A holomorphic function is a complex function that is differentiable at every point in its domain, which also implies that it is continuous. This differentiability means the function can be represented by a power series around any point within its domain, showcasing its smooth nature. Holomorphic functions possess various important properties, including satisfying Cauchy-Riemann equations, which connect real and imaginary parts of the function and link them to complex analysis concepts like contour integrals and Cauchy's integral theorem.
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