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In [[mathematics]], an '''analytic function''' is one that is locally given by a convergent [[power series]].
[[Complex analysis]] teaches us that if a function ''f'' is differentiable in some open disk ''D'' centered at a point ''c'' in the complex field, then it necessarily has derivatives of all orders in that same open neighborhood, and the power series
:<math>\sum_{n=0}^\infty {f^{(n)}(c) \over n!} (z-c)^n</math>
converges to ''f''(''z'') at every point within ''D''. Consequently, the term ''analytic function'' is often used synonymously with ''[[holomorphic function]]''.
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