Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:class |
Order and type
|
| gptkbp:definedIn |
Functions holomorphic on the entire complex plane
|
| gptkbp:example |
gptkb:Exponential_function
gptkb:Logarithm_function gptkb:Polynomial_functions gptkb:Cosine_function gptkb:Sine_function Reciprocal function |
| gptkbp:field |
Complex analysis
|
| https://www.w3.org/2000/01/rdf-schema#label |
Entire Functions
|
| gptkbp:property |
Analytic everywhere in the complex plane
Can be represented by a power series with infinite radius of convergence Can be transcendental or algebraic Closed under addition and multiplication Closed under composition Closed under differentiation Essential in the study of complex dynamics Growth can be classified by order If bounded, must be constant (Liouville's theorem) Infinite product representations possible May have an essential singularity at infinity No singularities in the finite complex plane Taylor series converges everywhere Zeros are isolated unless identically zero Can be factorized using Weierstrass factorization theorem |
| gptkbp:relatedTo |
gptkb:Liouville's_theorem
gptkb:Picard's_theorem Meromorphic functions |
| gptkbp:studiedBy |
Mathematicians
|
| gptkbp:bfsParent |
gptkb:Analytic_Functions
|
| gptkbp:bfsLayer |
6
|