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entire function (Definition)

An entire function is a function $ f: \mathbb{C} \longrightarrow \mathbb{C}$ which is holomorphic everywhere on the complex domain $ \mathbb{C}$.

For example, a polynomial is holomorphic everywhere, as is the exponential function. The function $ z\mapsto 1/z$ is not holomorphic at zero, so it is not entire; it is meromorphic.



"entire function" is owned by djao. [ full author list (2) ]
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Other names:  entire

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properties of entire functions (Result) by pahio
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Cross-references: meromorphic, exponential function, polynomial, domain, complex, holomorphic, function
There are 77 references to this entry.

This is version 6 of entire function, born on 2001-12-28, modified 2004-11-28.
Object id is 1148, canonical name is Entire.
Accessed 11004 times total.

Classification:
AMS MSC: 30D20 (Functions of a complex variable :: Entire and meromorphic functions, and related topics :: Entire functions, general theory)
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