Concurrent universal Padé approximation

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∞. 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. © 2021 Elsevier Inc.