Abstract: Implicit equations play a crucial role in Engineering.
Based on this importance, several techniques have been applied to
solve this particular class of equations. When it comes to practical
applications, in general, iterative procedures are taken into account.
On the other hand, with the improvement of computers, other
numerical methods have been developed to provide a more
straightforward methodology of solution. Analytical exact approaches
seem to have been continuously neglected due to the difficulty
inherent in their application; notwithstanding, they are indispensable
to validate numerical routines. Lagrange-s Inversion Theorem is a
simple mathematical tool which has proved to be widely applicable to
engineering problems. In short, it provides the solution to implicit
equations by means of an infinite series. To show the validity of this
method, the tree-parameter infiltration equation is, for the first time,
analytically and exactly solved. After manipulating these series,
closed-form solutions are presented as H-functions.