Starting from the representation of a function $f(x,y)$ as a formal power series with Taylor coefficients $f_{ m,n}$, we establish a formal series for the implicit function $y=y(x)$ such that $f(x,y)=0$ and the coefficients of the series for $y$ depend exclusively on the $f_{ m,n}$. The solution to this problem provided here relies on using partial Bell polynomials and their orthogonal companions.
Categories: math.CO