We prove concurrent universal Padé approximation for several universal Padé approximants of several types. Our results are generic in the space of holomorphic functions, in the space of formal power series as well as in a subspace of $A^{\infty }$. These results are valid for one center of expansion or for several centers as well. The Padé approximants allow generic approximation on arbitrary compact sets, not necessarily having connected component, in contrast with the partial sums of power series. We also establish affine genericity for a class of universal functions.

中文翻译：

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并行通用Padé逼近

我们证明了几种类型的多个通用Padé逼近的并发通用Padé逼近。我们的结果在全纯函数空间，形式幂级数空间以及${\mathrm{一种}}^{\infty }$。这些结果对于一个扩展中心或多个扩展中心均有效。与幂级数的部分和相反，Padé近似值允许对任意紧凑集（不一定具有连接的分量）进行泛型近似。我们还为一类通用函数建立仿射通用性。