Entire function: Difference between revisions
(New page: ==Definition== An '''entire function''' is defined in the following equivalent ways: * It is a holomorphic function on the set of all complex numbers * It is a global analytic functi...) |
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Latest revision as of 19:12, 18 May 2008
Definition
An entire function is defined in the following equivalent ways:
- It is a holomorphic function on the set of all complex numbers
- It is a global analytic function: it can be expressed by a globally convergent power series about any complex number
- It is a complex-differentiable function on the set of all complex numbers
- It is an infinitely differentiable function on the set of all complex numbers