二元函数的多维Padé逼近：等式
Multidimensional Padé approximation of binomial functions: Equalities
摘要：
令$ω_0,\dots,ω_M$为复数。如果$H_0,\dots,H_M$是次数至多为$ρ_0,\dots,ρ_M$的多项式，并且$G(z)=\sum_{m=0} ^M H_m(z) (1-z)^{ω_m}$在最大阶的$z=0$处有一个零（对于给定的$ω_m,ρ_m$），我们说$H_0,\dots,H_M$是一个\emph{multidimensional Padé approximation of binomial functions}，并称$G$为Padé余数。在这里，我们收集与证明所有已知的表达式$G$和$H_m$，包括一个新的：泰勒系列的$G$。我们还给出了一个新的标准系统的Padé近似的二项式函数是完美的（一种特定的独立性在应用中使用）。
英文摘要：
Let $ω_0,\dots,ω_M$ be complex numbers. If $H_0,\dots,H_M$ are polynomials of degree at most $ρ_0,\dots,ρ_M$, and $G(z)=\sum_{m=0} ^M H_m(z) (1-z)^{ω_m}$ has a zero at $z=0$ of maximal order (for the given $ω_m,ρ_m$), we say that $H_0,\dots,H_M$ are a \emph{multidimensional Padé approximation of binomial functions}, and call $G$ the Padé 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 Padé approximations of binomial functions to be perfect (a specific sort of independence used in applications).
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