Let $\omega_0,\dots,\omega_M$ be complex numbers. If $H_0,\dots,H_M$ are polynomials of degree at most $\rho_0,\dots,\rho_M$, and $G(z)=\sum_{m=0} ^M H_m(z) (1-z)^{\omega_m}$ has a zero at $z=0$ of maximal order (for the given $\omega_m,\rho_m$), we say that $H_0,\dots,H_M$ are a \emph{multidimensional Pad\'e approximation of binomial functions}, and call $G$ the Pad\'e remainder. We collect here with proof all of the known expressions for $G$ and $H_m$, including a new one: the Taylor series of $G$. We also give a new criterion for systems of Pad\'e approximations of binomial functions to be perfect (a specific sort of independence used in applications).

翻译：Let\ omega_ 0,\ dots,\ dots,\\\ dots,\\\ dots,H_M$是多元学位,最多为$\rho_0,\\ dots,\rho_M$, $G(z)\sump ⁇ m=0} ⁇ MH_m(z) (1-z)\\\\ ⁇ omega_m}$Z=0美元最高顺序(对于给定的$\omega_m,\rho_m$),我们说$H_0,H_M$是一个多维度的Pad\e pad_e punomial 函数的近似值。我们在此收集所有已知的$G$和$H_m$的表示, 包括一个新的 $G 系列: $G$的泰勒。 我们还给出了一个新标准, 用于将二流函数精确化( 应用中所使用的某种特定独立性) 。