Starting from the representation of a function f(x, y) as a formal power series with Taylor coefficients fm,n, a formal series is set up for the implicit function y = y(x) so that f(x, y) = 0 and the coefficients of the series for y depend exclusively on the fm,n. The solution to this problem provided here relies on using partial Bell polynomials and their inverse companions. Some examples and applications are discussed.
Alfred Schreiber (Wed,) studied this question.