Entire function

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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