If formula_4 and formula_5 are matrices, one can compute formula_114 using the power series for the exponential and logarithm, with convergence of the series if formula_4 and formula_5 are sufficiently small. It is natural to collect together all terms where the total degree in formula_4 and formula_5 equals a fixed number formula_119, giving an expression formula_120. (See the section "Matrix Lie group illustration" above for formulas for the first several formula_120's.) A remarkably direct and concise, recursive proof that each formula_120 is expressible in terms of repeated commutators of formula_4 and formula_5 was given by Martin Eichler.