  The so called Gell-Mann formula, a prescription designed to provide an
inverse to the Inonu-Wigner Lie algebra contraction, has a great versatility
and potential value. This formula has no general validity as an operator
expression. The question of applicability of Gell-Mann's formula to various
algebras and their representations was only partially treated. The validity
constraints of the Gell-Mann formula for the case of sl(n,R) and su(n) algebras
are clarified, and the complete list of representations spaces for which this
formula applies is given. Explicit expressions of the sl(n,R) generators matrix
elements are obtained, in these cases, by making use of the Gell-Mann formula.
