A holomorphic function is a complex function that is differentiable at every point in its domain, which implies it is also continuous. This property of being differentiable in the complex sense allows holomorphic functions to have well-defined derivatives and leads to many powerful results in complex analysis, including the existence of Taylor series expansions. Holomorphic functions exhibit many nice features, such as being infinitely differentiable and conformal at points where their derivatives are non-zero.
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