Over intervals, functions can be almost equivalent to power-series functions {Comega-smooth function} {analytic function}. Real analytic functions {Cinfinity-smooth function} can be differentiable at domain points any number of times. Complex analytic functions are complex differentiable, typically only once, at domain points. Complex entire functions are differentiable at all complex-plane finite points. Non-analytic functions are not differentiable at some singularity point or along branch cut.
Mathematical Sciences>Calculus>Analysis
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Date Modified: 2022.0224