标题： 关于通过多变量斯特林多项式展开隐函数为形式幂级数的注记 显示英文标题

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

摘要： 从函数$f(x,y)$的形式幂级数表示开始，其泰勒系数为$f_{m,n}$，我们建立了一个隐函数$y=y(x)$的形式级数，使得$f(x,y)=0$，并且该级数的系数$y$完全取决于$f_{m,n}$。 此处提供的该问题的解依赖于使用偏贝尔多项式及其正交伴随多项式。 显示英文摘要

摘要： 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.