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== Examples ==
Typical examples of analytic functions are
* All [[elementary function]]s:
** All [[polynomial]]s: if a polynomial has degree ''n'', any terms of degree larger than ''n'' in its Taylor series expansion must immediately vanish to 0, and so this series will be trivially convergent. Furthermore, every polynomial is its own [[Maclaurin series]].
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** [[gamma function]]s
Typical examples of functions that are not analytic are
* The [[absolute value]] function when defined on the set of real numbers or complex numbers is not everywhere analytic because it is not differentiable at 0. [[Piecewise|Piecewise defined]] functions (functions given by different formulae in different regions) are typically not analytic where the pieces meet.
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