KnowraEntire functionLinked fromLinked fromThe 18 pages that link to Entire function, each with the reason it gives.All 18Broader topic 6Related 4Narrower topic 4Compared with 4Holomorphic functionBroader topic: It is the global special case obtained when the domain has no boundary.Complex analysisBroader topic: Entire functions show how global domain size constrains growth and possible forms.Rational functionCompared with: A nonpolynomial rational function has poles, so it is not entire.Riemann mapping theoremCompared with: The plane itself is excluded; no entire bijection can map it conformally onto the disk.Möbius transformationCompared with: Most entire functions are not Möbius maps, which are rational and have at most one finite pole.Liouville's theoremNarrower topic: The theorem applies precisely to functions holomorphic throughout the plane.Jacques HadamardRelated: Hadamard’s factorization theorem describes entire functions through their zeros and growth.Joseph LiouvilleRelated: Entire functions are the objects governed by his boundedness theorem.Cauchy estimatesBroader topic: Applying the estimates on larger and larger circles constrains entire functions globally.Weierstrass factorization theoremNarrower topic: The theorem classifies this broad family through zeros and a zero-free exponential factor.Émile PicardBroader topic: The little Picard theorem limits the values a nonconstant entire function can omit.Hadamard factorization theoremNarrower topic: The theorem applies to entire functions, whose zeros can be listed with multiplicities.Jensen's formulaRelated: Jensen developed the identity as a tool for studying zeros and growth of entire functions.Gösta Mittag-LefflerCompared with: Entire functions have no poles, unlike the meromorphic functions central to his theorem.Borel–Carathéodory theoremBroader topic: Applying the disk estimate on increasingly large disks helps constrain entire-function growth.Analytic functionBroader topic: Entire functions are analytic everywhere in the complex plane.Carlson's theoremNarrower topic: The theorem applies to entire functions and constrains their growth.Cramér's decomposition theoremRelated: Analytic properties of Gaussian characteristic functions help constrain their factors.
KnowraEntire functionLinked fromLinked fromThe 18 pages that link to Entire function, each with the reason it gives.All 18Broader topic 6Related 4Narrower topic 4Compared with 4Holomorphic functionBroader topic: It is the global special case obtained when the domain has no boundary.Complex analysisBroader topic: Entire functions show how global domain size constrains growth and possible forms.Rational functionCompared with: A nonpolynomial rational function has poles, so it is not entire.Riemann mapping theoremCompared with: The plane itself is excluded; no entire bijection can map it conformally onto the disk.Möbius transformationCompared with: Most entire functions are not Möbius maps, which are rational and have at most one finite pole.Liouville's theoremNarrower topic: The theorem applies precisely to functions holomorphic throughout the plane.Jacques HadamardRelated: Hadamard’s factorization theorem describes entire functions through their zeros and growth.Joseph LiouvilleRelated: Entire functions are the objects governed by his boundedness theorem.Cauchy estimatesBroader topic: Applying the estimates on larger and larger circles constrains entire functions globally.Weierstrass factorization theoremNarrower topic: The theorem classifies this broad family through zeros and a zero-free exponential factor.Émile PicardBroader topic: The little Picard theorem limits the values a nonconstant entire function can omit.Hadamard factorization theoremNarrower topic: The theorem applies to entire functions, whose zeros can be listed with multiplicities.Jensen's formulaRelated: Jensen developed the identity as a tool for studying zeros and growth of entire functions.Gösta Mittag-LefflerCompared with: Entire functions have no poles, unlike the meromorphic functions central to his theorem.Borel–Carathéodory theoremBroader topic: Applying the disk estimate on increasingly large disks helps constrain entire-function growth.Analytic functionBroader topic: Entire functions are analytic everywhere in the complex plane.Carlson's theoremNarrower topic: The theorem applies to entire functions and constrains their growth.Cramér's decomposition theoremRelated: Analytic properties of Gaussian characteristic functions help constrain their factors.