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Starting from the representation of a function $f(x,y)$ as a formal powerseries with Taylor coefficients $f_{m,n}$, we establish a formal series for theimplicit function $y=y(x)$ such that $f(x,y)=0$ and the coefficients of theseries for $y$ depend exclusively on the $f_{m,n}$. The solution to thisproblem provided here relies on using partial Bell polynomials and theirorthogonal companions.

Note on expanding implicit functions into formal power series by means of multivariable Stirling polynomials