Complex-valued function: Difference between revisions

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== Complex analysis ==

{{main|Complex analysis}}

Complex analysis considers [[holomorphic function]]s on [[complex manifold]]s, such as [[Riemann surface]]s. The property of [[analytic continuation]] makes them very dissimilar from [[smooth function]]s, for example. Namely, if a function defined in a [[neighborhood (mathematics)|neighborhood]] can be continued to a wider [[___domain (mathematical analysis)|___domain]], then this continuation is [[uniquenessunique (mathematics)|unique]].

As real functions, any holomorphic function is infinitely smooth and [[analytic function|analytic]]. But there is much less freedom in construction of a holomorphic function than in one of a smooth function.