analytic with Take to obtain Then for the inverse (satisfying ), we have

which can be written alternatively as

where is an operator which extracts the coefficient of in the Taylor series of a function of .

A generalization of the formula is known as the Lagrange-Bürmann formula:
:

where is an arbitrary analytic function.

Sometimes, the derivative can be quite complicated. A simpler version of the formula replaces with to get

which involves