analytic function

Meaning

Noun

• Any smooth (infinitely differentiable) function $f$, defined on an open set $D\backslash subseteq\; \backslash mathbb\{C\}\backslash \; (\backslash textit\{\; or\; \}\backslash subseteq\backslash mathbb\{R\})$, whose value in some neighbourhood of any given point $x\_0\; \backslash in\; D$ is given by the Taylor series $\backslash textstyle\; \backslash sum\_\{n=0\}^\{\backslash infty\}\; \backslash frac\{f^\{(n)\}(x\_0)\}\{n!\}\; (x-x\_0)^\{n\}$.

Related

Narrower meaning words

• complex analytic function, monogenic analytic function, real analytic function

Broader meaning words

• function