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- Identity_theorem abstract "In complex analysis, a branch of mathematics, the identity theorem for holomorphic functions states: given functions f and g holomorphic on a connected open set D, if f = g on some open non-empty subset of D, then f = g on D. Thus a holomorphic function is completely determined by its values on a (possibly quite small) neighborhood in D. This is not true for real-differentiable functions. In comparison, holomorphy, or complex-differentiability, is a much more rigid notion. Informally, one sometimes summarizes the theorem by saying holomorphic functions are "hard" (as opposed to, say, continuous functions which are "soft").The underpinning fact from which the theorem is established is the developability of a holomorphic function into its Taylor series.".
- Identity_theorem wikiPageID "3553654".
- Identity_theorem wikiPageLength "3813".
- Identity_theorem wikiPageOutDegree "14".
- Identity_theorem wikiPageRevisionID "662165719".
- Identity_theorem wikiPageWikiLink Analyticity_of_holomorphic_functions.
- Identity_theorem wikiPageWikiLink Category:Articles_containing_proofs.
- Identity_theorem wikiPageWikiLink Category:Theorems_in_complex_analysis.
- Identity_theorem wikiPageWikiLink Closed_set.
- Identity_theorem wikiPageWikiLink Complex_analysis.
- Identity_theorem wikiPageWikiLink Connected_space.
- Identity_theorem wikiPageWikiLink Continuous_function.
- Identity_theorem wikiPageWikiLink Holomorphic_function.
- Identity_theorem wikiPageWikiLink Mathematics.
- Identity_theorem wikiPageWikiLink Open_set.
- Identity_theorem wikiPageWikiLink Proof_that_holomorphic_functions_are_analytic.
- Identity_theorem wikiPageWikiLink Radius_of_convergence.
- Identity_theorem wikiPageWikiLinkText "Identity theorem".
- Identity_theorem wikiPageWikiLinkText "identity theorem".
- Identity_theorem hasPhotoCollection Identity_theorem.
- Identity_theorem wikiPageUsesTemplate Template:Cite_book.
- Identity_theorem subject Category:Articles_containing_proofs.
- Identity_theorem subject Category:Theorems_in_complex_analysis.
- Identity_theorem type Proof.
- Identity_theorem type Theorem.
- Identity_theorem comment "In complex analysis, a branch of mathematics, the identity theorem for holomorphic functions states: given functions f and g holomorphic on a connected open set D, if f = g on some open non-empty subset of D, then f = g on D. Thus a holomorphic function is completely determined by its values on a (possibly quite small) neighborhood in D. This is not true for real-differentiable functions. In comparison, holomorphy, or complex-differentiability, is a much more rigid notion.".
- Identity_theorem label "Identity theorem".
- Identity_theorem sameAs Identitätssatz_für_holomorphe_Funktionen.
- Identity_theorem sameAs משפט_היחידות_(אנליזה_מרוכבת).
- Identity_theorem sameAs 一致の定理.
- Identity_theorem sameAs 항등_정리.
- Identity_theorem sameAs m.09l56_.
- Identity_theorem sameAs Özdeşlik_teoremi.
- Identity_theorem sameAs Q1038716.
- Identity_theorem sameAs Q1038716.
- Identity_theorem sameAs 惟一性定理.
- Identity_theorem wasDerivedFrom Identity_theorem?oldid=662165719.
- Identity_theorem isPrimaryTopicOf Identity_theorem.