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The absolute value function is elementary but not analytic. It is not correct to say that "all elementary functions" are analytic. |
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== Examples ==
Typical examples of analytic functions are
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** 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]].
** The [[exponential function]] is analytic. Any Taylor series for this function converges not only for ''x'' close enough to ''x''<sub>0</sub> (as in the definition) but for all values of ''x'' (real or complex).
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