher-order terms in the Magnus expansion of the time-displacement operator are discussed from a unified point of view. It is shown that a quadratic recursive scheme recently introduced in the average Hamiltonian formalism of NMR spectroscopy can be extended to other cases, including the original multiple commutator approach developed by Magnus [Commun. Pure Appl. Math. 7, 649 (1954)].