Entire function: Difference between revisions

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(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