{"paper":{"title":"Generic approximation of functions by their Pad\\'{e} approximants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"G. Fournodavlos, V. Nestoridis","submitted_at":"2011-06-01T13:14:09Z","abstract_excerpt":"Generic approximation of entire functions by their Pad\\'{e} approximants has been achieved in the past (\\cite{3}). In the present article we obtain generic approximation of holomorphic functions on arbitrary open sets by sequences of their Pad\\'{e} approximants. Similar results hold with functions smooth on the boundary of their domain of definition. In addition, the approximation is valid simultaneously with respect to all centers of expansion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0169","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}