标题： 关于利用多变量斯特林多项式将隐函数展开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$f(x,y)=0$并且该级数对于$y$的系数仅依赖于$f_{m,n}$。 这里提供的这个问题的解依赖于使用部分贝尔多项式及其正交伴生多项式。 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.